HHlHHI Hi LIBRARY UNIVERSITY OF CALIFORNIA. Class I EXERCISES IN QUANTITATIVE CHEMISTEY BY HAEM01ST NOETHKOP MOKSE PROFESSOR OF ANALYTICAL CHEMISTRY IN THE JOHNS HOPKINS UNIVERSITY GINN & COMPANY BOSTON NEW YORK - CHICAGO LONDON ffr COPYRIGHT, 1905 BY HARMON NORTHROP MORSE ALL BIGHTS RESERVED 55.7 GINN & COMPANY PRO- PRIETORS BOSTON U.S.A. PREFACE The essential portions of this book have been in use in the author's laboratory for several years in the form of mimeo- graphed notes, which were revised and expanded from time to time until they became too voluminous for further duplication by this process. Hence they have been put in book form for the use of the author's students and of any others who may find them of service. The purpose which the author had in view in preparing the notes was twofold. First, to economize the energy of the student by placing in his hands a working guide sufficiently precise to keep him in the right path during the absence of his teacher, and secondly, to increase the efficiency of the teacher by saving him waste of time and effort in repairing the grosser mistakes of inexperienced students. The book is not intended as a complete guide, even in the matters contained therein. Enough and probably more than he can do to his satisfaction has been left for the teacher, from whom the student may justly expect at all times the warn- ing, suggestion, or amplification which will contribute most effectively to his progress and discipline. The problem of a wise choice of exercises for the student of quantitative chemistry is a difficult one. It is much more com- plex than formerly, when the greater portion of the student's time in the laboratory was devoted, as a matter of course, to analytical chemistry. It was possible then to train expert analysts. At the present time this is not practicable, except at the expense of other work which is everywhere regarded as indispensable. The chemical student in training for his calling iii 194607 iv PREFACE is now required to take somewhat protracted courses of experi- mental work, which are arranged with a view to familiarizing him with the importantjreactions of substances, and that with- out any reference to the utility of such work for the purposes of analytical chemistry. To this end, he is expected to prepare a great number of typical compounds, both organic and inor- ganic. He is also required to exercise himself in the methods peculiar to physical chemistry. Hence the time which can be devoted to his training in quantitative chemistry is shorter than formerly, and the problem of what to give him to do in this field is a perplexing one. To the author it has seemed best to select the limited amount of work which the student can do with a view to giving him a familiarity with the greatest prac- ticable variety of quantitative methods and operations, and not to endeavor to train him especially as an analyst. This book is, therefore, not an analytical chemistry. It is believed, how- ever, that a student who, under competent guidance, has done well the work which is here prescribed will have acquired a skill in quantitative manipulation and a knowledge of methods which will enable him quickly and easily, with the aid of the many existing excellent works of reference, to become proficient in any of the several lines of quantitative analytical chemistry ; and this, it appears to the author, is the end to be sought, and the best that can be hoped for under the present conditions. In the last two chapters of the book an account is given of certain new electrical heating appliances for laboratory use, which the author has found quite serviceable; also of a new electrical method for the combustion of organic compounds, which in his laboratory has almost entirely supplanted the older process. HARMON N. MORSE MAT 1, 1905 CONTENTS CHAPTER I THE BALANCE PAGE Description 1 Precautions to be observed in Weighing 8 Exercise I. Practice with the Balance . . . . 10 i. Determination of the Time of Vibration . . . 10 ii. Determination of Zero Points . . . . . 11 in. Determination of Sensibility . . . . . .13 iv. To determine whether the Arms are Equal . . . 16 Exercise II. Practice in Weighing . . . . . . 19 i. Weighing by the Usual Method . . . . 19 ir. Weighing by the Method of Borda ." . . 20 in. Weighing by the Method of Gauss . . . . 21 iv. Correction for the Air Displaced 22 Weighing by Tares . 2'5 Exercise III. Correction of Weights ..... 26 i. Comparison of the Different Pieces of a Set with Each Other 26 ii. To compare a Set of Weights with a Standard Weight . 28 Materials for Weights . . . 28 CHAPTER II THE BAROMETER AND THE THERMOMETER The Barometer 30 Corrections of the Barometer 33 i. For Temperature ........ 33 ii. For Capillary Depression ....... 35 in. For Latitude and Altitude ...... 35 iv. For the Moisture in the Air . 38 The Thermometer 38 Exercise IV. Determination of the Zero Point . . . 38 Exercise V. Determination of the Boiling Point ... 43 Exercise VI. Calibration of the Thermometer 45 vi CONTENTS PAGE Correction for the Exposed Part of a Mercury Column ... 50 The Comparison of Thermometers 51 Thermometers filled with Gas ....... 51 The Beckmann Thermometer ....... 52 The Air Thermometer ......... 52 Alcohol and Toluene Thermometers . . . . . 54 Determination of Temperatures by Substances of Known Melting Points 54 CHAPTER III THE CALIBRATION OF EUDIOMETERS AND THE MEASUREMENT OF GASES Exercise VII. Calibration of a Eudiometer .... 57 i. Purification of the Mercury 57 ii. Calibration of the Eudiometer 60 in. Determination of the Value of the Meniscus ... 66 iv. Determination of the Volume of the Calibration Unit . 68 Measurement of Gases over Water 69 The Absorption of Gases by Liquids . . . . . . 70 The Correction of Gas Volumes for Pressure .... 73 The Correction of Gas Volumes for Temperature . . . . 74 The Correction of Gas Volumes for Water Vapor . . . 75 The Passage of Gases through Rubber 77 CHAPTER IV CALIBRATION AND GRADUATION OF APPARATUS FOR THE MEASUREMENT OF LIQUIDS Exercise VIII 79 i. Determination of the Capacity of a Measuring Flask by weighing Water 79 ii. The Graduation of a Measuring Flask . . . . 81 in. The Calibration of Burettes by Means of Mercury . . 83 The System of Mohr 83 Exercise IX. The Calibration and Graduation of Measuring Flasks and the Calibration of Burettes ... 85 The Graduation of Glass Tubes . . . . .. . . 94 Standard and Normal Solutions . . 99 The Correction of Standard Solutions for Temperature . . . 102 CONTENTS vii CHAPTER V THE PREPARATION OF STANDARD SOLUTIONS OF ACIDS AND ALKALIES PAGE Indicators 110 1. Litmus . Ill 2. Phenolphthalein 113 3. Methyl Orange 114 4. Tropseolin 115 5. Cochineal . 115 Exercise X. The Preparation of Standard Solutions of Acids and Alkalies 116 i. By Means of Oxalic Acid 116 ii. By Means of Carbonates 123 Other Methods of standardizing Acids and Alkalies . . . 125 1. By Means of Potassium Tetroxalate .... 126 2. By Means of Sodium Carbonate 127 3. By Means of Sulphuric Acid derived from Copper Sulphate 127 CHAPTER VI THE DETERMINATION OF SPECIFIC GRAVITY Density and Specific Gravity 128 Exercise XI. Determination of the Specific Gravity of Solids . 130 i. Determination of the Specific Gravity of a Silver Coin . 130 ii. Determination of the Specific Gravity of Glass in Frag- ments . . . . . . . . . . 131 Exercise XII. Determination of the Specific Gravity of Liquids 133 i. With the Pycnometer 133 ii. By weighing an Object in Two Liquids . . . 134 in. By the Mohr-Westphal Balance . . . . 135 Hydrometers (Areometers, Densimeters) 136 Class A. Instruments of Constant Immersion 1. Fahrenheit's Hydrometer . . . . . . 137 2. Nicholson's Hydrometer ....... 138 Class B. Instruments of Variable Immersion 1. Gay-Lussac's Volumeter 138 2. Specific-Gravity Hydrometers ...... 140 3. Beaume's Hydrometer . . . . . . . 141 4. Beck's Hydrometer 143 viii CONTENTS PAGE 5. Twaddell's Hydrometer . . . . . . . 143 6. The Alcoholometer 144 7. The Lactometer 144 Specific-Gravity Bulbs . . . . . . . . . 145 Determination of Specific Gravity by Dilution .... 145 The Density of Gases Determination of . . . . . 146 1. By weighing the Gases directly 147 2. By weighing the Gases after Absorption .... 148 3. By the Time required for Diffusion 149 CHAPTER VII THE DETERMINATION OF MOLECULAR WEIGHTS Atomic Ratios . . . . . . ' . . . 150 1. Copper Oxide 150 2. Potassium Permanganate 151 3. Acetic Acid 151 4. Propyl-Amine . . . . . . . . . 151 5. Benzene 152 Molecular Weights . . . 153 The Chemical Method 153 Physical Methods 157 i. Dumas' Method 158 ii. The Method of Gay-Lussac 161 Hofmann's Method . 162 Determination of the Volume of a Vapor by Means of the Pres- sure which it Exerts . . . . . . . 164 Exercise XIII. Determination of the Molecular Weight of Chloroform by the Method of Meyer . . . . 165 The Freezing-Point Method 169 Exercise XIV. Determination of Molecular Weights by the Freezing-Point Method 177 1. Urea . . . ... . . . . ' . 177 2. Cane Sugar , . . . 179 3. Chloroform 179 The Boiling-Poiut Method 179 Exercise XV. Determination of Molecular Weights by the Boiling-Point Method .... .183 1. Iodine 183 2. Naphthalene 184 CONTENTS ix CHAPTER VIII THE PURIFICATION OF SUBSTANCES PAGE 1. Evaporation of Liquids ... 186 2. Recrystallization .... 190 3. Desiccation Hot-Air Baths 194 Liquid Baths .... 197 4. Precipitation ........ 198 5. Filters 200 6. Filtration 203 7. The Washing of Precipitates 205 CHAPTER IX SILVER AND THE HALOGENS Exercise XVI. Determination of Chlorine and Silver . . 209 i. Gravimetrically as Silver Chloride 209 ii. Volumetrically by Mohr's Method 216 in. Volumetrically by Volhard's Method . 218 Exercise XVII. lodometric Determinations .... 222 i. Preparation of Standard Solutions 223 a. Resublimed Iodine 223 b. Potassium Iodide 224 c. Starch 224 d. The Solution of Iodine 224 e. The Solution of Sodium Thiosulphate . . 225 f. Standardization of Solutions d and e 225 ir. lodometric Determination of Sulphurous Acid . . 226 in. lodometric Determination of Chromic Acid . . . 228 iv. lodometric Determination of Arsenious Acid . . . 229 Exercise XVIII. Determination of Hypochlorous Acid . . 229 i. By Wagner's Method 229 ii. By Penot's Method 230 Exercise XIX. Determination of Halogens in Organic Com- pounds 232 i. By the Lime Method ....... 232 ii. By Carius' Method 234 The Separation of the Halogens . . . . . . . 236 Exercise XX. The Separation of Chlorine, Bromine, and Iodine 239 CONTENTS PAGE By the Method of Jannasch and Aschoif . . . . 239 Determination of the Iodine 240 Determination of the Bromine ...... 241 Determination of the Chlorine . 241 CHAPTER X SULPHUR Exercise XXI. Determination of Sulphuric Acid in Barium Sulphate 244 Exercise XXII. Determination of Sulphur in Sulphides . . 247 Exercise XXIII. Determination of Sulphur in Iron by Frese- nius' Method . . . . . . . . 252 Exercise XXIV. Determination of Sulphur in Organic Com- pounds 256 i. By Liebig's Method 256 ii. By Carius' Method 257 Hi. By Sauer's Method 258 CHAPTER XI NITROGEN Exercise XXV. Determination of Nitric Acid . . . 261 i. By the Tiemann-Schulze Method 261 ii. By Crum's Method 265 Exercise XXVI. Colorimetric Determination of Nitrous Acid by Method of Griess, Preusse, and Tiernann . . 267 Exercise XXVII. Colorimetric Determination of Ammonia . 270 Determination of Free and Albuminoid Ammonia in Water by the Method of Wanklyn, Chapman, and Smith . 270 Exercise XXVIII. Determination of Nitrogen in Organic Com- pounds ......... 272 i. By Kjeldahl's Method . . ... . . . 272 a. Wilfarth's Modification 273 b. Gunning's Modification ...... 274 c. Jodlbauer's Modification 275 d. Foerster's Modification . . . ..'.., . 275 ii. By Dumas' Method 276 in. By Varrentrapp and Will's Method .... 281 Ruffle's Modification . 281 CONTENTS xi CHAPTER XII PHOSPHORUS AND ARSENIC PAGE Exercise XXIX. The Determination of Phosphoric Acid in Phosphate Rock . . 283 Exercise XXX. The Determination of Phosphorus in Iron by the Stoeckmann-Fresenius Method 287 Exercise XXXI. The Determination of Phosphoric Acid in Fertilizers 288 a. Determination of the Water-Soluble Phosphoric Acid . 289 b. Determination of the Citrate-Insoluble Phosphoric Acid 290 c. Determination of Total Phosphoric Acid . . . 291 d. Optional Volumetric Method for the Determination of Phosphoric Acid in Fertilizers 292 Other Volumetric Methods for the Determination of Phosphoric Acid 293 The Determination of Phosphorus in Organic Compounds . . 297 The Separation of Phosphoric Acid from Other Substances . . 298 Exercise XXXII. The Determination of Arsenic as Magne- sium Pyroarseniate 301 CHAPTER XIII SILICATES Silicates 303 The Determination of Water in Silicates 304 1. Sipcoecz's Method 305 2. Jannasch's Method 306 3. Chatard's Method 307 4. The Lead Oxide Method 307 5. The Borax Method 307 Exercise XXXIII. The Determination of Water in Silicates by Means of Lead Oxide 307 Exercise XXXIV. The Decomposition of a Silicate with an Al- kaline Carbonate and the Determination of the Silica 310 Other Methods of Decomposing Silicates . . . . . 312 1. Decomposition by Lead Oxide 312 2. Decomposition by Bismuth Oxide . 314 3. Decomposition by Hydrochloric Acid . 314 4. Decomposition by Acids under Pressure . . . . 315 5. Decomposition by Hydrofluoric Acid . . . . 316 xii CONTENTS 6. Decomposition by Barium Hydroxide and Carbonate . 317 7. Decomposition by Ammonium Chloride and Calcium Carbonate 318 Exercise XXXV. The Determination of Silicon in Iron . . 318 The Separation of Silica from Other Substances . . . . 319 CHAPTER XIV THE DETERMINATION OF CARBONIC ACID Exercise XXXVI 320 i. The Volumetric Determination of Free and Semi-Com- bined Carbonic Acid in Water . . . . . 320 Pettenkofer's Method 320 n. The Determination of Total Carbonic Acid in Water . 323 Exercise XXXVII. Determination of Carbonic Acid in Car- bonates 326 i. By Absorption in a Weighed Quantity of Soda-Lime . v 326 ii. The Volumetric Determination of Carbonic Acid . . 328 The Separation of Carbonic from Other Acids .... 330 Filtration in an Atmosphere Free from Carbonic Acid . . . 330 Determination of Carbonic Acid in the Air . . . . . 332 The Preparation of Carbonic Acid Gas Free from Air . . . 336 CHAPTER XV THE DETERMINATION OF CARBON AND HYDROGEN IN ORGANIC COMPOUNDS The Drying of Gases 339 1. Calcium Chloride 339 2. Sulphuric Acid 342 3. Phosphorus Pentoxide 343 4. Anhydrous Copper Sulphate . . . . . 345 5. Calcium Oxide 345 6. Potassium Hydroxide 345 Materials employed in the Determination of Carbon and Hydrogen in Organic Compounds ...... 347 1. Copper Oxide : 347 2. Lead Chromate- 349 3. Metallic Copper 351 4. Oxygen 353 5. An Apparatus for the Purification of Oxygen and Air . 353 CONTENTS xiii PAGE 6. An Absorption Apparatus for Water . . . . 354 7. An Absorption Apparatus for Carbon Dioxide . . . 355 8. Tubes for Protection against Atmospheric Water and Carbon Dioxide 356 Exercise XXXVIII. Determination of Carbon and Hydrogen . 356 i. Combustion of a Solid in the Open Tube . . . 356 ii. Combustion of a Liquid in the Open Tube . . . 359 in. Combustion in the Closed Tube ..... 361 iv. Combustion of a Compound containing Sulphur . . 363 o. Combustion in the Open Tube .... 364 b. Combustion in the Closed Tube . . . p . 364 v. Combustion of a Compound containing a Halogen . 364 CHAPTER XVI THE DETERMINATION OF CARBON IN IRON AND STEEL. THE INCINERATION OF ORGANIC SUBSTANCES. THE DETERMINATION OF ORGANIC MATTER IN WATER Exercise XXXIX. Determination of Total Carbon in Iron and Steel 366 i. By Direct Combustion in a Current of Oxygen . . 366 ii. By Oxidation with Chromic Acid 368 in. By Oxidation of the Carbon after Removal of the Iron . 371 Exercise XL. Determination of Graphitic Carbon in Iron . 372 Exercise XLI. Determination of Combined Carbon in Steel . 373 Colorimetric Method of Eggertz . . . . 373 Exercise XLII. Determination of the Fuel Value of Coal . 375 i. Determination of Water 376 ii. Determination of the Volatile Combustible Matter . 376 in. Determination of Fixed Carbon 377 Incineration ........... 377 Determination of Organic Matter in Water 380 The Method of Kubel 381 The Method of Schulze ..... 381 The Method of Tidy 382 The Method of Wolff, Degener, and Hergfeld ... 383 The Method of Dupre" and Hake .... 384 The Method of Dittmar and Robinson 385 1. Determination of Organic Carbon . . . . 385 2. Determination of Organic Nitrogen .... 385 The Method of Frankland and Armstrong . . . 386 Determination of Organic Carbon and Nitrogen . . 386 xiv CONTENTS CHAPTER XVII GAS ANALYSIS PAGE Exercise XLIII. Determination of Oxygen in the Air . . 392 i. By Explosion with Hydrogen 392 ii. By Absorption with Phosphorus . . .'".'. . 395 in. By Absorption with Potassium Pyrogallate . . . 397 Exercise XL IV. Determination of Hydrogen . . . . 398 i. By Explosion with Oxygen 398 n.%Jy Absorption with Palladium 399 Exercise XLV. The Analysis of Illuminating Gas . . . 401 Method of Hempel .401 CHAPTER XVIII THE METALS OF THE ALKALIES AND OF THE ALKALINE EARTHS Exercise XL VI. Determination of Potassium as Double Potas- sium-Platinum Chloride . . . . . . 407 The Monroe Filter 409 Other Methods of determining Potassium 409 Exercise XL VII. Separation and Determination of Potassium and Sodium . . . . . . . . 410 The Separation of Potassium and Sodium from Other Substances 411 1. Sulphates 412 2. Phosphates 412 3. Borates 413 Exercise XL VIII. Determination of Potassium and Sodium in a Silicate 413 The Determination of an Alkaline Carbonate in a Caustic Alkali 415 The Determination of Acid Carbonates in the Presence of Neutral Carbonates 416 Exercise XLIX. Separation and Determination of Barium, Strontium, and Calcium ...... 417 By the Methods recommended by Fresenius . . . . 417 The Detection of Barium, Strontium, and Calcium . . . 421 The Process recommended by Fresenius .... 421 The Quantitative Determination of the Individual Alkaline Earths 423 1. Barium . 423 2. Strontium 427 3. Calcium , 429 CONTEXTS XV CHAPTER XIX THE ALKALINE EARTHS (continued) AND MAGNESIUM PAGE The Separation of the Alkaline Earths from the Acids . . 432 1. Sulphuric Acid . ...*.. 432 2. Phosphoric Acid . 433 3. Hydrofluoric Acid 434 The Separation of the Alkaline Earths from the Alkalies . . 435 The Determination of Magnesium ...... 437 The Separation of Magnesium from the Alkalies . . . . 438 Other Methods of separating Magnesium from the Alkalies . . 438 The Separation of Magnesium and Barium . . . . 440 The Separation of Magnesium from Strontium .... 440 The Separation of Magnesium from Calcium .... 441 The Separation of Magnesium from Barium, Strontium, and Cal- cium . . 442 The Analysis of a Solution containing the Alkalies, Alkaline Earths, and Magnesium ...... 443 The Precipitate 445 The Filtrate 446 The Hardness of Water 448 Exercise L. Determination of the Hardness of Water . . 450 1. Determination of Total Hardness ..... 451 2. Determination of Permanent Hardness .... 452 CHAPTER XX POTASSIUM PERMANGANATE Potassium Permanganate 454 1. Oxalic Acid 456 2. Potassium Tetroxalate 459 3. Ferrous Ammonium Sulphate ...... 459 Exercise LI. Determination of Iron by Means of Potassium Permanganate ........ 459 i. Preparation of the Permanganate Solution . . . 459 ii. Determination of Metallic Iron 461 in. Confirmation of the Results by the Gravimetric Method . 463 Exercise LIT. Determination of Ferrous and Ferric Iron in a Silicate 464 Exercise LIII. Determination and Separation of Iron and ' Aluminium 466 CONTENTS Exercise LIV. Determination of Manganese by Potassium Per- manganate ......... 468 By Volhard's Method ....... 468 Reduction of Permanganic Acid by the Oxides of Manganese . 470 Exercise LV. Determination of Manganese as Pyrophosphate . 471 By Gibbs' Method ........ 471 Exercise LVI. Determination of Hydrogen Peroxide . . . 472 Exercise LVII. Determination of Nitrous Acid . . . 472 CHAPTER XXI THE ELECTROLYTIC DETERMINATION OF METALS Electrical Units and their Relations ...... 474 1. The Ampere and the Coulomb ....... 474 2. The Ohm . 474 3. The Volt 475 4. Ohm's Law 476 Determination of the Strength of the Current . . . 476 Determination of Voltage ...... 477 5. The Joule 477 6. The Watt . . 478 Sources of Current . 479 Storage Batteries . . 483 Electrolysis 488 1. The Electrodes 2. Rheostats 490 3. Faraday's Laws 491 4. Polarization Currents 493 Exercise LVIII. Electrolytic Determinations .... 495 1. Copper 495 a. Classen's Method ... 495 b. Deposition in the Presence of Nitric Acid . 496 2. Nickel 496 Classen's Method .... 496 3. Iron 497 Classen's Method ' . 497 4. Zinc 498 Classen's Method . .... 498 CONTP:NTS xvii CHAPTER XXII BUTTER PAGE Acids occurring in Fats and Oils 500 Exercise L1X. Determination of the Insoluble Acids . . 502 Hehner's Method 502 Exercise LX. Determination of the Volatile Acids . . . 504 Exercise LXI. Determination of the Alkali required for Sapon- ification ......... 506 Koettstorfer's Method 506 Exercise LXII. Determination of the Alkali neutralized by the Soluble and the Insoluble Acids 508 Method of Morse and Burton . 508 Exercise LXIII. Determination of the Iodine Absorbed . . 508 Htibl's Method ... . 508 Exercise LXIY. Determination of Butter in Milk . . . 512 i. Determination by the Ordinary Gravimetric Method . 512 ii. Determination by Adams' Method . .. . . 515 in. Determination by the Method of Morse, Piggot, and Burton 515 CHAPTER XXIII Electric Heating Appliances for Laboratory Use .... 517 1. Crucible Furnace . 518 2. Air Baths with Graphite Stoves 524 3. Tube Furnace 531 4. Platinum Wire Stoves .... 533 CHAPTER XXIV An Electrical Method for the Combustion of Organic Compounds 537 The Combustion of Substances containing Nitrogen . . . 543 The Combustion of Halogen Compounds 544 The Combustion of Sulphur Compounds 545 Table of International Atomic Weights ..... 546 INDEX . . 547 LIST OF EXERCISES I. Practice with the Balance 10 i. Determination of the Time of Vibration .... 10 ii. Determination of Zero Points . . . . . . 11 in. Determination of Sensibility . . . . . . 13 iv. To determine whether the Arms are Equal . . . .16 II. Practice in Weighing .... .... 19 i. Weighing by the Usual Method . ii. Weighing by the Method of Borda in. Weighing by the Method of Gauss iv. Correction for the Air Displaced . 19 20 21 22 III. Correction of Weights . 26 i. Comparison of the Different Pieces of a Set with Each Other 26 n. To compare a Set of Weights with a Standard Weight . . 28 IV. Determination of the Zero Point of Thermometers .... 38 V. Determination of the Boiling Point of Thermometers ... 43 VI. Calibration of the Thermometer ....... 45 VII. Calibration of a Eudiometer ....".... 67 i. Purification of the Mercury 57 ii. Calibration of the Eudiometer ...... 60 in. Determination of the Value of the Meniscus ... 66 iv. Determination of the Volume of the Calibration Unit . . 68 VIII. i. Determination of the Capacity of a Measuring Flask by weighing Water 79 ii. Graduation of a Measuring Flask 81 in. Calibration of Burettes by Means of Mercury ... 83 IX. Calibration and Graduation of Measuring Flasks and the Calibra- tion of Burettes ......... 85 X. Preparation of Standard Solutions of Acids and Alkalies . .116 i. By Means of Oxalic Acid 116 ii. By Means of Carbonates ....... 123 XL Determination of the Specific Gravity of Solids . . . .130 i. Determination of the Specific Gravity of a Silver Coin . 130 ii. Determination of the Specific Gravity of Glass in Frag- ments 131 XII. Determination of the Specific Gravity of Liquids . . . .133 i. With the Pycnometer 133 n. By weighing an Object in Two Liquids . . . .134 in. By the Mohr-Westphal Balance 135 XIII. Determination of the Molecular Weight of Chloroform by the Method of Meyer 165 XIV. Determination of Molecular Weights by the Freezing-Point Method 177 XV. Determination of Molecular Weights by the Boiling-Point Method . 183 xviii LIST OF EXERCISES xix XVI. Determination of Chlorine and Silver 209 i. Gravimetrically as Silver Chloride 209 ii. Volumetrically by Mohr's Method .... 216 in. Volumetrically by Volhard's Method .... 218 XVII. lodometric Determinations ....... 222 i. Preparation of Standard Solutions .... 223 ii. lodometric Determination of Sulphurous Acid . . 226 in. lodometric Determination of Chromic Acid. . . 228 iv. lodometric Determination of Arsenious Acid . . 229 XVIII. Determination of Hypochlorous Acid ..... 229 i. By Wagner's Method 229 ii. By Penot's Method 230 XIX. Determination of Halogens in Organic Compounds . . . 232 i. By the Lime Method . . . . . . .232 ii. By Carius' Method 234 XX. Separation of Chlorine, Bromine, and Iodine .... 239 XXI. Determination of Sulphuric Acid in Barium Sulphate . . 244 XXII. Determination of Sulphur in Sulphides . . . . .247 XXIII. Determination of Sulphur in Iron by Fresenius' Method . 252 XXIV. Determination of Sulphur in Organic Compounds . . . 256 i. By Liebig's Method 256 ii. By Carius' Method 257 in. By Sauer's Method .258 XXV. Determination of Nitric Acid 261 i. By the Tiemann-Schulze Method 261 ii. By Crum's Method 265 XXVI. Colorimetric Determination of Nitrous Acid by the Method of Griess, Preusse, and Tiemann .... 267 XXVII. Colorimetric Determination of Ammonia .... 270 XXVIII. Determination of Nitrogen in Organic Compounds . . . 272 i. By KjeldahTs Method 272 ii. By Dumas' Method 276 in. By Varrentrapp and Will's Method . . . .281 XXIX. Determination of Phosphoric Acid in Phosphate Rock . . 283 XXX. Determination of Phosphorus in Iron by the Stoeckmann- Fresenius Method 287 XXXI. Determination of Phosphoric Acid in Fertilizers . . .288 XXXII. Determination of Arsenic as Magnesium Pyroarseniate . . 301 XXXIII. Determination of Water in Silicates by Means of Lead Oxide 307 XXXIV. Decomposition of a Silicate with an Alkaline Carbonate and the Determination of the Silic'a . . . .310 XXXV. Determination of Silicon in Iron . 318 XXXVI. i. The Volumetric Determination of Free and Semi-Com- bined Carbonic Acid in Water ..... 320 n. The Determination of Total Carbonic Acid in Water . 323 XXXVII. Determination of Carbonic Acid in Carbonates . . . * 326 i. By Absorption in a Weighed Quantity of Soda-Lime . 326 n. The Volumetric Determination of Carbonic Acid . 328 XXXVIII. Determination of Carbon and Hydrogen 356 i. The Combustion of a Solid in the Open Tube . . 356 n. The Combustion of a Liquid in the Open Tube . . 359 in. Combustion in the Closed Tube , . 361 XX LIST OF EXEKCISES 1'AGE iv. The Combustion of a Compound containing Sulphur . 363 v. The Combustion of a Compound containing a Halogen . 364 XXXIX. Determination of Total Carbon in Iron and Steel . . . 366 i. By Direct Combustion in a Current of Oxygen . . 366 ii. By Oxidation with Chromic Acid 368 in. By Oxidation of the Carbon after Removal of the Iron . 371 XL. Determination of Graphitic Carbon in Iron .... 372 XLI. Determination of Combined Carbon in Steel .... 373 XLII. Determination of the Fuel Value of Coal 375 i. Determination of Water ....... 376 ii. Determination of the Volatile Combustible Matter . . 376 in. Determination of Fixed Carbon . . . . . 377 XLIII. Determination of Oxygen in the Air 392 i. By Explosion with Hydrogen 392 ii. By Absorption with Phosphorus 396 in. By Absorption with Potassium Pyrogallate . . . 397 XLIV. Determination of Hydrogen 398 i. By Explosion with Oxygen ...... 398 ii. By Absorption with Palladium ..... 399 XLV. Analysis of Illuminating Gas 401 XLVI. Determination of Potassium as Double Potassium-Platinum Chloride 407 XL VII. Separation and Determination of Potassium and Sodium . .410 XLVIII. Determination of Potassium and Sodium in a Silicate . . 413 XLIX. Separation and Determination of Barium, Strontium, and Calcium . . . 417 L. Determination of the Hardness of Water 450 LI. Determination of Iron by Means of Potassium Permanganate . 459 i. Preparation of the Permanganate Solution . . . 459 ii. Determination of Metallic Iron ..... 461 in. Confirmation of the Results by the Gravimetric Method . 463 LII. Determination of Ferrous and Ferric Iron in a Silicate . . 464 LIII. Determination and Separation of Iron and Aluminium . . 466 LIV. Determination of Manganese by Potassium Permanganate . 468 LV. Determination of Manganese as Pyrophosphate . . .471 LVI. Determination of Hydrogen Peroxide ..... 472 LVII. Determination of Nitrous Acid 472 LVIII. Electrolytic Determinations . - 495 LIX. Determination of the Insoluble Acids in Butter . . . 502 LX. Determination of the Volatile Acids in Butter . . . .504 LXI. Determination of the Alkali required for Saponification of Butter 506 LXII. Determination of the Alkali neutralized by the Soluble and Insoluble Acids in Butter 508 LXIII. Determination of the Iodine absorbed by Butter . . . 510 LXIV. Determination of Butter in Milk 512 i. Determination by the Ordinary Gravimetric Method . 512 ii. Determination by Adams' Method . . . . .515 in. Determination by the Method of Morse, Piggot, and Burton . 515 OF THE f. UNIVERSITY ) OF QUANTITATIVE EXERCISES CHAPTER I THE BALANCE The object to be accomplished by weighing is to determine the amount of matter in materials, i.e. their mass; and the weights which are used in the process are to be regarded merely as standard masses. In weighing, that is in comparing objects with the weights with respect to their mass, the force of gravity is utilized. This force varies with latitude and with elevation above sea level ; but the results of weighing are not altered by change of locality, since the object and the standard with which it is compared are affected in the same degree by the change. It is only in the weighing of gases, when the relation of weight to volume is to be determined, that the fact of the variable intensity of the earth's attraction must be taken into considera- tion by the chemist. The balance used by chemists in determining weight is a lever whose two arms are of equal length and weight. This lever is known as the beam, and the form which is given to it is that which is supposed to combine a maximum of rigidity with a minimum of weight. The material of which it is made is usually brass, though sometimes an alloy of aluminium with other metals is used. The axis about which the beam rotates is the sharp edge of a wedge-shaped piece of agate or of hardened steel. This is known as the central knife edge. It is placed at right angles to the vertical plane in which the beam is to move, and a little above the center of gravity. Hence the beam can move in but l 2 QUANTITATIVE EXERCISES one plane, and it always tends, when left alone, to take a hori- zontal position. The central knife edge rests upon a plate of agate which is fixed in a horizontal position at the top of the standard. The loads the object to be weighed and the weights are suspended from the two ends of the beam at equal distances from the axis of rotation. The arrangement for the suspension of each of the two loads consists of three parts : (1) a terminal knife edge of agate or steel which is fastened to the beam with its sharp edge parallel to the central knife edge and pointing upwards; (2) a stirrup holding an agate plate which is hung upon the knife edge ; and (3) a pan which is suspended from the stirrup (usually) by means of a jointed hook. Two things are essential with respect to the position of the loads : (1) the points from which they are suspended must always maintain, during any given experiment, the same relative distance from the axis ; (2) the point of suspension and the center of gravity of a load must fall in the same vertical line whatever the position of the beam. The first condition is fulfilled by placing the terminal knife edges parallel to the central one; and the second, by giving the pan freedom of rotation in two planes, one of which is the plane in which the beam moves, and the other a plane at right angles to it, i.e. about the terminal knife edge and on the jointed hook. A second knife edge placed in the stirrup at right angles to the terminal one upon the beam is sometimes substituted for the joint in the hook. Again, in some balances the pan is suspended from the stirrup by means of a chain of several links. If the knife edges are allowed to remain continuously in con- tact with their bearings, the former soon become dull, and fur- rows are worn into the latter, rendering the balance incapable of accurate weighing. Every instrument is therefore provided with a device called the arrest, which raises the beam and at the same time lifts the stirrups and pans, thus separating all three of the knife edges from their bearings. THE BALAKCE 3 Owing to corrosion, accumulation of dust, or unequal expan- sion of the arms, one side of the balance (arm, stirrup, and pan) sometimes becomes heavier or acquires a greater leverage than the other, so that the beam does not assume a horizontal posi- tion in a state of rest. To remedy this difficulty balances are provided with an arrangement by which the leverage of one of the arms may be increased or diminished. This consists some- times of a movable vane placed above the center of the beam, and sometimes of a nut running upon a screw which is attached to one end of the beam. To determine when the beam is in a horizontal position and also to enable one to judge its movements with precision, a long pointer is attached to it in front of the central knife edge. The pointer makes right angles with the plane of the three knife edges, and its lower end vibrates, when the beam is in motion, before or just above a graduated ivory scale which is situated at the base of the standard. An essential feature of every balance is the device by which the distance between the center of gravity of the beam and the axis of its rotation is regulated. This consists sometimes of an adjustable bob upon the pointer, and sometimes of a screw and nut placed vertically above the center of the beam. Finally, every balance is provided with a spirit level or a plumb line to determine when the plane of the knife edges is horizontal, and with a case to protect it from dust, sudden changes of temperature, and draughts of air. A balance must be accurate and sufficiently sensitive to meet the requirements of the work to be done with it. The follow- ing are the more important of the conditions which affect these qualities. The Position of the Center of Gravity. In order that the beam may always tend to take a horizontal position, the center of gravity of the balance (beam, stirrups, and pan) together with 4 QUANTITATIVE EXERCISES the loads upon the pans must lie below the axis of rotation. If the center of gravity were in the axis, the equilibrium would be indifferent and the beam would remain in any position which might be given to it. If it were above the axis, the equilibrium would be unstable and the beam once moved from its horizontal position could not return to it. The Distance between the Center of Gravity and the Axis. The sensibility of the balance (which is the angle through which the beam will turn for a given difference of load upon the two pans, and which, therefore, determines the precision with which objects may be weighed) depends mainly upon the distance between the center of gravity and the axis of the beam's rotation. The shorter the distance between them the more sensitive is the balance. Hence the utility of the pro- vision which is made in the construction of every fine balance for the raising or lowering of the center of gravity according to the fineness of the work which is required of it. Of the two arrangements for this purpose already referred to in the descrip- tion of the balance, namely the threaded post and nut placed above the center of the beam and the movable bob attached to the pointer by means of a set-screw, the former is much more easily managed, and is therefore to be preferred. As the distance between the center of gravity and the axis is diminished by raising the former, the beam vibrates more slowly. The sensibility of any given balance may therefore be judged by the time of vibration of the beam, or, what is the same thing, by the time consumed by the end of the pointer in making two successive excursions past any fixed point of the scale at the foot of the standard. The Knife Edges must be Parallel. The evil consequences of the lack of parallelism are numerous, and they vary according to the character of the defect. It will suffice to mention a single possible result, namely an unequal and varying dis- tribution of the burdens along the knife edges, the effect of which would be a changeable ratio of the arm lengths. THE BALANCE 5 The Three Knife Edges must lie in the Same Plane. This is a consequence of the fact that the loading of the pans (which is in effect the same as the loading of the terminal knife edges) changes the distance between the center of gravity and the axis, and thereby affects the sensibility of the balance. If the ter- minal knife edges are below the central one, the loading of the pans lowers the center of gravity and diminishes the sensibility. If they are in the same plane with it, or above it, the opposite effect is produced, and the loading of the pans increases the sen- sibility. But in the former case, i.e. when the three knife edges are in the same plane, the center of gravity can never reach the axis; hence the equilibrium can never become indifferent or unstable. In the construction of balances, however, it is per- missible to elevate the plane of the terminal knife edges very slightly above the central one. When this is done, it is for the purpose of compensating for a loss of sensibility due to bending of the beam and to friction upon the knife edges. The bending of the beam diminishes the sensibility by lower- ing the terminal knife edges ; and, since no beam is perfectly rigid, the effect of bending upon the sensibility is usually noticed when a balance is heavily loaded. It will be seen that the extent to which the balance maker may elevate the terminal knife edges above the central one is limited by the condition that the center of gravity must not rise quite to the axis when the instrument is loaded to its maximum capacity. The Length and Weight of the Beam. The sensibility of the balance depends also upon the length and weight of the beam. The longer the beam the greater the sensibility. The lighter the beam the greater the sensibility. Hence the rivalry between the long and the short beam balances. The former have the advantage of greater length of arm and the latter that of lighter weight. The short beam vibrates more quickly than the long one, and this fact is often cited as its principal advan- tage, the assumption being that quick vibration saves time in weighing. The benefit to be derived from this property of the 6 QUANTITATIVE EXERCISES short beam is, perhaps, overestimated, for in careful weighing by correct methods rapid vibration is a positive disadvantage. The Effect of Friction. Friction upon the knife edges dimin- ishes the sensibility of the balance bj- increasing the difficulty with which the beam and the pans turn upon their axes. Any undue friction upon the terminal knife edges may also prevent the loads from acting downward in vertical lines, and thus, in effect, change the relative lengths of the arms. Great pains is taken in the construction of balances to reduce the friction to a minimum, and any considerable development of it in an instru- ment should be investigated at once. It may be due to dust between the knife edges and their bearings, to the rusting of the knife edges if they are made of steel, or to the dullness of the knife edges and the furrowed condition of the bearings. The last conditions develop in balances which are carelessly used or left to swing when not in use, and also in those which are subjected to constant jarring. Equality of Arm Lengths. Equality in the length of the two arms is desirable but not essential, since for most purposes it is only necessary that the weights to be determined shall be relatively correct. If it is desired to obtain correct weighings, methods are employed which eliminate the errors arising from the inequality of the arms. The Location of a Balance. A balance should be so located that the two arms will maintain, as nearly as possible, the same temperature and consequently the same relative length. Hence it should not be placed near a window, a door which is fre- quently opened, or an aperture through which hot or cold air enters the room. Other things being equal, it should be placed in the center of a room rather than at the side. If the light is sufficient, it is well to protect the balance from air currents by surrounding it on three or all sides by curtains of white material. A balance which is unfavorably situated as regards sources of heat or cold will manifest the fact by con- stantly changing its zero point, i.e. the position which the THE BALANCE 7 pointer would take before the scale if the beam should come to rest after having been set in motion. If artificial light is used in weighing, the lamp or burner should be placed above and back of the head of the observer, and so located with respect to the beam that the heat from it will affect both arms equally. Whether the light is properly placed or not can be ascertained by taking several zero points in succession, that is, by releasing the beam and pans at short intervals and determining by observing its excursions before the scale where the pointer will rest when the beam ceases to vibrate. If the arms are unequally heated by the lamp, the zero points will vary, tending constantly toward the side of the arm which is less rapidly warmed. The foundation on which the balance rests should be as firm as possible. The constant jarring of a balance interferes with weighing by rendering the correct determination of zero points difficult or impossible, and it may seriously injure the knife edges and their bearings. The extent to which a balance is affected by the unsteadiness of its foundation may be ascer- tained by placing a thin glass bottle partly filled with mercury within the case and observing the movements on the surface of the metal. It is well, if practicable, to place the balance on a solid pier of masonry which extends some distance into the earth, and whose vertical sides do not come into contact either with the earth or with any of the floors of the building. A heavy wall is much more steady than a light one ; hence a wall of brick or stone is to be preferred as a support to one of wood. A balance shelf may be attached to such walls by means of heavy iron brackets, but in no case should the shelf be partially supported by legs resting upon the floor. The effect of jarring upon a table resting on the floor may be considerably diminished by placing heavy weights upon it. An arrangement which is said to be effective for localities where it is otherwise impos- sible to secure a sufficiently steady foundation for balances is that which was first used in the provisional office of the K. K. Normal-Aichungs Commission of Austria. An air-tight box 8 QUANTITATIVE EXERCISES capable of supporting a balance in a bath of glycerin is sus- pended in a frame by diverging chains attached to its four corners. Underneath this is placed a tank of glycerin. The balance is so located upon the box as to equalize the strain upon the chains, and glycerin is poured into the tank until the box with its burden is on the point of floating. There is also an arresting device operated by a wheel by means of which the box and balance on it may be raised and made steady during the introduction and removal of weights, etc. Some basic substance, such as lime or an alkaline carbonate, should be kept in the balance case to neutralize acid vapors. It is also customary to place in the case some drying agent, like calcium chloride. The practice is, however, of doubtful utility except when the room in which the balance is kept is one of unusual humidity. Strong sulphuric acid should not be used as the drying agent, since the dust which falls into it may reduce the acid with formation of volatile products which are injurious to the balance. PRECAUTIONS TO BE OBSERVED IN WEIGHING 1. Sit directly in front of the center of the balance so as to avoid parallax while observing the movements of the pointer. 2. See that the balance is level. 3. Release and arrest the beam and pans with a slow and steady movement of the hand. Jerky movements are sure to injure the knife edges. If practicable, the beam should be arrested only when it is in a horizontal position. The pads, or brushes, under the pans, which are designed to steady them while their loads are being placed in position or removed, should be lowered before releasing and raised again after arrest- ing the beam and pans. 4. Avoid giving to the pans any rotary motion in a horizontal direction, and all other movements which would cause a knife edge to scrape on its bearing. THE BALANCE 9 5. Arrest the beam and pans before placing anything upon the latter or removing anything from them. 6. Place the object to be weighed and the larger weights in the middle of the pans. If the terminal knife edges are parallel with the central one, and if there is no considerable friction either upon them or in the jointed hook or chain by which the pans are suspended from the stirrups, the weighings will be correct whatever may be the position of the loads upon the pans. The above precaution is nevertheless to be observed, because the placing of a heavy load at a distance from the center causes a somewhat violent displacement of the pan, which is followed by oscillations not easily quieted. 7. See that the rider is not so near the beam as to be hit by it while swinging. 8. All weighings should be made with the balance case closed. 9. If the beam does not begin to swing as soon as it is released, set it in motion by wafting the air over one of the pans with the hand, or by raising and releasing it again. 10. Objects cannot be correctly weighed while hot, owing to the upward air currents which they create about the pans on which they rest. They may also, through their heating effects on the beam, produce a change in the relative lengths of the arms. Neither should objects be weighed while they are colder than the atmosphere of the balance room, since in that con- dition they may condense moisture on their surfaces. 11. Hygroscopic and volatile substances, also those which absorb carbon dioxide from the air, must be weighed in closed vessels. If the vessels have been tightly closed while warm, there may be diminished pressure within, in which case they must be opened for a moment before weighing. 12. Substances which are exposed to the air condense mois- ture on their surface to an extent which sensibly affects their weight. The amount of moisture thus condensed varies with the humidity of the atmosphere ; hence a substance which is 10 QUANTITATIVE EXERCISES transferred from a desiccator to the balance pan will gain in weight for a time, while one which is brought from a damper atmosphere than that within the balance case will lose weight. One must therefore assure himself, before regarding an observed weight as final, that the object is neither gaining nor losing from this cause. Powdered and porous substances which have been dried in a desiccator or in a hot-air bath should be weighed in closed vessels, since owing to the great surface which they present to the air they condense large quantities of moisture. By keeping drying agents in the case it is endeavored to main- tain a fairly uniform condition of humidity, and thus to reduce the errors arising from the condensation of water upon the surface of the objects weighed. It is a question, however, whether the use of such agents does not, in practice, bring about greater fluctuations of humidity within the balance case than are observed outside of it. If this is true, it would manifestly be of advantage to discard them wherever their presence is not necessary to prevent corrosion, as, for instance, of steel knife edges. 13. An object which, like glass, is likely to become electri- fied by friction should not be wiped or brushed immediately before weighing. Glass and quartz weights sometimes become strongly electrified when lifted out of their places in the box in which they are kept. 14. Long tubes and other objects not easily centered on the pans should be suspended from the hooks above the pans. EXERCISE I PRACTICE WITH THE BALANCE I. DETERMINATION OF THE TIME OF VIBRATION (a) Dust the pans, the beam, the knife edges, and their bear- ings with a camel's-hair brush. Cautiously release first the pans and then the beam. After the beam has oscillated a few or THE * E 6 ? SITY niE BALANCE 11 times long enough to recover from the effects of any jar it may have received when released determine the time con- sumed by the pointer in making ten excursions past the central line on the scale. One tenth of this is the time of vibration. (b) Repeat the experiment with long, short, and medium excursions of the pointer. (c) Determine the time of vibration with loads of five, ten, twenty, thirty, forty, and fifty grams upon each pan. The time of vibration will be found to vary somewhat with the load. It also varies with the length of the beam, as was stated in a previous paragraph ; but with a given length of beam and a given load the time of vibration is a good test of the sensi- bility of the balance. A marked decrease in time of vibration with increased loads indicates a bending of the beam. II. DETERMINATION OF ZERO POINTS (a) Release the balance and, after the pointer has made a few excursions over the scale, begin to note and record the distances from the center of the scale at which the pointer stops and begins to return, estimating to tenths of a division. A large magnifying glass may be used with advantage, especially if the oscillations are rapid. Place the readings to the right in a column marked 72, and those to the left in another column marked L. Take a number of observations, say three or four, on one side, and a number which is greater or less by one on the other. Add the two columns and divide each sum by the number of observations. The results thus obtained represent the mean excursion of the pointer to either side of the center of the scale. Add these together, divide by 2, and subtract the quotient from the greater of the two mean excursions. The result gives the distance from the center of the scale on the side of the longer swings at which the pointer would stop if the beam were to come to rest, i.e. the zero point. 12 QUANTITATIVE EXERCISES Example L E 3.8 divisions 3.5 divisions 3.6 " 3.3 3.4 2)O 3)10.8 3.4, mean excursion E. 3.6, mean excursion L. Q * I O A = 3.5, one half of the total mean excursion, which taken 2i from 3.6, mean excursion to the left, gives the zero point 0.1. The pointer will come to a rest one tenth of one division to the left of the middle line on the ivory scale. It will be seen that, if any two successive readings, as L 3.8 and E 3.5, or L 3.6 and E 3.3, or successive pairs of readings, as L 3.8, 3.6 and E 3.5, 3.3, had been treated in the same way, the zero point would have been located at 0.15 of a division to the left instead of 0.1. The first method is obviously the more correct, since it takes into account the fact that the excursions become shorter and shorter in consequence of friction on the knife edges and the resistance of the air. If the zero point is found to be more than one half of one division to the right or the left of the middle line on the scale, an examination should be made to ascertain whether the dis- placement may not be due to the accumulation of dust on the beam or pans. If it is not, that is, if it persists after a careful dusting of the balance, it is probably the result of corrosion, and the zero point should be adjusted to its proper position by means of the arrangement for that purpose which is to be found on every balance. Exact adjustment, however, is useless, since, as chemical balances are usually located, the relative lengths of the arms and consequently the zero points are constantly changing. A slight displacement of the zero point may be due to the fact that the balance is not level. (5) Repeat experiment (a) with long, short, and medium excursions of the pointer. The zero points should remain nearly constant. THE BALANCE 13 (c) Determine the zero point every fifteen minutes for an hour. If the zero points are found to vary regularly in one direction, or for a time in one direction and then in the other, it is prob- able that the ratio of the arm lengths is changing in consequence of unequal changes of temperature. Lack of constancy in a series of zero points may also be due to dust between the knife edges and their bearings, to the defective condition of the same resulting from wear, rust, or imperfect workmanship, or to the jarring of the balance. If it is due to dust, wear, or to rusted knife edges, the irregularity will generally be found to be in some way related to the length of the swings employed in determining the points. But whether any relation of this kind can be discovered or not, the working parts of the balance should be carefully brushed and the knife edges and their bearings should be examined with a magnifying glass. The stability of the foundation on which the balance rests should also be tested by placing on it or within the balance case the mercury bottle previously mentioned. Lack of con- stancy in the loaded balance may be due to the unequal bending of the two arms. III. DETERMINATION OF SENSIBILITY Strictly speaking, the sensibility of a balance is the angle through which the beam will turn for a given small load upon one side when there is no corresponding counterpoise upon the other. In ordinary parlance it is the displacement of the zero point, in scale divisions, which is produced by adding to or subtracting from the burden borne by one of the arms a weight of one milligram. (a) Determine the zero point of the balance without load. Place the rider on the one-milligram division of the graduated arm and again determine the zero point. The distance between the two points is the sensibility. The true sensibility, i.e. the angular displacement of the beam 14 QUANTITATIVE EXERCISES produced by one milligram, can be calculated if the length of the pointer and the width of the scale divisions are known. Other things being equal, i.e. length of beam, weight of beam and pans, and friction, the sensibility depends on the nearness of the center of gravity to the beam axis. A balance is sufficiently sensitive for ordinary quantitative work when the addition, of one milligram to either side will move the zero point from two to three divisions of the scale. For more delicate work, such as the determination of atomic weights, the center of gravity is raised until the same difference of load will give a deflection of six or seven divisions. With a sensibility of two and a half or three divisions, -fa milligram can be weighed with a fair degree of certainty, while a sensibility of five or six divisions will enable one to detect differences of weight amounting to not more than ^ milligram. The adjustment of the sensibility of a balance should not be undertaken by inexperienced persons. (b) Remove the rider, place five grams upon each pan, and determine the zero point. Replace the rider on the one-milli- gram division of the arm and again determine the zero point. Repeat the experiment with loads of ten, fifteen, twenty, twenty- five, thirty, forty, and fifty grams upon each pan. If the terminal knife edges are below the central one, the sensibility will rapidly decline with increasing loads. Any bending of the beam will, of course, produce the same result. If the knife edges are in bad condition, the sensibility will also decline with increasing loads in consequence of undue increase of friction. If the three knife edges are in the same plane, or if the terminal knife edges are above the central one, the center of gravity will rise when the loads upon the pans are increased, and the balance might therefore be expected to exhibit greater sensibility. But any advantage from this source is usually some- what more than offset by the loss of sensibility which results from the augmentation of the mass to be moved in the opera- tion of weighing, i.e. beam, pans, and loads, and from the THE BALANCE 15 bending of the beam. Hence, as a matter of fact, most balances become less sensitive when heavier loads are placed upon the pans. If a balance exhibits a reasonably uniform sensibility up to a given load and then a sharp decline for greater burdens, it is certain that the beam is bending under the heavier weights, and that the limit to which it ought to be loaded has been reached. There are two methods of securing constant sensibility in balances, i.e. a sensibility which does not vary with the weight to be determined. One of them was first employed by Verbeek and Peckholdt and the other by Bunge. The former enhance the increase of sensibility resulting from the rise of the center of gravity when additional loads are placed upon the pans by fixing the terminal knife edges above the central one and, by exact adjustment, make the gain from this source just equal to the loss of sensibility from all other causes. The adjustment must, of course, be such that the maximum load for any balance can neither throw the terminal knife edges below the central one nor raise the center of gravity so high as to produce indifferent equilibrium. In Bunge's balance of constant sensibility the arms are of different length and weight, and only the shorter and lighter one is supplied with a pan. This difference in the length and weight of the two arms is so regulated that the maximum weight which the balance is intended to carry, say 200 grams, just suffices to bring the beam into equilibrium. The object to be weighed is placed upon the pan and weights are added until the balance is brought to a state of equilibrium. The difference between the weight which is known to produce equilibrium and the sum of the weights placed on the pan is the weight of the object. It will be observed that the balance always carries the same load, and that for this reason its sen- sibility is constant. Any balance of ordinary construction can be used as an instrument of constant sensibility in the following manner : A tare of suitable character, which is heavier than the heaviest 16 QUANTITATIVE EXERCISES object to be weighed, is placed upon one of the pans. The object to be weighed is placed upon the other pan and weights are added until the beam is in equilibrium. The object is then removed and more weights are added until the beam is again in equilibrium. The difference between the weights necessary to produce equilibrium on the two occasions is the weight of the object. This method of weighing with the ordinary balance is an excellent one, since it offers the double advan- tage of constant sensibility and elimination of errors due to an unequal or variable ratio of arm lengths. The distance between the center of gravity and the beam axis varies somewhat with the temperature, shortening in cold and lengthening in warm weather. Hence a balance with a given adjustment is found to be more sensitive in winter than in summer, and it sometimes happens that a. balance which has been adjusted to great sensitiveness in hot weather exhibits indifferent equilibrium in very cold weather. IV. To DETERMINE WHETHER THE ARMS ARE EQUAL (a) Determine the zero point of the empty balance. Place a one-milligram weight on the right-hand pan and determine the zero point. Transfer the weight to the other pan and again determine the zero point. If the arms are of the same length, the last zero point will lie as much to the right as the second does to the left of the first. This test is decisive only when the balance is very sensitive and the knife edges and their bearings are in good condition. (b) Determine the zero point of the empty balance. Place a ten-gram weight upon each pan and determine the zero point. Exchange the weights and again determine the zero point. If the arms are equal and the weights are equal, the second and third zero points will coincide with the first. If the arms are equal and the weights unequal, the second and third zero points will deviate equally to the right and left of the first, If the THE BALANCE 17 arms are unequal and the weights equal, the second and third zero points will coincide with each other, but not with the first. If both arms and weights are unequal, the second and third zero points cannot coincide with each other, neither can they deviate equally to the right and left of the first. It follows that if the second and third zero points coincide with the first, or if they deviate equally to the right and left of it, the arms are of equal length. Any other relation of the three points indicates inequality. Of course any slight difference in the length of the arms may escape detection by this, as by all other methods, if the knife edges or their bearings are in bad condition. As has been stated already, the exact ratio of the arm lengths is of little concern to the chemist, since, whatever the ratio may be, if it remains constant, his weighings are relatively correct, and this suffices for most purposes. The ratio, if known, may be utilized to correct weighings ; but as a matter of fact it is not so used, because, first, being changeable, it must be redetermined for every new experiment; and, second, there are easy methods of weighing which eliminate the errors resulting from the inequality of the arm lengths. The ratio is ascertained by weighing an object, usually a brass weight, first upon one pan and then upon the other. Any apparent difference of weight found by the two operations is due to the inequality of the arms. The procedure is as follows. Determine the zero point of the empty balance. Place a ten-gram weight upon each pan, representing them by P and P' respectively. Determine the zero point and the sensibility of the balance with the weights upon the pans, and calculate what weight must be added to or subtracted from P to produce equilibrium, i.e. to make the zero point coincide with that of the empty balance. Exchange P and P', and, in the same manner as before, find how much, plus or minus, must be added to P to produce equilibrium. Let p represent the weight which must be added when P is on the left pan, and p' that which 18 QUANTITATIVE EXERCISES must be added when P is on the right pan. Let It and L rep- resent the length of the right and left arm respectively. Then L (P + p} = P'R, and LP* = (P + /) P. Multiplying together the corresponding terms, L*P' (P + p) = R*(P + /)P'. Dividing by P', i 2 (P + p) = R* (P + /), Z /P or Dividing numerator and denominator of the second term by P, Extracting the square root of numerator and denominator separately, we have, approximately, L & 1 + + Dividing numerator by denominator, 2P THE BALANCE 19 EXERCISE II PRACTICE IN WEIGHING I. WEIGHING BY THE USUAL METHOD (a) Determine the zero point of the empty balance. Place the object to be weighed a crucible, coin, or something else which does not change its weight in the air in the center of the left-hand pan, and the weights which are supposed to be about equal to it in the center of the right-hand pan. Slowly release the balance pans first, and then the beam until it is seen which way the pointer turns, and then, as slowly, arrest it again. Add or remove weights, as may be required, and again release and arrest the beam as before. Repeat these trials, using the rider for weights under a centigram until the zero point is found to coincide with that of the empty balance. (b) Proceed as directed under (a) until' it is found that not more than one milligram must be added to or taken from the weights in order to produce equilibrium, and then determine the zero point. Add or subtract one milligram by moving the rider along the beam and again determine the zero point. The last operation gives the sensibility of the balance for the load which is upon the pans, and from this is to be calcu- lated what weight is to be added or subtracted in order to produce equilibrium. Example Suppose the zero point of the empty balance is 0.5 division to the left of the middle line on the scale, and the zero point when the weights nearly balance the object is 1.0 to the right, while the sensibility is 3.0 divisions. It is clear that the addi- tion of one half milligram to the weights already in the balance will produce equilibrium, since that is the weight required to move the zero point 1.5 divisions, i.e. from 1.0 right to 0.5 left. Of the two methods, (a) and (&), the latter is the better, and it should be generally employed in quantitative work. 20 QUANTITATIVE EXERCISES Instead of determining the sensibility of the balance each time a weighing is made, one may utilize, in the form of a table or a curve, the sensibilities for different loads as determined in Exercise I, III. This course, however, is not to be recommended, since it is not safe to assume that the sensibility has not changed in the meantime. It will be seen that balances of constant sensibility have this distinct advantage over others, namely, that all weights less than a milligram can be read directly from the scale. It is assumed, whenever either of the methods (a) or (b) is employed, that the arms are of equal length, whereas they are usually to some slight extent unequal. But no harm results from this assumption if, as in ordinary analytical work, it is only necessary that the various weighings shall be correct with respect to each other ; and they are thus relatively correct, how- ever unequal the arms may be, provided the ratio of the arm lengths does not change. If the ratio of the arm lengths were known, the errors in weighing due to inequality could be cor- rected; but corrections of this sort are seldom undertaken because the ratio is not constant. It varies in consequence of unequal changes of temperature and also because of unequal bending under the strain of the loads upon the pans. If the work to be done is of such a character that the errors in weigh- ing due to inequality or varying ratio of the arm lengths cannot be neglected (i.e. if exact weighings are required rather than those which are correct with respect to each other), one of the two following methods is employed. Both eliminate the errors due to the inequality and to the changeable ratio of the arms. II. WEIGHING BY THE METHOD OF BORDA (a) Determine the zero point of the empty balance. Place the object to be weighed upon the right-hand pan and balance it to within one milligram by placing weights upon the left- hand pan. Determine the zero point and the sensibility, and THE BALANCE 21 from these calculate how much would have to be added to or subtracted from the weight of the object to produce equilibrium, i.e. to make the zero point coincide with that of the empty balance. Remove the object and put weights in its place until equilibrium is nearly obtained. Again determine the zero point and calculate from the sensibility how much must be added to or subtracted from the weights on the right-hand pan in order to produce equilibrium. Let P represent the unknown weight of the object, p the weights, plus or minus, which must be added to P to produce equilibrium, W the weight on the right-hand pan, and p 1 the weight, plus or minus, which must be added to W in order to produce equilibrium. Now, since P+p and W + p* both balance the load on the left-hand pan, they are equal to each other, and P = W+p' p. The proper algebraical sign must be given to p and p'. This procedure is also called the method of weighing by sub- stitution. (b) Place upon the left-hand pan something which is heavier than the object to be weighed. A weight or a small beaker containing shot will answer the purpose. Put the thing to be weighed upon the right-hand pan and add weights until equi- librium is obtained. Remove the object and add more weights until equilibrium is again obtained. The difference between the weights required in the two cases is the weight of the object. It will be seen that the principle involved in this method is identical with that on which Bunge's balance of constant sensi- bility is constructed. III. WEIGHING BY THE METHOD OF GAUSS Weigh the object as directed in Exercise II under II (b) first on one pan and then on the other. Multiply the two weights together and extract the square root of the product. 22 QUANTITATIVE EXERCISES Let W represent the true weight which is to be found, A the weight which is found when the object is on the right-hand pan, B the weight obtained when it is on the left-hand pan, It the length of the right arm, and L the length of the left arm. We then have WE = AL, W*RL = ABEL, WL = BR, W 2 = AB, Half the sum of A and B may be taken as the true weight whenever the difference between - and V 'AB is too small to be detected by the balance. IV. CORRECTION FOR THE AIR DISPLACED Just as objects which are weighed under water lose weight by an amount equal to the weight of the water which they dis- place, so those weighed in the air are lighter than they would be in a vacuum by the weight of the displaced air. Suppose two ten-gram brass weights which have been found to balance each other in a vacuum are again compared in the air. They will be found to balance each other with the same precision as before ; for, having the same specific gravity, their volumes are equal and they must therefore lose equally by the transfer. Suppose, on the other hand, that one of the two ten- gram weights which balance each other in a vacuum is made of brass. and the other of platinum. If these are compared in the air, they will no longer be found to be equal ; for, having differ- ent specific gravities, their volumes are unequal, and they must therefore lose unequally by the transfer. The brass weight, having a specific gravity of 8.4, has a volume of 1.19 cubic centimeters ; while the platinum weight, with a specific gravity of 21.5, has a volume of only 0.465 cubic centimeter. The average weight of a cubic centimeter of air is 1.2 milligrams. The brass weight will therefore lose in the air 1.428 milligrams, THE BALANCE 23 while the platinum weight will lose only 0.558 milligram. The former will appear to be lighter than the latter by the difference between 1.428 and 0.558, i.e. by 0.87 milligram. In the same way it may be shown that a piece of quartz weighing ten grams in a vacuum would appear in the air to weigh 9.99887 grams if weighed with brass weights, and only 9.99602 grams if weighed with platinum weights ; also that the error in weighing a liter of water in the air amounts to more than a whole gram whether the weights are of brass or of platinum. It appears that weighings conducted in the air are correct only when the object weighed and the weights have the same specific gravity, and that when the two the object weighed and the weights differ largely in respect to specific gravity, the errors arising from the buoying effect of the air are too large to be neglected. To find the true weight of an object weighed in the air, it is clear that we must add to or subtract from its apparent weight the difference between the weights of the air displaced by the object and by the weights. If the object has a smaller specific gravity (i.e. a larger volume) than the weights, this difference must be added ; otherwise it must be subtracted. The volumes in cubic centimeters of the object weighed and of the weights and consequently of the air displaced by each- are found by dividing their apparent weight (weight in air) in grams by their respective specific gravities. Strictly speaking, the method is slightly erroneous because the weights found in the air are not true weights, and the calculated volumes are therefore not quite the true volumes*. In a few cases this error may require correction, as, for example, in weighing a liter of water, in which instance it amounts to something over a milligram. Let W represent the true weight of an object (i.e. its weight in a vacuum), P its apparent weight (i.e. its weight in the air), d the specific gravity of the object, d l the specific gravity of the weights, and a the weight of one cubic centimeter of air at the 24 QUANTITATIVE EXERCISES time of weighing. Then we have as a general formula for the corrections of weighings made in the air d The weight of a cubic centimeter of air varies with the pres- sure, the temperature, and the latitude, also with the moisture and the carbonic acid which it contains ; but for all ordinary corrections of this kind, a is assumed to have a value of 1.2 milligrams, and the equation accordingly becomes W=P + P 0.0012 A -i- \d d d 1 = 8.4 when the weights are of brass, 21.55 " " " " " platinum-iridium, 21.50 " " " " " platinum, 2.65 " " " " " quartz, 2.60 " u " " " aluminium. If, as happens in nearly all weighing operations, weights of two different materials are used, a correction for each must be applied. Suppose, for example, it is desired to find the true weight of a porcelain vessel (specific gravity 2.29) which balances in the air 15 brass grams and 5 platinum decigrams. The for- mula for the corrections would then become =15.506 grams. A table will be found in Landolt-Boernstein's PJiysikaliscJi- Chemische Tabellen, 2. Auflage, page 10, which gives the com- puted values of 0.0012 (-.. - ~-J between d = .7 and d = 22 for \d dj d 1 = 8.4 (brass weights), d 1 = 2.65 (quartz weights), and d 1 = 21.55 (platinum weights containing ten per cent of iridium). The first chemist to adopt the practice of correcting weigh- ings for air displacement was Edward Turner (1796-1837). THE BALANCE 25 Problem 16.13161 grams of zinc gave 20.08608 grams of zinc oxide. 14 grams of the metal and 15 grams of the oxide were weighed with brass weights, and the remainders with platinum. The specific gravity of zinc is 7.15 and that of the oxide 5.65; what were the true weights of the metal and of the oxide? If the atomic weight of oxygen is 16, what is that of zinc? Weighing by Tares The accuracy of weighings may be considerably increased by employing as counterpoises for the vessels in which sub- stances are weighed (such as flasks, crucibles, tubes, etc.) other vessels of the same material, form, size, and weight. The advantages of so doing are : (1) the vessels and their tares being of the same material and presenting the same area of surface to the air, condense or absorb the same amount of moisture, and the weighings are thus freed to a great extent from the errors which arise from the varying humidity of the atmosphere; (2) having the same density, no corrections for air displacement are necessary; (3) any errors resulting from changes in the weight of the vessel (due to heating, immersion in liquids or vapors, or to other necessary treatment) may be avoided by subjecting the tare to precisely the same treatment. In practice, the lighter of the two vessels, the weights of which should be very nearly equal to begin with, is selected as the tare ; and to this fragments of the same kind of material are added until the vessels do not differ in weight more than a fraction of a milligram. The difference in their weights is then carefully determined by means of the displacement of the zero point which it produces and the sensibility of the balance, and allowance is made for it in all subsequent weighings. 26 QUANTITATIVE EXERCISES EXERCISE III CORRECTION OF WEIGHTS I. COMPARISON OF THE DIFFERENT PIECES OF A SET WITH EACH OTHER Wherever there are two nominally equal weights in the set, mark one of them by making a slight indentation upon it with a piece of steel having a smooth point. Such stamped weights will be designated in what follows by the letter s. Determine the zero point of the empty balance. Place the one- gram weight upon one pan and the fractional pieces nominally equal to it on the other. Determine the zero point and the sensibility of the balance, and from these calculate the differ- ence between the two loads. Reverse the loads and again find their differences in weight in the same manner. Find their true difference in weight by the method of Gauss. Regard the one- gram piece as the standard weight and the difference between it and the sum of the fractional pieces as the error of the latter. To determine the value of the larger weights as compared with the standard, make the following weighings. 2 s against 1 plus the fractional weights, assigning to the latter their true value as compared with 1, 2 against 2 s , 5 2 + 2 8 + 1, 10 s " 5 + 2 + 2 8 + l, 10 " 10 s , also against 5 -f- 2 -f 2 s + 1, 20 " 10 + 10 s , also against 10 s + 5 + 2 + 2 s + 1, 50 " 20 + 10 + 10 8 + 5 + 2 + 2 s + 1. It remains to be discovered how the error of the sum of the fractional weights is distributed among the several pieces. Weigh 0.010 s against 0.00*5 + 0.002 + 0.002 + 0.001. Regard 0.010 s as the standard fractional weight, and the difference between it and the smaller pieces as the error of the latter. THE BALANCE 27 To find the value of the larger fractional pieces, weigh : 0.010 against 0.010 s , 0.020 0.010 + 0.010 s , 0.050 0.020 + 0.010 + 0.010 s + 0.005 + 0.002 + 0.002 + 0.001, 0.100 s 0.050 + 0.020 + 0.010 + 0.010 s + 0.005 + 0.002 + 0.002 + 0.001, 0.100 0.100 s , 0.200 0.100 + 0.100% 0.500 " 0.200 + 0.100 + 0.100 s + 0.050 + 0.020 + 0.010 + 0.010 + 0.005 + 0.002 + 0.002 + 0.001. Having thus found the value of the fractional pieces above 0.005, as compared with 0.010 s , bring them all to the standard of the larger weights, the one-gram piece, by correcting each for its share of the total error (i.e. the difference in weight between the sum of the fractional pieces and the standard one- gram weight). In making this correction, 0.005, 0.002, 0.002, and 0.001 will, of course, be regarded as a single weight. If the arms of the balance are so graduated that ten full milligrams can be added to them by means of the rider, as in the Becker balance, it is not necessary- to carry the comparison of the weights below the 10-milligram pieces. If the arm is divided into only ten equal parts, and the construction of the beam is such that the rider cannot be carried quite to the terminal knife edges, it is necessary to begin the work upon the fractional weights by weighing 0.005 against 0.002 + 0.002 + 0.001. The value of the riders is found by weighing them against a corrected 0.010-gram piece. If only one arm of the balance is graduated and the riders weigh twelve milligrams each, it will be necessary, in order to obtain weighings on both sides, to weigh the riders against 0.010 + 0.002. In this case the correction of the weights must be extended so as to include the milligram pieces. Having found the values of the various weights with respect to the one-gram piece, any other weight in the set may be made 28 QUANTITATIVE EXERCISES the standard of comparison. Suppose it is desired to find the value of the various weights with respect to the stamped ten- gram piece. Let x represent the value of any weight as compared with the new standard (i.e. the value to be found), a the value of the same weight as compared with the one-gram piece, and b the value of 10 s as compared with the one-gram piece. The equation for finding the value of x will then be 6:10: iaix, or x= 10 - II. To COMPARE A SET OF WEIGHTS WITH A STANDARD WEIGHT Find the difference between the standard and the piece of the same nominal weight in the set by the method of Gauss. Com- pare the weights with each other and find, in the manner pre- scribed under I, the value of each piece with respect to the standard weight. As a rule, the balances of a chemical laboratory are so unfa- vorably located and so destitute of the accessories required for refined weighing, that it is difficult to make satisfactory com- parisons of weights with them. Fortunately, however, the ad- justment of weights has been carried by several makers to a very high degree of precision, and the weights which are fur- nished by them need not be tested unless the work to be done demands very great accuracy. Materials for Weights The substances commonly employed as material for weights are brass, platinum, platinum-indium, quartz, and glass. Brass is inexpensive and is easily formed and adjusted, but is too readily corroded. This defect, however, is often remedied by gold plating the weights. Platinum is noncorrodible and readily adjusted, but it is too costly and has a specific gravity too far THE BALANCE 29 above that of a majority of the substances commonly weighed. Quartz and glass are not easily attacked by substances likely to find their way into the air, and they have specific gravities quite near to those of many of the substances to be weighed ; they are, however, in consequence of their greater hardness, more difficult than the metals to fashion and adjust, and the weights made from them easily become electrified when they are removed from their places in the box, especially when the box is lined with velvet or leather. CHAPTER II THE BAROMETER AND THE THERMOMETER THE BAROMETER The principal use of the barometer in a chemical laboratory is in connection with the measurement of gases and the determination of the boiling points of liquids. The instrument usually employed is either the Fortin modification of the cistern barometer or the so-called siphon barometer. The simplest form of the cistern barometer consists of a wide vessel, the cistern, and a long glass tube closed at one end and open at the other. The tube is filled with mercury, inverted, and its open end immersed in mercury which partly fills the cistern. The pressure of the air is then measured by the height to which the mercury rises in the tube, i.e. by the vertical distance between the upper surfaces of the mercury in the cistern and in the tube. The principal objection to this form of the instrument is the necessity of employing either an adjustable scale, or if fixed one so contrived as to compensate for the difference between the cistern and the tube in respect to cross section. In the Fbrtin barometer, Fig. 1, this difficulty is obviated by employing a cistern having a flexible leather bottom which can be raised or lowered by means of an adjusting screw placed underneath. By this means, when- ever a reading is to be taken, the level of the 30 FIG. 1 THE BAROMETER AND THE THERMOMETER 31 mercury in the cistern is made to coincide with the lower extrem- ity of the graduated scale upon or at the side of the barometer tube. The correct adjustment of the surface is made possible by a sharp-pointed ivory indicator, which is fixed in a vertical position above the mercury in the cistern in such a manner that its lower, pointed end lies in the same horizontal plane with the lower extremity of the graduated scale. The slightest contact between the ivory point and the metal pro- duces a visible depression in the surface of the latter. The scale may be etched upon the tube, but it is usually of brass and is often provided with a vernier, Fig. 2, and with accessories designed to obviate those errors in reading which are due to parallax. The siphon barometer, Fig. 3, is so called with reference to its form only. It consists of a U-shaped tube having one limb much longer than the other. The long limb is closed at the top and bent so as to bring its upper portion into line with the shorter limb. The scale is usually etched upon the glass and extends over both limbs. The point from which the enumeration of the divisions of the scale begins may be above the high- est or below the lowest possible level of the mercury in the shorter limb. In the former case the numbers increase in the upward direction on the longer and in the downward direction on the shorter limb, and the readings on the two limbs are to be added ; while in the latter case the num- bers increase in the upward direction on both limbs and the readings are to be subtracted. There are certain facts concerning the barometer and its use which require attention. FIG. 3 FIG. 2 32 QUANTITATIVE EXERCISES 1. The mercury must be pure in order that its density may be normal and its movements in the tube free. 2. The tube of a cistern barometer must be of sufficient internal diameter ; since, otherwise, the height of the mercury column is sensibly affected by capillary depression. In the siphon barom- eter this difficulty disappears except in so far as the meniscuses in the two limbs of the instrument differ in form owing to the fact that one of them is in the air and the other in a vacuum. 3. The inclosed space in the tube above the mercury must be free from air and moisture. The simple filling of a tube with mercury does not completely remove the air. A small portion of it clings to the glass and this can be expelled only by boiling the mercury in the tube ; hence all barometers are "boiled out" at the time of filling. Whether the inclosed space is free from air or not may be ascertained by tilting the instrument to one side until the mercury rises to the top of the tube, when, if air is absent, the mercury will fill the entire space. Another way of testing for. the presence of air is cau- tiously to set the column of mercury in motion until it strikes against the top of the tube. If the vacuum is complete, a sharp ringing sound will be produced which is unmistakable. The depression of the barometer which is produced by the vapor of the mercury itself is insignificant, amounting at 20 only to 0.02 mm. 4. The scale by which the height of the barometer is read, if not known to be correct, must be tested. This may be done with sufficient accuracy for most purposes in the following manner. A pair of slender sharp-pointed dividers with screw adjustment are opened on any part of the graduation until some whole number of divisions, e.g. ten, are included between the points. Thus adjusted, the dividers are run several times over the whole scale, beginning each time at a new place. If the points are always found to span the same number of divi- sions, the graduation is sufficiently uniform, and it remains only to ascertain whether it is sufficiently correct. The latter THE BAROMETER AND THE THERMOMETER 38 question is quickly settled by placing the dividers, without alteration of adjustment, upon a scale known to be correct, which should be of the same material as that under examination. 5. The barometer, when read, must have a vertical position, and care must be taken to avoid errors of parallax. If practi- cable, a telescope should be employed. 6. The siphon barometer should be gently tapped before read- ing in order to overcome a tendency on the part of the mercury to lag in its movements in the tube. This treatment is not necessary in the case of the Fortin barometer when the column has been set in motion by the adjustment of the level of the mercury in the cistern. CORRECTIONS OF THE BAROMETER I. For Temperature Since the density of mercury decreases with rising tempera- ture, the height of the column supported by a given atmospheric pressure will vary somewhat with the temperature of the air (e.g. the pressure which supports a column 760 mm. high at will, at 20, support one 762.76 mm. in length). It is necessary, therefore, to select some standard temperature for the mercury and to correct accordingly all readings made at other tempera- tures. The standard temperature is 0, and the term " height of the barometer" signifies not the observed height but that which it would have at 0. Since the height of the column of mercury supported by the weight of the air is, in general, inde- pendent of the diameter of the tube, the corrected height (b) will be found by dividing the observed height (b ! ) by unity plus the cubical expansion of mercury (0.0001818 t) from to the temperature at which the reading was made. The general formula for the correction is b = z ., ^ when the tem- 1 -\- O.UUUlolo t perature is above 0; and b = ^ A AAAI QI Q S wnen the tem- 1 U.UUUlolo t perature is below 0. 84 QUANTITATIVE EXERCISES The effect of change in temperature upon the length of the scale must also be taken into account, for its graduation is correct only at the standard temperature of 0. Obviously the divisions are too far apart at temperatures above 0, and too near together at temperatures below that point. If b and t have the same significance as in the previous formulas, while 7 represents the linear-expansion coefficient of the material of the scale, the formula for the correction of the scale is Z = 6(1 4-7*), or 1 = 6(1 7*), according as the temperature is above or below at the time of reading. Letting h represent the true height of the barometer, we have, by combining the two corrections, the formulas r j, 0.0001818* for temperatures above 0, and , ,, I-* 1-0.0001818* for temperatures below 0. 7 = 0.0000085 when the scale is of glass, and 0.0000184 when it is of brass. It will be observed that the two errors the one due to change in the density of the mercury and the one due to change in the length of the scale tend to compensate each other at all temperatures. Simpler formulas for the temperature correction of the barom- eter which, though not entirely accurate, are sufficiently so for most purposes, are : h = b'(l- (0.0001818 - 7) t) for temperatures above 0, and h = b'(I + (0.0001818 - 7) t) for temperatures below 0. These become h = b' (1-0.0001733*) and h = b f (1 + 0.0001733 t) when the scale is of glass, and h = fc'(l- 0.0001634 ) and h = b' (1 + 0.0001634 t) when the scale is of brass. THE BAROMETER AND THE THERMOMETER 35 II. For Capillary Depression As previously stated, there is no correction to be made for capillary depression in the siphon barometer. The depression is likewise negligible in cistern barometers when the diameter of the mercury column is equal to or exceeds 25 mm. In narrower tubes, however, the depression sensibly affects the height of the barometer, and is to be added to the readings of the instrument unless the correction has already been provided for in the scale itself. The following table gives the amount of the correction for tubes of various small diameters. DIAMETER OF TUBE DEPRESSION DIAMETER or TUBE DEPRESSION 4 mm 1.64 mm. 14 mm 0.12 mm. G 0.91 16 0.07 8 0.54 18 0.04 10 " 0.32 20 " 0.03 12 0.19 III. For Latitude and Altitude The atmospheric pressure which will support a column of mercury of given height, e.g. 760 mm., is not a fixed quantity, but diminishes as the distance from the earth's center of gravity increases. It varies, therefore, with latitude and elevation above sea level. Hence it is necessary, even for meteorological com- parisons, to establish a unit for the earth's attraction and to reduce observations on the height of the barometer in all parts of the earth's surface to this standard. The unit agreed upon is the force of gravity which is found to prevail at sea level in latitude 45. If it is desired to reduce a reading of the barom- eter made at any other latitude and altitude to the height which it would have with the same atmospheric tension at latitude 45 and sea level, the observed height, corrected for temperature, is to be multiplied by the expression (1 - 0.0026 cos 2c) (1 - 0.0000002 H), 36 QUANTITATIVE EXERCISES in which $ is the latitude of the place and If its elevation in meters above sea level. The latter term, (1 - 0.0000002 H), may be neglected except when the altitude of the place is con- siderable, since at an elevation of 500 meters the correction for altitude amounts to only 0.07 mm. The following table will give an idea of the magnitude of the corrections for latitude when the observed height of the barometer is 760 mm. Latitude = 12 18 ' 24 30 36 42 45 Correction ^ = 1.97 1.80 1.59 1.31 0.98 0.61 0.21 0.0 mm. Latitude = 90 78 72 66 60 54 48 45 The correction is subtracted from the height of the barometer, or added to it, according as the latitude of the place of obser- vation is below or above 45. It will be observed that, with equal atmospheric pressure at the two places, a barometer at the equator would stand 3.94 mm. higher than one at the pole. What has been said of the mutual relations of barometric height, atmospheric pressure, and the force of gravity is also true of every other column of mercury which is supported by the pres- sure of a gas or by the difference between two gas pressures. The bearing of this fact upon the work of the chemist will be made clearer by outlining the most common method of measur- ing a gas. A tube, closed at one end and graduated, is filled with mercury, inverted, and its open end immersed in mercury in an open vessel. The apparatus thus prepared resembles a cistern barometer, and is one, in fact, if the length of the tube is equal to or greater than a barometric height. The gas tq be measured, on being introduced into the tube at the open end, rises to the top and depresses the column of mercury. Its volume is then read upon the graduation of the tube. But the term volume has no significance in the case of a eras unless o o the pressure under which it is measured is known, because its volume, leaving temperature out of the consideration, depends on the pressure. Hence it is necessary to ascertain THE BAROMETER AND THE THERMOMETER 37 the pressure resting upon a gas at the time of determining its volume. This is a very simple matter ; for, evidently, the pres- sure upon the gas which determines the space it can occupy is the difference between the pressure of the air and the pressure of the column of mercury in the eudiometer, and this will be found by subtracting the height of the column of mercury in the tube from the height of the barometer. Stated in another way, the sum of the pressure exerted by the gas and that exerted by the column of mercury in the eudiometer is equal to the pres- sure of the atmosphere ; and hence, to find the pressure exerted by the gas, we have only to subtract the height of the one mer- cury column from that of the other. The result is the height of the mercury column which the gas is capable of supporting, and it is the measure of its pressure or tension in the same sense that the height of the barometer is the measure of the pressure or tension of the atmosphere. Having thus found the volume of a gas when measured under some known pressure, we can calculate what space it would occupy under any other pressure, for instance, under the conventional standard pressure, which is the pressure required to support at a vertical column of mercury 760 mm. in length. Having found its volume under standard pressure, we can find its weight through the known density of the gas. This procedure for finding the weight of gases suffices for all ordinary purposes ; but when great accuracy is required, as in the determination of an atomic weight, it is necessary to take into account the fact already explained that the height of a col- umn of mercury is not an unvarying measure of the pressure which supports it. In other words, it is necessary to multiply the height of the mercury column which expresses the pressure under which the gas was measured by (1 0.0026 cos 2$) (1 - 0.0000002 H) in order to find what its height would be in the standard locality, i.e. latitude 45 and sea level. If this correction is neglected, equal volumes of the same gas will be found to have different weights in different parts of the earth. 38 QUANTITATIVE EXERCISES IV. For the Moisture in the Air It is sometimes desired to know what portion of the observed height of the barometer or of another mercury column is due to air or gas in the dry condition. This is found by subtracting from the observed height of the column the tension of the water vapor expressed in millimeters of mercury. If the gas is saturated, the tension of the water vapor will be known. Other- wise it must be determined. THE THERMOMETER Three things are to be ascertained with respect to a ther- mometer before it can be used with confidence. They are : (1) the position of the upper end of the mercury column when pure water freezes, its zero point; (2) the position of the same when pure water boils, its boiling point; and (3) the inequalities of its bore. An instrument having the scale upon the glass and without the white opaque background so common in laboratory ther- mometers is to be preferred for the exercises which follow. EXERCISE IV DETERMINATION OF THE ZERO POINT There are required : 1. A strong test tube, 25 X 175 mm. 2. A stout platinum wire, 250 or 275 mm. long. 3. Two corks, one of which fits the test tube, and the other large enough to bore for the tube. 4. A beaker, 100 x 175 mm., or, better, a glass battery jar of approximately the same dimensions. 5. A cover of wood or metal for the jar. 6. A glass tube or copper wire, 8 x 600 mm. THE BAROMETER AND THE THERMOMETER 39 Bore the smaller cork centrally for the thermometer, and near the outer edge for the platinum wire ; and the larger cork for the test tube. Bend one end of the platinum wire into a ring which fits loosely the inside of the tube (1), and the rest of the wire into a right angle with the ring. This stirrer may also be made from a thin glass rod or tube ; or a ring of platinum wire with a short overlap of wire bent to a right angle may be made, and the standing end of the wire fused into the end of a glass tube. Make a similar stirrer for the jar or beaker (4) out of the glass tube or copper wire. Bore the cover (5) for the cork on the test tube and for the stirrer. The apparatus ready for use is shown in Fig. 4. Partly fill the test tube with distilled water and insert the thermometer. The distance between the lower extremity of the bulb and the bottom of the test tube should be somewhat greater than that between the bulb and the side of the tube, and the level of the water should be above the zero point of the FIG 4 thermometer. Move the stirrer up and down and make sure that it does not rub against the bulb at any point. Fill the outer vessel with a mixture of pulverized ice, or snow, and a little salt; and if the ice is quite dry, add a little water. Place the tube containing the thermometer and the water in position in the larger vessel, and stir from time to time the freezing mixture. The temperature of the water in the inner vessel will fall somewhat below the freezing point before the formation of ice begins. As soon as the thermometer indicates an under-cooled condition, stir the water vigorously in order to prevent the formation of coarse ice and to secure a uniform distribution of temperature. The mercury will fise slightly and become stationary, giving the point to be recorded. Remove the test tube from the freezing mixture and resume the 40 QUANTITATIVE EXERCISES stirring. The thermometer will remain unchanged until a large portion of the ice has melted. When so much of the ice has disappeared that the thermometer again begins to rise, return the tube to the freezing mixture and repeat the experiment. Immerse the thermometer bulb in the steam from boiling water for half an hour and then redetermine the zero point. It will be found that the second zero point is lower than the first. Repeat the heating in steam and again determine the zero point. The second and third results should agree. It is of some advantage to "jacket" the .apparatus with a larger tube, and thus provide an air space between the cooling mixture and the water. The freezing of the water and the melting of the ice are then slower, giving more time for the observation of the thermometer. A very common but less satisfactory procedure for the deter- mination of the zero points of thermometers will be described. A piece of rubber tubing provided with a pinchcock is attached to the stem of a large funnel, which is placed in the ring of an iron stand and filled with snow or finely powdered ice. The ice, if dry, is then moistened with enough distilled water to expel the air. The bulb of the thermometer, thinly wrapped in flannel to prevent actual contact with the icej is imbedded in the ice to a point on the stem above the zero mark. From time to time the thermometer is raised, or the funnel lowered, in order to observe the height of the mercury. There are two objections to this method: (1) the tempera- ture of the ice may be below the freezing point of water, in which case the water in contact with the bulb, despite the flannel covering, may be under-cooled ; (2) the ice may con- tain soluble impurities, which, even in small quantities, sensibly depress the melting point. The latter difficulty may be avoided in the following man- ner. A metallic rod of the same diameter as the thermometer is fixed in a vertical position, its lower end immersed in a vessel filled with distilled water, which is afterwards frozen to a solid THE BAROMETER AND THE THERMOMETER 41 cake pf ice by surrounding it with a freezing mixture. The rod is loosened by heating its free end, and removed, leaving a cavity for the bulb of the thermometer. The stem of the ther- mometer is provided with a rubber ring wider than the hole, which rests on the ice when the instrument is in position. The difference which was observed in the foregoing experi- ment between the zero points determined before and after heat- ing the thermometer to the boiling point of water is due to the fact that when glass is heated and again cooled to its former temperature it .does not immediately shrink to its original vol- ume. In other words, the depression of the zero point which follows a heating of the thermometer is the result of an enlarge- ment of the bulb. The extent of the depression varies greatly with the composi- tion of the glass, being large in the Thuringian, and small in the so-called Jena normal glass, which contains in addition to the more common constituents of glass silica, alkalies, and lime about 7 per cent of zinc oxide and 2 per cent of boric acid. It also varies with the temperature to which the ther- mometer is heated and with the duration of the heating. The dilatation is not permanent. The shrinkage of the bulb begins at once ; for if a thermometer which has been heated to the boiling point of water is placed in melting ice, the mercury is observed to sink to a certain point, and then slowly to rise. This lowest reading is known as the " zero of maximum depres- sion." The rate at which the bulb returns to its original vol- ume, like the degree of the dilatation, is variable. The recovery may last a few hours or several months according to the com- position of the glass, the temperature to which the thermometer has been heated, the duration of the heating, and the rapidity of the cooling. In the case of new thermometers, a gradual slow rise of the zero point is observed which may require years for its completion. 42 QUANT1TATJV1. K\1.K< [SE8 If a thermometer is heated for a long time to a hi^li tem- perature, the zero point rises, and in some cases to an ishing extent Crafts, after heating certain thermometers of common German and of French crystal glass to 355 for < . days, observed elevations of the zero points ranging from 11 to 26. At the same time the intervals between the free/in^- and boiling points had increased by quantities ranging from 0.45 to 0.9, showing that the expansion coefficient of the glass had been diminished by the prolonged heating. The lack of constancy in the position of the zero point from which temperature is reckoned does not seriously inter- fere with the accuracy of the thermometer as an instrument for the measurement of temperature since, in practice, one proceeds in such a manner as to eliminate errors from this source. When a determination is to be made with a thermometer, the instru- ment is first heated for some time to the temperature which it is afterwards to register, and its zero point then ascertained. Or, what is better, if the heating is a prolonged one, the zero point of the thermometer is determined immediately after the completion of the experiment. A thin column of mercury moving through a glass tube is considerably retarded by capillary resistance ; consequently, at the same temperature, somewhat different readings mav l>e obtained according as the thermometer is observed after a rise or after a fall of the mercury. This effect, known as "stiction," is especially troublesome in thermometers with very fine threads, i be overcome to a great extent by jarring the instrument; hence it is customary before reading a thermometer to tap it sharply with one of the fingers, with a piece of hard wood, or more lightly with a piece of metal. A very satisfactory device for this purpose is a minute electrical hammer constructed like a vibrating bell, which is attached to the upper end of the thermometer and kept in operation while the mercury is moving up or down to its position of rest TILE IJAIIOMETEK AND THE THERMOMETER 43 ~ DETERMINATION OF THE BOILING POINT A metallic vessel constructed on the plan of that represented in Fig. 5 is required. One of the small horizontal tubes serves for the escape of the steam. To the other is attached a glass U-tube partly filled with water to indicate and to measure if necessary any difference in pressure between the steam within the vessel and the external atmosphere. The bulb must be above the water in the vessel and the column of mercury should reach only a very short distance above the cork which holds the thermometer in place. In pre- paring the cork provision is to be made for the pliiH||jT of steam through it along the stem of the thermometer. Boil the water rapidly for ten or fifteen min- utes ; then note the height of the thermometer and any difference in the level of the water in the two limbs of the manometer. Record also the height and the temperature of the barometer. The temperature at which water boils depends, of course, upon the pressure of the air. The next step, therefore, is to correct the observed height of the barometer to the height which it would have at the standard temperature of 0, and to correct the true height of the barometer, in turn, for any differ- ence of pressure indicated by the manometer. The reduction of the barometer reading has already been explained. The amount of fhe second correction is found in the following manner. The temperature of the water in the manometer is ascertained and the density of water at that temperature is found in the appro- priate tables. The product of the difference in the level of the water in the two limbs and the density of the water, as found in the appropriate table, is then divided by the density of mer- cury at 0, Le. by 13.5956. 44 QUANTITATIVE EXERCISES The pressure found could, of course, be further reduced to its value at latitude 45 and sea level ; but this last refinement would hardly be justified in the case of thermometers which can- not be accurately read to within less than 0.05, since the effect of a correction for latitude upon the boiling point of water amounts with a pressure of 760 mm. of mercury only to 0.037 at latitude 30, 0.025 at 35, and 0.013 at 40. The correction for any moderate altitudes is much smaller, amount- ing at an elevation of 500 meters only to 0.0026. Having found the pressure under which the water was boiled, the temperature corresponding to that pressure, i.e. the true boiling point, may be obtained from the tables. The following table gives the boiling points of water at pressures between 740 and 780 mm. of mercury. Boiling Points of Water at Latitude 4$ and Sea Level 740 99.26 750 .... 99.63 760 . . . . 100.00 770 100.37 741 99.30 751 . . . . 99.67 761 . . . . 100.04 771 . . . . 100.40 742 99.33 752 99.71 762 . . . . 100.07 772 . . . . 100.44 743 99.37 753 99.74 763 . . . . 100.11 773 100.47 744 99.41 754 99.78 764 . . . . 100.15 774 . . . . 100.51 745 . . . . 99.45 755 99.82 765 . . .. . 100.18 775 .... 100.55 746 . . . . 99.48 756 99.85 766 . . . . 100.22 776 100.58 747 . . . . 99.52 757 99.89 767 . . . . 100.26 777 100.62 748 . . . . 99.56 758 99.93 768 . . . . 100.29 778 100.65 749 99.59 759 99.96 769 . . . . 100.33 779 100.69 780 . 100.73 Within all ordinary ranges of the barometer a change of 1 mm. in its height affects the boiling point of water 0.0375. THE BAROMETER AND THE THERMOMETER 45 EXERCISE VI CALIBRATION OF THE THERMOMETER There are required : 1. A strip of good mirror glass if the thermometer is a trans- parent one. Otherwise it cannot be used. 2. A strong magnifying glass, or, better still, a small reading telescope which is mounted on, and movable along, a stationary horizontal rod. The first step to be taken is the separation of a thread of mercury of suitable length. If the thermometer to be cali- brated is one of wide range, e.g. from a few degrees below zero to 360, as will probably be the case, a thread spanning from 30 to 50 divisions of the scale will suffice. Invert the thermometer and give it a smart tap against the table top or the palm of the hand. If a thread separates, it will probably be too long or too short. If too long, return the thread nearly to the bottom of the scale and note the position of its lower end. Warm the bulb until the mercury in it rises and joins the thread in the stem, removing the thermometer from the source of heat the moment the junction is established. The cause of the detachment of the thread is a minute bubble of air which is usually located at the point where the stem joins the bulb. If the bulb is subsequently heated, the air bubble is pushed along until the rising mercury joins the thread, when it lodges on the side of the tube and remains attached to the glass in its new position. The next break in the thread will occur at this point. Now cool the bulb until a thread of the right length remains above the place of junction ; then invert and tap as before. A thread of the desired length should sepa- rate. If it does not, the operation is to be repeated until it is successful. If, on the other hand, the thread first detached is too short, proceed as before and continue to warm the bulb until a column 46 QUANTITATIVE EXERCISES of mercury of the right length has risen above the place of junc- tion and then effect the separation in the usual manner. When a thermometer is inverted and struck against a hard object in the manner described, it frequently happens that the air bubble which is expected to cause the detachment of a thread at the junction of the stem and the bulb glides along the wall of the bulb towards its highest part, while the mercury flows out of the bulb and fills the entire stem. In such cases the bubble is to be brought back to the junction of the stem and the bulb. This can be done by returning the thermometer with a quick movement to the upright position and by tapping the -bulb simultaneously against the table. The thread may then be broken off, and shortened or lengthened in the manner described. The detached thread may be brought with great exactness to any desired position under the graduation by inclining the ther- mometer and tapping against the ends, but skill in placing the thread can be acquired only by practice. The correct determination of the position under the scale of the ends of the mercury column is also a matter of some dif- ficulty at first, owing to errors of parallax and to inability to estimate correctly fractions of a division of the graduation. The latter difficulty disappears with practice, but errors of parallax can be avoided only by the employment of suitable means. The best of these is the reading telescope mounted in the manner previously referred to. If this instrument is not to be had, the scale may be observed through a powerful pocket lens which is fixed in a ring supported by three legs. Under such a glass, a line Avhich crosses the optical axis will appear straight, while lines on either side of it will appear to be curved. A weak lens is of little assistance owing to the slightness.of the curvature which it gives to lines not crossing its axis. Finally, if the thermometer is a transparent one, it may be mounted on blocks over a strip of mirror glass. The proper position -for reading will then be found by bringing the eye, the end of the thread, and its image into line. THE BAROMETER AND THE THERMOMETER 47 Having made the best practicable arrangements for the avoid- ance of parallax and for magnifying the scale, and having detached a thread of mercury of the desired length, run the thread nearly down to the bulb and place its lower end exactly opposite the scale division at which it is proposed to begin the calibration. Record the position of both ends, and then run the thread up the stem until its lower end exactly coincides with the previous position of its upper end. Record the new position of the upper end. Proceed hi this way until the thread has passed through as much of the stem as it is desired to calibrate, and then reverse the operation, running the thread down the stem and recording the succeeding positions of its lower end. The readings while returning should not be compared with those recorded while going up until the work is completed. On comparing the two records, the readings at corresponding points should be found to agree very closely ; though they need not and probably will not be identical if one attempts to esti- mate very small fractions of a scale division. If the discord- ance is considerable, it is probably due to the inexperience of the experimenter and the work should be repeated until a satis- factory agreement between the upward and the downward read- ings is obtained. When readings at corresponding points are found to disagree slightly, the mean of all is to be accepted as probably safer than any single, observation. The errors in reading will tend to accumulate in a single direction ; but since one reads in opposite directions, the errors made in going up will neutralize, to a great extent, those made in coming down the stem. The spaces successively filled by the thread of mercury are spaces of equal capacity or volume, and how these are to be employed in the calibration of the stem will be explained by means of the following example of a first calibration by a student. A thermometer graduated in whole degrees and ranging from - 10 to 360 was placed in steam from boiling water for half an 48 QUANTITATIVE EXERCISES hour. Immediately afterwards, its freezing and boiling points were determined and found to be located at 2 and 102 respectively. The height of the barometer corrected was 764.28 mm., which gave for the boiling point of water 100.16. A thread spanning 35 divisions in the lower end of the scale was broken off and manipulated up and down the tube in the prescribed manner. The following readings were obtained. i ii in iv v TT-, DIVISIONS T.--, DIVISIONS MEAN OF FILLED FILLED II AND IV 0.0 0.0 35.0 .... 35.0 35.0 .... 35.0 . 35.0 70.2 .... 35.2 70.4 .... 35.4 35.3 106.0 .... 35.8 106.0 .... 35.6 35.7 142.0 .... 36.0 142.0 .... 36.0 36.0 178.2 .... 36.2 178.4 .... 36.4 36.8 215.1 .... 36.9 215.2 .... 36.8 36.9 251.6 .... 36.5 251.8 .... 36.6 36.6 288.0 .... 36.4 288.0 .... 36.2 36.3 324.8 .... 36.8 324.8 .... 36.8 36.8 The whole number of scale divisions filled by the thread when placed nine times end to end was 324.8, while the average number filled was - - = 36.09. The thread was therefore 7 regarded as containing 36.09 volume or calibration units. The differences between the averages of the corresponding upward and downward readings, and the number of calibration units in the thread, multiplied by 1, 2, 3 ... 9, gave the cor- rections to be added at nine points on the scale in order to convert actual into calibrated readings. THE BAROMETER AND THE THERMOMETER 49 VI VII VIII CALIB. READINGS CORRECTIONS 35.0 36.09 x 1 = 36.09 .......+ 1.09 70.3 36.09 x 2 = 72.18 1.88 106.0 36.09x3 = 108.27 2.27 142.0 36.09 x 4 = 144.36 2.36 178.3 . 36.09 x 5 = 180.45 2.15 215.2 36.09 x 6 = 216.54 1.34 251.7 36.09 x 7 = 252.63 0.93 288.0 36.09x8 = 288.72 ...... 0.72 324.8 36.09 x 9 = 324.80 0.00 The values in column VIII were then used as ordinates to plot on cross-ruled paper a curve of corrections, the thermometer scale serving as the axis of abscissas. It will be seen that the calibrated readings in such a curve are correct at certain fixed points, in this case at nine points on the scale ; further, that it is assumed that any change in caliber between two adjacent fixed points is uniform throughout the whole of the included space. This assumption is usually incor- rect, but the errors resulting from it are not large because they are confined to the particular space in which a reading falls. In other words, errors of this kind do not accumulate from space to space, but cease altogether at the fixed points. In the case of a thermometer of very irregular caliber it may, however, be desirable to increase the number of correct ordinates for the curve, and thus to diminish the error referred to. To do this, the lower end of the thread is placed about halfway between the first two readings and the calibration is repeated . The number of correctly established points will thus be doubled, and by repeating the process, starting each time from some new point on the scale, the number may be increased to any desired extent. In order that a thermometer which has been calibrated in the manner described may be used for the correct determination of temperature, it is necessary to ascertain the temperature equiva- lent of the calibration unit. In the case of the instrument used 50 QUANTITATIVE EXERCISES as an illustration, the correct readings found on the curve for the freezing and boiling points were 2.20 and 104.2 respectively ; i.e. there were 102.0 calibration units included between these two points. But at the time of determining the freezing and boiling points the boiling temperature of water was 100.16; therefore the temperature equivalent of the calibration unit was 10016, Or0 . 98196 o. To ascertain the temperature corresponding to any reading of the thermometer, the difference between it and the zero point, in calibration units, is to be multiplied by the tempera- ture equivalent of the unit. When a thermometer is employed to register a high temperature its zero point should be deter- mined immediately after, rather than before, the experiment. Correction for the Exposed Part of a Mercury Column If a portion of the mercury in the stem of a thermometer is outside of the area whose temperature is sought, the temperature of the exposed part is different from that of the mercury in the bulb. The column is accordingly too short or too long, and requires a correction ; i.e. there must be added to or subtracted from its length the amount which it would be lengthened or shortened if the temperature of the exposed part were raised or lowered to the temperature of the mercury in the bulb. The correction to be applied is (t t') n% in which t is the temperature observed on the thermometer ; t', the mean temperature of the exposed part of the column, determined by placing another thermometer near its middle point ; 7i, the length in calibration units of the exposed part ; and 7, the apparent expansion of mercury in glass, i.e. the differ- ence between the cubical-expansion coefficients of mercury and glass, which is 0.0001818 - 0.000025 or 0.0001568. THE BAROMETER AND THE THERMOMETER 51 Obviously t is not exactly the temperature of the mercury in the bulb. The correction is therefore slightly faulty ; but any desired approximation to the truth may be secured by substitut- ing for t its corrected value and repeating the calculation. The temperature of the exposed part of the mercury column cannot be determined with certainty. It is assumed to have the temperature of the medium immediately surrounding the portion of the stem which it occupies, but a little reflection upon the conditions which determine its temperature will convince one that the assumption is not altogether warranted. It is better, therefore, if practicable, to subject the whole column to the same temperature conditions as the bulb rather than to rely on a correction for an exposed fraction of the mercury. The Comparison of Thermometers When two thermometers "are to be compared, great care must be taken to insure perfectly uniform conditions. They are best compared by placing them in the vapors of boiling liquids. If the comparison is made by immersing them in a liquid, the liquid should be stirred. An air bath is not to be trusted. Thermometers filled with G-as When the ordinary thermometer in which there is a vacuum above the mercury is heated nearly to the boiling point of the metal (357), the column in the stem separates in conse- quence of the formation of vapor. If, on the other hand, the space is filled with a gas under pressure, the boiling point of the mercury is raised and the thermometer will register much higher temperatures. But progress in this direction is limited by the comparatively low temperatures at which most varieties of glass begin to soften. Within recent years, however, a borosilicate glass with high fusing point has been produced in Jena from which thermometers are made and filled with carbon dioxide 52 QUANTITATIVE EXERCISES under a pressure of 17 or 18 atmospheres. These thermometers register temperatures up to 550. The Beckmann Thermometer A thermometer much used in the determination of molecu- lar weights by the freezing- and boiling-point methods is that devised by Beckmann, Fig. 35. In this instrument the bulb is so capacious that the entire scale covers not more than five or six degrees, permitting a graduation of the stem to hundredths, and, in some cases, even to thousandths of a degree. In order now that the thermometer may be used for a considerable variety of temperatures, notwithstanding the narrow range of its gradu- ation, a reservoir is placed in its upper end to which any desired portion of the mercury in the bulb may be transferred. It will be seen that the value of a scale division in such an instrument depends on the amount of the mercury left in the bulb. The manner of using the Beckmann thermometer and of correcting its readings, when a portion of the mercury has been removed from the bulb to the reservoir, will be explained in the chapter on the determination of molecular weights. The Air Thermometer The simplest form of the gas thermometer, Fig. 6, consists of a glass, porcelain, or platinum bulb connected by means of a capillary tube with a U-shaped adjustable column of mercury. Its use for the determination of temperature is based on the experience that, with constant pres- sure, a gas expands very nearly uniformly for equal increments of temperature (^3- part of its volume at for each degree); or, if the volume is con- stant, the pressure increases in the same ratio. In practice the volume is kept constant and the temperature is deduced from the pressure. For the measure- ment of high temperatures the bulb is filled with hydrogen rather THE BAROMETER AND THE THERMOMETER 53 than air because under heavy pressures the former gas obeys the law with greater precision than the latter. Measurements of temperature by the mercury and by the gas thermometer do not perfectly agree except at the experimentally fixed points, the freezing and boiling points of water. The reason for the divergence is to be found in the irregularity of the expansion of both mercury and glass. In the mercury ther- mometer temperatures are measured by the apparent expansion of mercury, and this depends, in turn, on the absolute expansion of both the metal and the glass, which is not perfectly uniform in the case of either material. Moreover, different varieties of glass exhibit different degrees of irregularity in respect to their expansion coefficients ; hence thermometers made from different kinds of glass, though carefully calibrated, will not perfectly agree with one another except at experimentally fixed points. A difficulty of the same character is experienced in connec- tion with the gas thermometer, inasmuch as the expansion of the material of the bulb as well as that of the gas must be taken into account. The former, however, is so minute as compared with the latter that the mere irregularities in the expansion of the bulb have no appreciable effect on the results. Since the expansion of a gas, especially hydrogen, is much more regular than that of either mercury or glass, and since the gas thermometer is but little affected by the irregularities of the expansion of its bulb, the gas rather than the mercury thermome- ter is to be regarded as the standard instrument, and determi- nations of temperature by the latter are to be corrected by adding the ascertained divergences between the two classes of instru- ments. These divergences are sometimes positive and some- times negative in character. They are to be found in tabular form in the Physikalisch-Chemische Tabellen of Landolt and Boernstein. 54 QUANTITATIVE EXERCISES Alcohol and Toluene Thermometers Owing to its low freezing point alcohol has been much used in the preparation of thermometers for temperatures under the solidifying point of mercury. It is, however, an exceed- ingly defective material for the purpose. Its rate of expansion increases very rapidly with rising temperature and is greatly affected by the presence of small quantities of water. The amount of the alcohol which adheres to the wall of the ther- mometer tube increases with falling temperature to such an extent that, at different temperatures, very different quantities of the liquid are employed in the mere wetting of the glass. It is customary, in preparing these instruments, to fix the zero point in the usual way and to locate some second point by com- parison with a standard thermometer. By means of these two fixed points the whole scale is then uniformly graduated. When the alcohol and air thermometers are compared, large discrepancies are found. The divergence increases rapidly with falling temperature, and amounts to about 10 at 100. In some respects toluene is superior to alcohol as a material for low-temperature thermometers. It can be prepared in uni- formly pure condition so that the instruments agree with one another, and its high boiling point (110) makes it practicable to locate experimentally both of the usual fixed points of a thermometer, i.e. the freezing and boiling points of water. Nevertheless, the disagreement with the air thermometer at low temperatures is even greater in the case of the toluene than in that of the alcohol thermometer. Determination of Temperatures by Means of Substances of Known Melting Points It is often necessary in the laboratory, when the circum- stances do not permit the use of a thermometer or a pyrometer, to ascertain within narrow limits the temperature which is THE BAROMETER AND THE THERMOMETER 55 produced by a given heating arrangement, or to know that the highest temperature reached during an experiment lies between two limits. In such cases substances of known fusing points can generally be used with advantage. If it is found, for instance, that the temperature attained under the given con- ditions suffices for the fusion of sodium chloride but not for that of potassium carbonate, then it is known that the highest tem- perature reached is above 776 and below 835. If the former fuses very readily while the latter shows no signs of having been in the least degree softened, it is reasonable to assume that the temperature was about 800. In this connection should be mentioned the so-called " Seger cones." These are triangular truncated pyramids six centimeters in height which are made up of mixtures of silicates of gradu- ally diminishing fusibility. They are much used in the baking of pottery and are often serviceable in the laboratory. The following table gives the number and the melting point of each one of the series of Seger cones. 022 = 590 09 = 970 4 = 1210 16 = 1450 28 = 1690 021 = 620 08= 990 5 = 1230 17 = 1470 29 = 1710 020 = 650 07 = 1010 6 = 1250 18=1490 30 = 1730 019 = 680 06 = 1030 7 = 1270 19 = 1510 31 = 1750 018 = 710 05 = 1050 8 = 1290 20 = 1530 32 = 1770 017 = 740 04 = 1070 9 = 1310 21 =1550 33 = 1790 016 = 770 03 = 1090 10 = 1330 22 = 1570 34 = 1810 015 = 800 02 = 1110 11 = 1350 23=1590 35 = 1830 014 = 830 01 =1130 12 = 1370 24 = 1610 36 = 1850 013 =860 1 = 1150 13 = 1390 25 = 1630 37 =1870 012 = 890 2 = 1170 14 =1410 26 = 1650 38 = 1890 Oil = 920 3 = 1190 15=1430 27 = 1670 39 = 1910 010 = 950 Pyrometers Of the many kinds of pyrometers which have been proposed or employed for the measurement of high temperatures, only two have any special interest for the chemist, the electric-resistance 56 QUANTITATIVE EXERCISES pyrometer and the thermoelectric pyrometer. The former is based on the fact that the electric resistance of metals varies with the temperature. Platinum is the metal employed in its construction. The best known instrument of this type is that of Callender. The thermoelectric pyrometer, on the other hand, utilizes the electro-motive force which is developed when a junction of two different metals or alloys is heated. The best known instrument of the second type is that of Le Chatelier. The metals employed in its construction are platinum and an alloy of platinum with ten per cent of rhodium. The electro- motive force which is developed when the junction of the two wires is heated is measured by means of a sensitive galvanometer. CHAPTER III THE CALIBRATION OF EUDIOMETERS AND THE MEASUREMENT OF GASES EXERCISE VII CALIBRATION OF A EUDIOMETER I. PURIFICATION OF THE MERCURY The apparatus represented in Fig. 7 is required. The large straight tube should have a length of not less than 1^ meters and an internal diameter of 15-20 mm. The vertical distance between the two ends of the doubly bent small tube should be about one-tenth the length of the larger tube. The straight tube which is attached to the stem of the funnel is to be drawn down at the lower end to a minute orifice which will just permit the mercury, when under some pressure, to pass through it in a fine stream. With the receiving vessel on the floor and the clamp- ing stand on the table, fix the apparatus at the side of the table. Pour in more than enough mercury to fill the bent tube at the bottom, and then a dilute solution of ferric chloride (1 : 15 or 20) until the larger tube is nearly full. Remove from the receiver the mercury crowded out of the apparatus by the pressure of the liquid above, and pass the mercury to be cleansed through the funnel into the solution of ferric chloride. The operation is to be repeated until the metal is sufficiently pure for eudiometric purposes, i.e. until, after washing and drying, it shows no disposition to " tail out " when 67 58 QUANTITATIVE EXERCISES running along a clean glass surface. If the solution of ferric chloride becomes green in color, it must be replaced by a fresh one. If it is too concentrated, the mercury shows a disincli- nation to collect at the bottom in a sufficiently liquid form, and the apparatus, especially the small orifice at the lower end of the funnel, becomes clogged. The frequently persistent refusal of finely divided mercury to coalesce is due to a coating of foreign matter which may be either solid or in solution, and the difficulty is to be overcome only by removing the covering which prevents contact between the minute globules. This may sometimes be accomplished by rubbing the material with a pestle or by warming and agitating it with water or hydrochloric acid. But the surest way of accomplishing the object is to force the mercury through finely woven cloth or a piece of chamois skin. Replace the ferric chloride by water and wash the mercury thoroughly, renewing the water as often as may be thought necessary. Dry the mercury by wiping its surface with filter paper and by passing it through filters in which a large number of pin holes have been made. Line a porcelain dish with several sheets of strong filter paper, place the mercury on the upper one, and dry still further at 105 in an air bath under a hood. The drying may be some- what facilitated by placing glass rods or tubes between the paper and the porcelain dish in such a manner as to keep the two quite apart. The advantage of this method of purification over those in which the mercury is simply agitated with the cleansing liquid lies in the very fine subdivision of the metal which is effected at the orifice of the funnel. The purification can take place only at the surface of contact between the two liquids ; hence the desirability of increasing this surface to the greatest possi- ble extent. THE CALIBRATION OF EUDIOMETERS 59 Solutions of other substances which readily attack the impuri- ties, but act only slowly or not at all on the mercury, may be used in the place of the ferric chloride. A supply of dry and sufficiently pure mercury may be main- tained by keeping the metal, when not in use, under strong sulphuric acid to which mercurous sulphate has been added. The foreign metals, excepting silver, gold, and platinum, are converted into sulphates. The apparatus which serves as a reservoir must be of such construction that the mercury may be drawn off at the bottom and returned at the top. Ordina- rily this apparatus consists of a glass globe with a tube and stopcock underneath and a neck for a stopper above. A large separating funnel may be used for the purpose. The neck is closed with a doubly perforated stopper through which are passed a funnel with a stopcock for the introduction of the mercury, and a calcium chloride tube to dry the air entering the apparatus. Distillation in a vacuum for which a variety of automatic stills have been devised is also an excellent method for the purification of mercury. Many of the metals when amalgamated oxidize very easily in contact with the air, giving rise to gray-colored films upon the surface of the mercury. The appearance of such films on mer- cury exposed to the air is, therefore, to be regarded as an evi- dence of impurity, while their absence is a sign of some value of the purity of the metal. The color of the films is due to the admixture of mercury in the metallic condition, and is not, as is often supposed, the result of the formation of gray sub- oxides of the metals attacked. Advantage may be taken of the fact that some metals when dissolved in mercury are easily attacked by free oxygen, to purify mercury by means of the air. For this purpose currents of air are forced through the metal ; or, better, the metal is allowed to fall through the air in fine streams, 60 QUANTITATIVE EXERCISES II. CALIBRATION OF THE EUDIOMETER Select a eudiometer with a millimeter graduation extending over not less than 70 centimeters. Compare the graduation, which is sometimes grossly incorrect, with that of some stand- ard supposed to be reliable, e.g. with that of the barometer. Examine it with a magnifying glass for the minute cracks which are apt to appear where the platinum wires pass through the glass. Fill it with mercury, taking care to dislodge all air bubbles which become entangled between the mercury and the wall of the tube. This may be accomplished with the aid of a long whalebone, or by inclining the tube from time to time while filling and slowly returning it again to the vertical posi- tion. The lodging of air bubbles against the glass may be avoided altogether by filling very slowly and without interrup- tion through a small glass tube which reaches to the bottom of the eudiometer. For this purpose it is necessary to have, placed above the eudiometer, a supply of mercury whose flow through the tube can be properly regulated. Invert the filled eudiometer in a mercury trough having transparent sides. Fix it in a cork-lined clamp, using plumb lines suspended from the ceiling to determine when its position is vertical. If the length of the tube is greater than a barometric height, determine the length of the column in the eudiometer from the level of the mercury in the trough to the top of the meniscus ; also the height of the barometer, using the telescope for both readings. After several hours repeat the readings. If the height of the barometer and that of the columns are unchanged, or if both have risen or fallen alike, the eudiometer does not leak. If, on the other hand, the tube is shorter than a barometric height, the existence of a leak will be detected by the accumulation of air in the top of the tube. Eudiometers into which platinum wires have been fused for the explosion of gas mixtures are often ruined in consequence of the formation especially at the time of an explosion of THE CALIBRATION OF EUDIOMETERS 61 cracks in the glass around the wires. The fact that these can- not be detected by the eye, even when aided by a lens, is never a certain proof of the soundness of the tube. The cause of the difficulty is a slight inequality in the expansion coefficients of glass and platinum. The calibrating cup, Fig. 8, is used for the introduction into the eudiometer of equal volumes of mercury. The capacity of the cup should not, in general, exceed 5 cc. Its edge is ground to a plane making a right angle with its axis. The covering glass is also ground on one side, while the other side is provided with a rubber ring cemented to the glass through which the thumb may be slipped. This arrangement enables the operator to manipulate the cup and its cover with one hand. As a reservoir for the supply of mercury, a separating funnel, or even a burette, may be used. It is necessary only that the delivery tube of the vessel should be of small bore and of sufficient length below the stopcock to reach the bot- tom of the calibrating cup. Bring the cup under the reservoir so that the outlet of the latter rests upon the bottom of the former and slowly fill with mercury, lowering the cup as the filling progresses, but not enough to expose the end of the delivery tube until the cup is full. In this way the lodging of air bubbles between the mercury and the glass will be avoided. Bring the ground glass plate, which is carried on the thumb of the hand holding the cup, vertically down upon the surface of the mercury and gently rub it from side to side to remove superfluous metal. Pour the cupful through a funnel with a long stem of small bore into the eudiometer. It will probably be found that air bubbles have lodged between the glass and mercury, also that minute globules of the metal have attached themselves to the glass for a considerable distance up the tube. The former must be removed and the latter added to the main body of the mercury. Cover the hands with towels or mittens. Incline the eudiometer 62 QUANTITATIVE EXERCISES with the closed end resting on the table and then revolve it to collect the scattered globules. Finally, bring the tube very slowly to the vertical position. The detached globules may also be gathered up and the air bubbles released with the aid of a long piece of whalebone. In this way the danger of warming the tube by handling is avoided. Fix the eudiometer in a vertical position with the aid of the plumb lines and read with the telescope the height of the mer- cury to the top of the meniscus. Continue the filling in of the mercury and the reading of the height of the column after each addition until the tube has been filled to a depth of not less than 400 mm. It is obvious that the temperature of the mercury must remain very nearly constant during the whole of the time occupied in filling the eudiometer. At some time during the calibration two cupfuls of mercury should be poured into weighing glasses and set aside for the purpose of determining the capacity of the calibrating cup. A record of the temperature of the mercury will also be required. The use which is to be made of the readings obtained during the filling of the eudiometer will be illustrated by means of an example. THE CALIBRATION OF EUDIOMETERS 63 1 II III IV V 21 596.4 28.4 28.54 x 21 = 599.34 difference = + 2.94 20 568.0 28.9 " x 20 = 570.80 " =+2.80 19 539.1 28.9 x 19 = 542.26 =+3.25 18 510.2 29.0 x 18 = 513.72 =+3.52 17 481.2 29.1 " x 17 = 485.18 " =+3.98 16 452.1 29.1 " x 16 = 456.64 =+4.54 15 423.0 29.1 x 15 = 428.10 " =+5.10 14 393.9 29.1 x 14 = 399.56 =+5.66 13 364.8 29.3 x 13 = 371.02 =+6.22 12 335.5 29.2 x 12 = 342.48 =+6.98 11 306.3 28.8 x 11 = 313.94 =+7.64 10 277.5 28.4 x 10 = 285.40 '" =+7.90 9 249.1 28.3 x 9 = 256.86 =+7.76 8 220.8 28.5 " x 8 = 228.32 = + 7.52 7 192.3 28.0 x 7 = 199.78 =+7.48 6 164.3 27.9 x 6 = 171.24 =+6.94 5 136.4 27.9 " x 5 = 142.70 =+6.30 4 108.5 27.7 " x 4 = 114.16 =+5.66 3 80.8 27.8 x 3= 85.62 =+4.82 2 53.0 27.5 x 2= 57.08 = + 4.08 1 25.5 x 1= 28.54 =+3.04 In column I the cupfuls of mercury are numbered from 1 to 21 in the order in which they were poured into the tube. Column II gives the successive readings on the graduation of the eudiometer, and column III the difference between each reading and the one which precedes it, i.e. the number of millimeter divisions filled by the various cupfuls. It will be observed that the equal volumes of mercury fill quite different fractions of the tube's length, showing considerable irregularity in the caliber of the eudiometer. The first cupful fills a much smaller number of divisions than any one of the others, but this is owing to the fact that the graduation is not extended to the end of the tube. If 25.5 (the first reading) is subtracted from 596.4 (the last), it is found that twenty cupfuls of mercury fill a space 570.9 mm. in length. The average length of tube filled by a cupful is 64 QUANTITATIVE EXERCISES therefore ^ , or 28.54 mm. For this reason it was decided to regard the cup as containing 28.54 volume or calibration units. It is obvious that the capacity of the tube, from the closed end to the various points reached by the different cup- fuls of mercury, can be found, in terms of the calibration unit, by multiplying 28.54 by the number of cupfuls which fill the tube to these points. This has been done for each cupful under IV. Column V contains the quantities which must be added to the actual readings in order to obtain their equivalents in calibration units. To obtain the value of other readings than those recorded in column II, a curve is employed. To con- struct this, the millimeter graduation on the tube is made the axis of abscissas, and the quantities to be added to the actual readings, i.e. those recorded under V, the ordinates. The curve is completed by drawing straight lines between the adjacent points thus established. It will be seen that in this case, as in the calibration of the thermometer by a similar method, only a limited number of points in the curve are established with cer- tainty. The assumption that all other points in the curve lie in the straight lines joining these in other words, that the change in the caliber of the tube is always uniform between two successive established points is not any more correct in the case of a eudiometer than in that of a thermometer. In the calibration of a thermometer, as already shown, the number of correctly established points in the curve can be multiplied to any desired extent without diminishing the length of the thread. In the case of a eudiometer, on the contrary, the size of the cupful the equivalent of the thread must be dimin- ished if a closer calibration is required. The curve should be plotted upon cross-ruled paper with lines one millimeter or one-tenth of an inch apart, in such a manner that each space on the horizontal lines represents a mil- limeter division of the graduation on the tube, and each space on the vertical lines, one-tenth of a unit of the correction to THE CALIBRATION OF EUDIOMETERS 65 be made. It is advisable, in order to keep the curve of the cor- rections near the line representing the eudiometer, to indicate the addition of whole numbers, and to employ the curve only for the fractional parts. The following is the usual, though less satisfactory, method of elaborating the calibration data. It will be seen that the second cupful of mercury which was poured into the tube occu- pied a space 27.5 mm. in length. If now 28.54 the number of calibration units in the cup is divided by this number, there will be obtained, in terms of the calibration unit, the average value of a millimeter division between the first and second readings. The value of the millimeter spaces in all other parts of the tube may be obtained in the same way. The results of twenty such divisions are given under VI. VI V.R. COB. V. V.R. COB. V. 21 1.0049 26 29.06 46 49.81 20 0.9875 27 30.10 47 50.85 19 0.9875 28 31.13 48 51.89 18 0.9841 29 32.17 49 52.93 17 0.9808 30 33.21 50 53.97 16 0.9808 31 34.25 51 55.00 15 0.9808 32 35.29 52 56.04 14 0.9808 33 36.32 53 57.08 13 0.9741 34 37.36 54 58.11 12 0.9774 35 38.40 55 59.13 11 0.9910 36 39.44 56 60.16 10 1.0049 37 40.47 57 61.19 9 1.0085 38 41.51 58 62.21 8 1.0014 39 42.55 59 63.24 7 1.0193 40 43.59 60 64.27 6 1.0229 41 44.63 etc. etc. 5 1.0229 42 45.66 4 1.0303 43 46.70 3 1.0266 44 47.74 2 1.0378 45 48.78 60 QUANTITATIVE EXERCISES The volume capacity of the tube to 25.5, the first reading, is 28.54 calibration units, and if there is added to this 0.5189, one half the value of the millimeter spaces in that part of the tube, the corrected volume to the twenty-sixth division of the scale will be obtained, i.e. 29.06. The volume to the twenty- seventh, and the volumes to the succeeding divisions as far as the fifty-third, are found by adding the number 1.0378. From the fifty-third to the eighty-first division the number 1.0266 is to be added, etc. The usual form of tabulation is shown under V.R. and Cor. V., which signify volume read and correct volume respectively. It will be found, on contrasting the two methods of dealing with the calibration data, that the first is less laborious and more correct than the second. It also presents the results in' a form which is more convenient for use. The first assumes that any change in the caliber of the tube, within the space filled by a cupful of mercury, is gradual from reading to reading ; while the second supposes the caliber of the tube to be uniform between two successive readings, i.e. that changes of caliber occur only where one cupful ends and another begins. The latter assumption is obviously more erroneous than the former. The corrections for the fractional parts of the readings must be found by calculation when the second method is employed, while the curve enables one to estimate them to the second decimal place by the eye. It will be seen that neither method provides for the measure- ment of a gas volume smaller than the cup itself. If it is desired to find the volumes of smaller quantities of gas, a smaller calibrating cup must be used. III. DETERMINATION OF THE VALUE OF THE MENISCUS A correction for the meniscus is to be applied to any volume of gas measured over a liquid. If the liquid is mercury, the meniscus is convex and the correction is to be added; if it is THE CALIBRATION OF EUDIOMETERS 67 water or an aqueous solution, the meniscus is concave and the correction is to be subtracted. Suppose, when the mercury is poured into the eudiometer for calibration purposes, that the first cupful gives a reading of 20 mm., as shown in Fig. 9. Then imagine the tube to be inverted and to contain enough gas collected over mercury to give the same reading, as shown in Fig. 10. It is evident, not- withstanding the fact that the readings are identical, that the volume of the gas in the second case is greater than that of the mercury in the first by the space aa\ and that whenever FIG. 9 FIG. 10 FIG. 11 any quantity of gas is measured, it will be necessary to add this space to its apparent volume in calibration units. This is known as the correction for the double meniscus, and the magnitude of the correction is now to be determined. Fix the eudiometer in a vertical position and partially fill it with mercury. Read on the graduation of the tube, with the telescope, the highest point in the meniscus. Pour over the top of the mercury a few drops of a dilute solution of mercuric chloride. In a few moments the end of the mercury column will lose its convex form and become horizontal. Read again. The difference between the two readings is the correction for the 68 QUANTITATIVE EXERCISES single meniscus, and twice this is the quantity always to be added to a gas volume measured in the tube. The correction value of the meniscus varies with the diame- ter of the tube and the nature of the liquid. The following table gives the amount of the correction, as determined by Bunsen, for tubes of various diameters. DIAMETER OF TUBE WATER 7 PER CENT Na OH MERCURY 14 mm. 1.10 mm. 0.70 mm. 0.57 mm. 15 1.03 0.63 0.53 16 0.97 0.57 0.48 17 0.91 0.51 0.44 18 0.87 0.47 0.38 19 0.84 0.44 0.32 20 0.82 0.42 0.26 21 0.80 0.40 0.20 IV. DETERMINATION OF THE VOLUME OF THE CALIBRATION UNIT For most gas analytical purposes an arbitrary unit of volume, like the calibration unit, is sufficient ; but it frequently happens that a knowledge of the volume of a gas in cubic centimeters is required. It is therefore desirable in every case to determine the value of the calibration unit in terms of the cubic centi- meter. To do this, weigh the two cupfuls of mercury which were set aside while calibrating the tube, and correct half the sum of the two weights for displacement of air. The volume of the calibration unit will then be found by substituting the value of #, , and V in the following equation : 1 + 0.0001818 t C=ff ~ 13.5956 V ' mwhlch c is the value to be found ; g is the weight of mercury ; 0.0001818 is the mean expansion coefficient of mercury between and 30; THE CALIBRATION OF EUDIOMETERS 69 t is the temperature of the mercury when measured off; 13.5956, the weight of one cubic centimeter of mercury at ; and F, the number of calibration units in the cup. Measurement of Gases over Water We have now to consider under what restrictions a tube which has been calibrated with mercury may be used for the measurement of gases over water or other liquids than mercury. If a quantity of gas is introduced into a eudiometer filled with water, there are two conditions affecting its measurement which require attention : first, the water, in descending to make room for the gas, leaves a film upon the glass, thereby diminishing the capacity of the tube ; second, the meniscus differs both in character and value from that of mercury. There are various ways of ascertaining the amount of the correction to be made for the film, but as this error is small as compared with others which are encountered when gases are measured over any liquid except mercury, the correction is rarely attempted. When a gas is collected over water in a tube which has been calibrated with mercury the correction for the meniscus is nega- tive, and amounts to the difference between the water and the mercury meniscus. Suppose, Fig. 11, in calibrating a tube, that the first cupful had filled to the twentieth division on the grad- uation, and that afterwards a quantity of gas giving the same reading had been collected over water. The mercury meniscus is represented by the line a a a, and that of the water by b a b. The volume of the mercury is known, it having been determined in the course of the calibration ; but the volume of the gas over water is less than that of the mercury by the space cc, which is equal to the difference between a water and a mercury meniscus. 70 QUANTITATIVE EXERCISES The Absorption of Gases by Liquids It is often convenient and sometimes necessary to collect and measure gases over other liquids than mercury. But it should be borne in mind that the absorption and diffusion of gases are serious obstacles in the way of employing such liquids when the work in hand demands a high degree of accuracy; and one must consider in situations where convenience would be pro- moted by the use of another liquid than mercury whether or not the resulting unavoidable errors will be of tolerable magnitude. A brief recapitulation of some of the more important facts relat- ing to the absorption of gases by liquids may be useful in this connection. 1. The absorption coefficient of a gas with respect to any par- ticular liquid is the volume of the gas, measured under standard conditions of temperature and pressure, which a unit volume of the liquid will absorb when exposed in an atmosphere of the pure gas. 2. The Effect of Temperature. The power of liquids to retain gases decreases with rising temperature, hence changes in tem- perature are followed by changes in absorption coefficients ; but the law which regulates the relation of absorption coefficients to temperature is not known. 3. The Effect of Pressure. The volume of a gas which a unit volume of a liquid will absorb is independent of the pressure. This is known as Henry's Law. But, since the amount of mat- ter in a given volume of gas is proportional to the pressure, the absorption coefficients are, according to the definition, also pro- portional to the pressure. It will be seen that the term absorp- tion coefficient is fully defined only when accompanied by a statement of both temperature and pressure. 4. Absorption from a Mixture of Gases. From a mixture of gases each constituent will be absorbed according to its partial pressure, i.e. according to the proportion of the total pressure which is due to its presence. Stated in another way, each constituent will be absorbed to the same extent that it would be THE CALIBRATION OF EUDIOMETERS 71 if, without changing the volume, all the other components of the mixture were removed. This is known as Dalton's Law of Par- tial Pressures. Its application to specific cases will be made clearer by an illustration. At and under a pressure equal to 760 mm. of mercury the absorption coefficients of nitrogen and oxygen are 0.02035 and 0.04114 respectively; that is, under the given conditions, a liter of water would absorb 20.35 cc. of gas in an atmosphere of pure nitrogen and 41.14 cc. in an atmosphere of pure oxygen. But suppose the liter of water is exposed under the same conditions of temperature and pressure to the air, which is a mixture of four volumes of nitro- gen with one of oxygen. According to the law of partial pres- sures the water will absorb | of 0.02035 of nitrogen and | of 0.04114 of oxygen; that is, after saturation, it will be found to contain 16.28 cc. of nitrogen and 8.23 cc. of oxygen. The embarrassing effects of absorption phenomena upon gas analytical operations when other liquids than mercury are used are quite obvious ; nevertheless it may not be superfluous to call attention to a few of them. Suppose a mixture of gases is required, for any purpose, to pass through a liquid. The liquid will become saturated with the various constituents of the mixture in accordance with the absorption coefficient of each and the law of partial pressures. The consequence is that for a time the gas which passes out of the liquid will differ in composition from that which entered. The alteration in the composition of the gas will cease, of course, when the liquid has become fully saturated. For the same reason, a mixture of gases standing over a liquid will suffer a change in composition unless the liquid is previously saturated with a mixture of identical composition. The prac- tice of first saturating a liquid with the same kind of gas that is afterwards to be passed through it, or collected over it, is very common in gas analysis but is not without its disadvantages. A simple example will illustrate this. Suppose a gas containing #, >, and c has been collected over water previously saturated 72 QUANTITATIVE EXERCISES with some of the same kind of gas, and is to be analyzed by removing the various constituents in turn by means of appro- priate absorbents and measuring the contraction which takes place after each withdrawal. If other gases, e.g. air, are kept out of the water, and changes of temperature do not bring about a change in the relative magnitudes of the absorption coeffi- cients of the different components, the gas would maintain its composition indefinitely. But suppose one of the constituents, e.g. a, is removed. The water will then be supersaturated as far as a is concerned, and probably undersaturated as regards b and c\ consequently a small portion of b and c will enter the water while the residue becomes contaminated with a. Another difficulty which is encountered when other liquids than mercury are employed for the isolation of gases is the fact that two gases cannot be permanently separated by a liquid which is capable of gas absorption. The usual source of trouble in this connection is the air. Suppose, by way of illustration, that a body of hydrogen is standing in a eudiometer over water which, as usual, is also in contact with air. From the one side the water will saturate itself with hydrogen, and from the other with the oxygen and nitrogen of the air ; and the law of partial pressures will require the hydrogen to pass out of the water into the atmosphere, while the constituents of the air, for the same reason, enter the space occupied by the hydrogen. Theo- retically this exchange would continue until the two gases became identical in composition; but since the volume of the air is infinitely greater than that of the hydrogen, the final result would be a complete replacement of the latter by the former. The facts cited above will suffice, it is hoped, to impress upon the student the need of great circumspection in dealing with gases. In this field, as in all other kinds of quantitative work, when a given course of procedure suggests itself or is recom- mended, one should first of all, and as a matter of habit, scruti- nize the sources of error and consider the means by which they may be avoided or minimized. THE CALIBRATION OF EUDIOMETERS 73 The Correction of G-as Volumes for Pressure, Temperature, and Water Vapor The space which any given mass of gas will occupy depends on the pressure to which it is subjected, its temperature, and the amount of water vapor which it contains. Hence, for the purpose of comparing gases with respect to mass, it is necessary to reduce the observed volumes to those which the gases would have if measured under the same conditions. I. The Correction for Pressure When a given mass of gas is measured under different pres- sures, without change of temperature, its various volumes are found to be inversely proportional to the pressures. That is, if the pressure is doubled, the volume will be halved; or if the pressure is halved, the volume will be doubled, etc. Stated in another way, the product of the pressure and the volume is a constant. This relation of the volume of a gas to the pressure upon it is known as Boyle's law also as the law of Mariotte. Gases which cannot be condensed to liquids except at very low temperatures like hydrogen, oxygen, nitrogen, carbon monox- ide, and methane obey the law within ordinary ranges of pressure but deviate from it more or less under high pressures. Gases easily condensed to liquids, likewise the vapors of liquids, do not conform to the law until heated considerably above their temperatures of liquefaction. If a gas is confined over a column of liquid which is, in turn, in free communication with the air, the pressure of the gas and that of the column of liquid are together equal to the pressure of the air. Hence, in order to find the pressure of the gas, we must subtract the pressure of the column of liquid from the height of the barometer. If the liquid employed to isolate the gas is mercury, the difference between its height, corrected to 0, and that of the barometer, also corrected, is the value 74 QUANTITATIVE EXERCISES required. But when another liquid is used the length of an equivalent column of mercury must first be found. To do this, the height of the column is multiplied by the specific gravity of the liquid and the product divided by 13.596, the density of mercury at 0. If the liquid is water, the specific .gravity corresponding to its temperature will be found in any collection of chemical tables ; otherwise it will probably have to be determined. The commonly accepted standard for pressure is that which at will support a column of mercury 760 mm. in height, and all gases measured under other pressures are corrected to the volumes which they would have under this. The formula for the correction is F/= F, is the volume under standard pressure, F the observed volume, and h the pressure with all necessary corrections applied under which the gas was measured. Ordinarily h is simply the difference between the height of the barometer and that of the mercury column over which the gas was measured both corrected for temperature; but in more refined work, such as the determination of atomic weights and the densities of gases, a correction for latitude and altitude is also to be made. This is to be applied, of course, not to the barometer and the column separately, but only to the difference between them, i.e. to h. II. The Correction for Temperature If the temperature of a gas is raised, without change of pres- sure, from to 100, its initial and final volumes are related to each other as 1 to 1.367. For each increase in temperature of one degree, the expansion amounts to 0.00367, 7^0 ^ ^ s volume Till; CALIBRATION OF EUDIOMETERS 75 at 0. This law was discovered simultaneously by Gay-Lussac and Dalton. The standard temperature for the measurement of gases is 0, and the formula for finding what volume any gas, measured at a higher temperature, would have at the standard temperature is jr , in which 1 + 0.00367* V is the observed volume, t the temperature of the gas at the time of measurement, and 0.00367 the expansion coefficient of gases. If the temperature at the time of measurement is below 0, the formula becomes 1-0.00367** The formula for finding the volume of gases under standard conditions, both of temperature and pressure, is 0.00367* 760* III. The Correction for Water Vapor Gases are measured either dry or fully saturated with water vapor usually in the latter condition. The correction of the volume of a saturated gas for the water vapor which it contains is effected by subtracting the known tension or pressure of the vapor expressed in millimeters of mercury from A, the pres- sure under which the gas was measured. The complete formula for the reduction of observed gas vol- umes to standard conditions of temperature, pressure, and dry ness is V h tension of water vapor 1 + 0.00367* > 760 A gas standing over water for any length of time necessarily becomes saturated with vapor. The same is true of a gas which 76 QUANTITATIVE EXERCISES is passed through water, but it is to be remembered with refer- ence to the latter method of effecting saturation that if the tem- perature of the gas should afterwards rise, more water will be required. When a gas is collected over mercury, the water necessary for its saturation may be provided by moistening the inner wall of the containing vessel before filling with mercury, or by introducing afterwards a small drop of water. It is also to be remembered that the tension of water vapor over an aqueous solution is, at a given temperature, always less than over pure water. It is therefore necessary as a rule, since the vapor tension of but few solutions is known, finally to measure a gas over water or mercury, or in the dry condition over a liquid which, like concentrated sulphuric acid, has prac- tically no vapor tension of any kind. The student should practice the reduction of gas volumes, applying all possible corrections, until he is thoroughly familiar with the principles on which these corrections are based, and until he has acquired some facility in computations of this kind. Afterwards tables which have been prepared to lighten the labor of such calculations may be resorted to. All required tables will be found in the collection of Landolt and Boern- stein. Those most frequently used in connection with gaso- metric work are : Corrections of the barometer for temperature, for latitude, and for altitude. Corrections for meniscus in tubes of different diameters. Reduction of water pressure to mercury pressure. Values of . Values of 1 + 0.00367 t. Tension of aqueous vapor over water and certain solutions. The weights of unit volumes of gases. Absorption coefficients of gases in liquids. THE CALIBRATION OF EUDIOMETERS 77 The Passage of G-ases through Rubber * It is important for the student to know that rubber, which in the form of tubing is constantly used in the laboratory to con- nect the different parts of apparatus and to direct the flow of gases, is permeable to gases including water vapor and to some of them to a high degree. The passage of gases through rubber does not obey the law of diffusion which requires that the rates of diffusion shall be inversely proportional to the square roots of the densities of the gases. This will appear from the following table which gives the relative volumes of some of the commoner gases which will pass through a rubber septum in a unit of time. GAS KATE OF DIFFUSION SQUARE ROOT OF DENSITY Nitrogen 1.000 3.7416 Carbonic oxide . . .-. 1.113 3.7416 Atmospheric air ... 1.149 3.7947 Marsh gas 2.148 2.8284 Oxygen 2.556 4.0000 Hydrogen 5.500 1.0000 Carbon dioxide .... 13.585 4.5825 According to the law of gaseous diffusion, carbon dioxide should pass through a septum only 0.22 as rapidly as hydrogen, while its actual rate of passage through rubber is 13.585 times as rapid as that of nitrogen and 2.47 times as rapid as that of hydrogen. In other words, carbon dioxide penetrates rubber 16.6 times too rapidly when compared with nitrogen and 11.23 times too rapidly when compared with hydrogen. Sulphur dioxide exhibits this power of penetrating rubber to an even more remarkable degree than carbonic anhydride. The disa- greeable odor of rubber tubes through which illuminating gas is passing and the well-known fact that the gas in passing * The student should read Thomas Graham, " On the Absorption and Dialytic Separation of Gases by Colloid Septa," Philosophical Transactions, 1866, p. 399; or Researches of Thomas Graham, p. 235. 78 QUANTITATIVE EXERCISES through such tubes suffers a notable loss in illuminating power are familiar proofs of the readiness with which rubber is pene- trated by gases. Equality of gaseous pressure upon the two sides does not prevent the passage of gases through an intervening wall of rubber; hence gases conducted through rubber tubing or in contact with rubber connections or stoppers must, in general, suffer some change in composition. The important practical rule to be deduced from the foregoing statements is that, in dealing with gases, rubber connections and 'rubber stoppers are to be avoided wherever it is practicable to dispense with them. If the parts of an apparatus must be connected by means of rubber, the ends to be joined should be accurately fitted to each other and brought close together in the connection. Again, if a gas is to be transported for a considerable distance, glass tubes, with a minimum of rubber connections, should be em- ployed. The common practice of using long stretches of rubber tubing for this purpose is a sure evidence either of ignorance or of a certain lack of aptitude for good experimental work. Figures 12 and 13 exhibit arrangements which may FIG 12 ften ke use d with advantage to prevent diffusion of gases through rubber connections. The outer or " jacket " tubes are filled with mercury. Such protection, how- ever, does not wholly remove the objection to the use of rubber connections, since rubber is capable of ab- sorbing and retaining considerable volumes of certain gases. This is especially true of = oxygen, carbon dioxide, sulphur dioxide, and some of the hydrocarbons. Rubber connecting tubes should usually be tied, especially when the gaseous pressure upon the inner and outer walls is unequal. The best material for such ligatures is waxed shoe- maker's thread so-called " waxed end." CHAPTER IV CALIBRATION AND GRADUATION OF APPARATUS FOR THE MEASUREMENT OF LIQUIDS EXERCISE VIII I. DETERMINATION OF THE CAPACITY OF A MEASURING FLASK BY WEIGHING WATER If a large and sufficiently accurate balance is at the disposal of the student, a liter flask should be employed in this exercise, otherwise a smaller one may be selected. Place near the balance, several hours before it is required for use, a sufficient quantity of distilled water. The containing vessel should be closed, since the temperature of evaporating water is usually somewhat below that of the surrounding atmosphere. Put upon the left-hand pan of the balance a weight a beaker containing shot will suffice which is heavier than both the flask and the water to be weighed. Suspend the closed flask from the right-hand stirrup by means of a platinum wire and add weights to the pan underneath until equilibrium is obtained, or until the deficit or excess of weight can be deduced from the sensibility of the balance. Take the temperature of the water and that of the air in the vicinity. If both are the same, fill the flask nearly to the mark on the neck through a funnel with a long stem, or one whose stem has been extended by attaching to it a small glass tube, taking care not to wet the glass above the mark. Remove the funnel and continue the filling with a glass tube one end of which is drawn out to a fine point until the bottom of the 79 80 QUANTITATIVE EXERCISES meniscus is on a level with the mark. If, in spite of precau- tions, the neck above the mark has been wet, the water must be removed. This is best done by means of a strip of filter paper rolled into the form of a small cylinder. Place the filled flask (closed) on the pan and add weights to equilibrium. The difference between the weights added when the flask was empty and afterwards when it was filled is the apparent weight of the water, i.e. its weight without correc- tion for air displacement. Find its weight in a vacuum. Divide the corrected weight of the water by its density. This will give its volume in cubic centimeters and the capacity of the flask at the temperature at the time of weighing. Find the capacity of the flask at 4, 15, 17.5, and 20, using 0.000025 as the cubical expansion coefficient of glass. The following table gives the density of water the weight of one cubic centimeter and the volume of one gram of water (corrected weight) between and 25. Density and Volume of Water between and 25 TEMPER- ATURE DEKSITY VOLUME cc. TEMPER- ATURE DENSITY VOLUME cc. 0.999878 1.000122 13 0.999430 1.000570 1 0.999933 1.000067 14 0.999297 1.000703 2 0.999972 1.000028 15 0.999154 1.000847 ~3 0.999993 1.000007 16 0.999004 1.000997 4 1.000000 1.000000 17 0.998839 1.001162 5 0.999992 1.000008 18 0.998663 1.001339 6 0.999969 1.000031 19 0.998475 1.001527 7 0.999933 1.000067 20 0.998272 1.001731 8 0.999882 1.000118 21 0.998065 1.001939 9 0.999819 1-000181 22 0.997849 1.002156 10 0.999739 1.000261 23 0.997623 1.002389 11 0.999650 1.000350 24 0.997386 1.002621 12 0.999544 1.000456 25 0.997140 1.002868 APPARATUS FOR MEASUREMENT OF LIQUIDS 81 II. THE GRADUATION OF A MEASURING FLASK Warm one side of a piece of paraffin or beeswax and with it rub the neck of the flask to be graduated ; then warm the neck over a flame and turn the flask until the molten wax distributes itself uniformly over the glass in a film thin enough to be mod- erately translucent when cold. The second step is to ascertain how much water of the tem- perature of the balance room must be weighed into the flask in order that the flask may have the desired capacity, below the mark, at some standard temperature which, of course, should be the prevailing temperature of the laboratory. We will suppose that the temperature of the balance room and of the water is 18, while the flask is to be graduated to hold a liter at 20, the latter being the usual temperature of the laboratory. If the capacity of a flask at 20 is 1000 cc., its capacity at any lower temperature will be AAAAOC ' At 18 it will be 1 + 0.000025 t 1.000050, or 999.95 cc. The volume of a gram of water at 18 (see table) is 1.001339 cc. ; the weight of water to be introduced into the 999 95 flask is, therefore, ' , or 998.613 grams. This, however, 1.001339 is weight in a vacuum. To find the weight of the water in the air, we must deduct the weight of 999.95 cc. of air, less the weight of the air displaced by the brass weights. The volume 998 613 of the weights is ' , or 118.88 cc. ; and the volume of the air whose weight is to be deducted is 999.95 118.88, or 881.07 cc. The average weight of a cubic centimeter of air is 1.2 milligrams; 881.07 X 0.0012, or 1.057 grams, is therefore the weight to be deducted. That is, in order that the flask may have a capacity of one liter at 20, there must be weighed into it at 18 998.613 - 1.057, or 997.556 grams of water. 82 QUANTITATIVE EXERCISES The general formula for finding the weight in the air of an object whose weight in a vacuum is known is W , in which JFis the weight in a vacuum, d the density of the object, and d, the density of the weights. Having ascertained the weight of water required and having weighed the flask, fill in through a funnel having a long stem until the water reaches the neck and then weigh. Calculate approximately what volume of water remains to be introduced and add very nearly the required amount from a graduated pipette. Weigh again, remove weights equal to the weight of the water still to be introduced, and then add water from a small glass tube with a fine delivering end until equilibrium is obtained. In view of the volume of water required to make an appreciable change in the level of the meniscus, it is probably useless, in graduating a measuring flask, to attempt to weigh the water accurately to within less than 10 milligrams, since this weight of water would have a volume of only about 0.01 cc. With a sharp-pointed piece of steel, e.g. a round file ground to a sharp point, scratch a number of short horizontal lines in the wax on a level with the bottom of the water meniscus. Continue the line entirely around the neck and etch it into the glass with hydrofluoric acid. In some laboratories there is in use a simple adjustable arrangement which holds the steel point in the proper position against the paraffined neck while the flask is revolved. Lines cut in this way are usually more satis- factory than those produced in the manner described above. APPARATUS FOR MEASUREMENT OF LIQUIDS 83 III. THE CALIBRATION OF BURETTES BY MEANS OF MERCURY A burette may be calibrated with mercury in much the same manner as a eudiometer; but, since these instruments are used mainly for the measurement of liquids which leave a film upon the glass, and hence deliver less than their full capacity, the volume of the film must be determined and applied as a correc- tion to the results obtained by the mercury. The method is sufficiently accurate, but so cumbersome that it is not often resorted to. The exercise may therefore be omitted. Never- theless the student should construct for himself a complete working plan for such a calibration. The System of Mohr Owing to the somewhat laborious corrections which are ren- dered necessary by a strict adherence to the liter as the unit of volume, Mohr proposed to regard as the standard for liquid- volumetric work the space occupied by a kilogram of water when the same is weighed in the air with brass weights at a temperature of 17.5. The advantages claimed by the author for his system are : 1. The correctness of graduated apparatus is easily tested. 2. The measuring apparatus can be used without correction at a temperature easily secured and maintained for the determination of the specific gravities of liquids. The system of Mohr obtained a wide currency in several countries, though modified here and there by the substitution of other temperatures, e.g. 15 for the standard 17.5 of its author. Of late, however, the system has rapidly lost ground and it is doubtless destined to disappear altogether in the near future. The following table gives for several temperatures the cor- rected weight and the volume of the water which in the air will balance a thousand grams of brass of specific gravity 8.4, i.e. a kilogram brass weight. 84 QUANTITATIVE EXERCISES TEMPEBATURE COBKECT WEIGHT VOLUME 1001.0573 gr. 1001.1851 cc. 4 1001.0511 1001.0571 10 1001.0575 1001.3218 12.5 1001.0578 1001.5811 15 1001.0582 1001.9168 17.5 1001.0587 1002.3301 20 1001.0592 1002.8122 22.5 1001.0599 1003.3626 25 1001.0606 1003.9742 27.5 1001.0614 1004.6505 30 1001.0623 1005.3804 It will be seen that the strictest adherence to a fixed temper- ature is necessary in order that a volume unit like that proposed by Mohr may have real value as a working standard. But the temperature recommended by the author of the system, 17.5, has not been adhered to in the graduation of apparatus ; neither has any other particular standard temperature been adopted by common consent. This divergence due apparently to the lack of uniformity among the different laboratories in respect to what may be called prevailing temperature has resulted in much confusion and, consequently, in a lack of precision in volu- metric work. More unfortunate still has been the confusion of mind and the errors in practice due to the custom of calling the Mohr volume unit a liter and its submultiples cubic centimeters. It may be asserted with considerable confidence that the intro- duction of the Mohr system is largely responsible for the wide- spread impression that the volumetric system of analysis is necessarily less accurate than the gravimetric, and that it is therefore suited only to work of a rough kind. A sufficient explanation of the origin of this mistaken judgment appears when one finds in use side by side and uncalibrated, as he often may, apparatus which has been graduated according to the Mohr system for 17.5 and for 15, and also according to the true liter. APPARATUS FOR MEASUREMENT OF LIQUIDS 85 EXERCISE IX THE CALIBRATION AND GRADUATION OF MEASURING FLASKS AND THE CALIBRATION OF BURETTES * With the aid of the apparatus which is explained below, the student should calibrate and regraduate if they are found to be incorrect the fol- lowing flasks : 1 1., J 1., and ^ 1. He should also calibrate not less three burettes. than .200 The apparatus repre- sented in Fig. 14 is employed both for the graduation and the cali- bration of half-liter and liter measuring flasks. The delivering capacity of the bulb between the mark on the upper stem and the zero mark on the lower one must not exceed 500 cc. at the highest temperature at which the instrument is to be used; while the combined delivering capacity of the bulb and the graduated portion of the lower stem must not be less than half a liter at 0. The lower stem is graduated in millimeter divisions which are numbered in both directions in order that the instrument may be used in the in- verted position if desired, FIG. 15 86 QUANTITATIVE EXERCISES For the purpose of explaining the method of preparing an instrument of this kind for use, an account of an actual calibra- tion will be given. The water delivered by the bulb and also that delivered by the graduated portion of the lower stem was weighed and its temperature noted. The delivering capacity of the bulb and of the stem was then calculated by the formula V=P^ in which a P is the weight of the water when weighed in the air with brass weights (497.769 grams for the bulb and 3.0708 grams for the stem), p is the weight in a vacuum of one gram of water weighed in the air with brass weights (1.001059 grams at ordinary tempera- tures), and d is the density of the water at the temperature of weighing (21.4). In this way the delivering capacity of the bulb at 21.4 was found to be 499.324 cc., and that of the stem at the same tem- perature 3.081 cc. The delivering capacity of the bulb at 0, 4, 10, 12.5, 15, 17.5, 20, 22.5, 25, 27.5, and 30 was calculated by the formula * V, = V (1 + 7 (t, - *)), in which 7 is the cubical expansion coefficient of glass (0.000025), t f is the temperature 0, 4, or 10, etc., and t is the temperature of the water at the time of weighing. The results of these calculations are given in the second column of the table which follows. No corresponding calcula- tion was made for the stem because the change in its capacity between and 30 amounts to less than 0.0025 cc. The inequalities of its bore were also found to be insignificant. Each millimeter division of the stem was therefore regarded as having a delivering capacity of 0.03081 cc. at all temperatures between and 30, APPARATUS FOR MEASUREMENT OF LIQUIDS 87 The instrument was then ready for rinding the capacity of any graduated half-liter or liter flask at any of the temperatures mentioned above. For this purpose a small glass tube drawn out and curved at one end, and long enough to reach the mark on the neck of the measuring flask, is attached to the delivering tube of the three-way stopcock, while the other tube of the stop- cock is connected with a supply of water situated somewhat higher than the pipette. Water is allowed to flow in and fill the whole apparatus including the delivery tube below the stopcock to the mark on the upper stem. The flask whose capacity it is desired to find is filled to the mark from the pipette. If the quantity delivered from the stem is added to any number in the second column of the table, we shall obtain the capacity of the flask at the corresponding temperature in the first column. This is true of a half-liter flask ; in the case of a liter flask the pipette must be twice filled, and the volume delivered by the stem is, of course, to be added to twice the numbers in the second column. Since the pipette and the flask are of the same material, and therefore expand and contract alike for equal changes of tem- perature, the temperature of the water at the time of the experi- ment need not be known. The next step was to find to what points on the graduated stem the water must be drawn in order to graduate a half-liter flask for each of the temperatures included in the first column. This was done by dividing the difference between 500 and the several numbers in the second column by 0.03081, the deliver- ing capacity of one division of the stem. The results are given in the third column. To graduate a half-liter flask for any of the temperatures in the first column, it is necessary only to empty into it the bulb and then the corresponding number of stem divisions indicated in the third column. If it is desired to have the flask correct at 0, 30.9 stem divisions will be added; at 4, 29.3 divisions, etc. Here again the result is correct whatever may be the temperature of the water at the 88 QUANTITATIVE EXERCISES time of the experiment. To graduate a liter flask, the bulb twice full and twice the indicated number of stem divisions must be added. To prepare the instrument for use in the graduation and veri- fication of apparatus when the so-called Mohr system is to be employed (i.e. when the correction for air displacement is to be dispensed with), the quantities in the second column were divided by the volumes at the different temperatures of one gram of water when weighed in the air with brass weights. These are : TEMPERATURE VOLUME TEMPERATURE VOLUME At 1.001185 CC. At 20 1.002812 CC. 4 1.001057 22.5 1.003363 10 1.001322 25 1.003974 12.5 1.001581 27.5 1.004651 15 1.001917 30 1.005380 17.5 1.002330 The results are recorded in the fourth column of the table. The final step was to find to what point on the stem the water must be drawn in order to graduate a half-liter flask on the Mohr system for each of the temperatures recorded in the first column. For this purpose the capacity of the stem (3.081 cc.) was divided by 1.00233, the true volume of the Mohr unit at 17.5, which gave 3.0738 as the capacity of the stem in Mohr units, or 0.030738 as the capacity of a single division. The differences between 500 and the several numbers in the fourth column were then divided by 0.030738, giving the numbers which are recorded in the fifth column. Strictly, each differ- ence should be divided by a different number, but the maximum error which could ever result from regarding the volume of a gram of air-weighed water as constant between and 30 is in this instance less than 0.01 cc. and therefore inappreciable. APPARATUS FOR MEASUREMENT OF LIQUIDS 89 TEMPERA- TURE CAPACITY OF BULB IN CC. DIVISIONS OF STEM TO BE ADDED CAPACITY OF BULB IN MOHR UNITS DIVISIONS OF STEM TO BE ADDED 499.048 30.9 498.457 50.2 4 499.098 29.3 498.571 46.5 10 499.176 26.7 498.517 48.2 12.5 499.208 25.7 498.420 51.4 15 499.241 24.6 498.286 56.1 17.5 499.273 23.6 498.112 61.4 20 499.304 22.6 497.937 67.1 22.5 499.338 21.5 497.664 76.0 25 499.372 20.4 497.395 84.7 27.5 499.403 19.4 497.091 94.6 30 499.436 18.3 497.763 105.3 Capacity of one stem division in cc. = 0.03081. Capacity of one stem division in Mohr units = 0.030738. The apparatus represented in Fig. 15 is used for the calibra- tion and graduation of smaller flasks. The capacities of the bulbs and of the graduated stems are subject to the same limita- tions as in the preceding case ; that is, the delivering capacity of the smaller bulb must not exceed 50 cc. and that of the larger one 200 cc. at the highest temperature at which the instrument is to be used, while the combined capacity of each bulb and its graduated stem must not be less than 50 cc. and 200 cc. respec- tively at 0. The delivering capacity of each bulb and stem at different temperatures is determined and the results are tabu- lated in the manner previously explained. 50-cc., 200-cc., and 250-cc. flasks can be graduated or their capacities determined by a single rilling of the pipette. To graduate or calibrate a 100-cc. flask, the smaller bulb must be twice filled. The stop- cock may, of course, be attached to either end of the instrument. The apparatus represented in Fig. 16 is for the calibration of burettes. The graduation upon the stem is in millimeters. The largest bulb has a delivering capacity of somewhat less than 90 QUANTITATIVE EXERCISES 50 cc. and, together with the graduated stem above, is employed to determine the total delivering capacity of a burette at any temperature. The limitations in respect to capacity are here the same as in the case of the pipettes previously described ; that is, the bulb must deliver less than 50 cc. at 30, while the bulb and stem together must deliver not less than 50 cc. at 0. The delivering capacity of the stem and the bulb at different temperatures is deter- mined in the same way as in the case of the pipettes, and the results are tabulated in the same form. The smaller bulbs are employed to determine the inequalities of caliber in a burette, The smaller one delivers less than 2 cc. at 30, while the bulb and the graduated portion of the stem underneath together deliver not less than 2 cc. at 0. The larger of the two bulbs and the graduated portion of the stem above it are subject to similar limitations. As will appear when the method of using the apparatus is ex- plained, the capacity of the small bulbs need not be determined by weighing the water which they deliver. Between the pipette and the burette a T tube is inserted whose third limb is connected with a supply of water situated above the upper limit of the graduation on the burette. By means of this arrangement the burette and the pipette may be filled independently. The procedure in calibrating a burette is as follows : The burette and the pipette are both filled with water to the upper FIG. 16 APPARATUS FOR MEASUREMENT OF LIQUIDS 91 limits of their graduation. The pipette is then emptied to the beginning of the graduation under the large bulk. Next, the water in the burette is allowed to flow into the pipette until the whole of the graduated portion is emptied. The water rises into the stem of the pipette, and the total delivering capacity of the burette at any temperature may be found by adding to the known delivering capacity of the bulb at that temperature the volume of the water in the stem. Having found its total capacity, the burette is again filled, and the water in the pipette is drawn down to the zero mark under the smallest bulb. The bulb is then filled from the burette and the reading on the burette recorded. The bulb is emptied, refilled, and a second reading recorded. This series of operations is repeated until less than a bulbful of water remains in the graduated portion of the burette. The next step is to find the volume of the water drawn off in the manner described, and through this the delivering capacity of the bulb. How this is to be accomplished will be explained by means of the follow- ing example of a calibration. A burette which had been graduated according to the Mohr sytem for 15, but which was to be used for solutions prepared for 20, that being the prevailing temperature of the laboratory, was found to have at 20 a delivering capacity of 50.258 cc. The burette was filled and the water drawn off in quantities which exactly filled the smallest bulb of the pipette. The read- ings upon the burette corresponding to the successive bulbfuls are given in the table under R. The twenty-fifth and last read- ing was 49.52. The capacity of the burette to this point on its graduation was found, by the proportion 50 : 50.258 : : 49.52 : z, to be 49.7755 cc. The capacity of the bulb used in the calibration was, therefore, 49 7755 , or 1.99102 cc. The true volumes corresponding to the 2b readings were then found by multiplying 1.99102 by the series of numbers from 1 to 25. The results are given in the table 92 QUANTITATIVE EXERCISES under C.R. The differences between the corresponding numbers under R. and C.R., i.e. the quantities to be added as corrections to the actual readings, are given under D. Finally, a curve of corrections for the burette was plotted upon cross-ruled paper, using a line representing the graduation upon the burette as the axis of abscissas and the corrections under D as ordinates. R. C.R. D. R. C.R. D. 1 1.95 1.99 + 0.03 14 27.70 27.87 + 0.17 2 3.94 3.98 + 0.04 15 29.70 29.87 + 0.17 3 5.93 5.97 + 0.04 16 31.68 31.86 + 0.18 4 7.94 7.96 + 0.02 17 33.65 33.85 + 0.20 5 9.91 9.96 + 0.05 18 35.62 35.84 + 0.22 6 11.90 11.95 + 0.05 19 37.60 37.83 + 0.23 7 13.85 13.94 + 0.09 20 39.59 39.82 + 0.23 8 15.84 15.93 + 0.09 21 41.58 41.81 + 0.23 9 17.83 17.92 + 0.09 22 43.56 43.80 + 0.24 10 19;78 19.91 + 0.13 23 45.55 45.79 + 0.24 11 21.74 21.90 + 0.16 24 47.54 47.78 + 0.24 12 23,75 23.89 + 0.14 25 49.52 49.78 + 0.26 13 25.74 25.88 + 0.14 50.00 50.26 + 0.26 The system of graduation and calibration of volumetric appa- ratus here described is equally applicable to all varieties of graduation whether according to the Mohr or the metric unit, or in millimeters and also to all temperatures. With its aid volumetric apparatus of the most miscellaneous character, as regards system and accuracy of graduation, can be brought into harmony and used side by side. All of the required apparatus excepting, of course, the three-way stopcock can be made in the laboratory from ordi- nary full-pipettes and without the aid of expert workers in glass. How simply this may be done in the case of the instru- ments for the graduation and calibration of measuring flasks will appear from the appended directions for the conversion of a 100-cc. pipette. APPARATUS FOR MEASUREMENT OF LIQUIDS 93 Select a 100-cc. full-pipette having the mark on the upper stem near the bulb. Substitute it delivery end up for the calibrating pipette in the arrangement represented in Fig. 16. Fill the burette and pipette with water and then empty the latter to the mark on the stem nearest the stopcock. Fill into the pipette from the burette about 99.5 cc. of water and mark the stem on a level with the meniscus. Paraffin the stem which was connected with the stopcock, graduate it in milli- meters beginning with the original mark, and etch the gradua- tion into the glass. Finally, determine accurately the capacity of the graduated portion of the stem and of the bulb by weigh- ing the water which they will deliver. For some purposes it is convenient to have both stems of the pipette graduated. Directions are also given for the conversion of a full-pipette into one for the calibration of burettes. Blow a small bulb one holding less than 2 cc. at a con- venient distance from the end of the upper stem of a 50-cc. pipette. Make a mark on the stem between the bulb and the end, but quite near the bulb. Place the pipette in the arrange- ment represented in Fig. 16, and fill burette and pipette with water. Empty the pipette to the mark which was made below the little bulb, and then fill into the pipette from the burette, as exactly as may be, 2 cc. of water. Mark the stem on a level with the meniscus. Fill in, further, about 49.7 cc. of water. If that volume of water fills the large bulb and enters the stem above, no second mark between the two bulbs will be required, and the upper stem is to be marked on a level with the menis- cus. If it does not enter the stem, attach a strip of gummed paper to the stem between the bulbs and empty the pipette to some point above the smaller bulb. Mark the place on the paper and again fill in 49.7 cc. of water from the burette. If the given volume of water now enters the upper stem, mark its limits on both stems and graduate the remainder of the upper one in millimeters. Finally, determine exactly the delivering capacity of the bulb and of the graduated stem. 94 QUANTITATIVE EXERCISES The Graduation of Glass Tubes The simple method of Bunsen (Gasometrische Methoden, 2. Auflage, p. 28) is to be recommended for the graduation in millimeters of tubes of all kinds. There are required for the work a thick board, 2 meters by about 2 decimeters, and a marking instrument resembling a beam compass. The board is usually cut transversely into two pieces of equal length which are hinged together. It is also provided with a semicircular or V-shaped groove, running from end to end, to receive the standard graduated tube and the tube to be grad- uated. When instruments having bulbs are to be graduated, the wood may be cut away in the proper places to receive the bulbs and thus allow the tubes to lie on the bottom of the groove. On each side of the groove, at a distance of about 60 mm. from its center and parallel to it, is a row of six threaded brass posts. Each post is provided with a thumb nut and a strip of brass (75 x 30 mm.) which has been bent to right angles at a distance of 6 mm. from the ends. There are also four rectangular strips of brass (850 x 45 mm.) which, in con- junction with the short strips upon the posts, are employed to hold the tubes in place in the groove and to assist in guiding the graduation. One of the long edges of two of them is notched at points 5 mm. apart, the alternate notches being some- what deeper than the others. The wooden beam of the compass has a length of one meter ; hence the curvature of the short lines cut by it is imperceptible. The point of the compass which is used in cutting away the wax should not be round in form but should resemble, rather, the cutting end of a woodworker's chisel. The tube to be graduated, by warming and turning it over a flame, is carefully covered with a thin coat of beeswax or paraf- fin and laid into one end of the groove. The notched strips of brass are brought up on either side until the space between them is equal to the length of the lines to be cut and are then APPARATUS FOR MEASUREMENT OF LIQUIDS 95 fastened in place by means of the strips and nuts on the posts. A tube with a correct scale, e.g. a eudiometer, is fastened in a similar manner in the other end of the groove. One of the steel points of the compass is dropped into a line on the stand- ard scale, and with the other a line is cut in the wax. The point is then dropped into the next groove and a second line cut, and so on until the graduation is completed. As is usual in a millimeter scale, the fifth and tenth lines, owing to the notching of the edges of the metallic strips, will be longer than the others, and the latter will be longer than the former. The tenth lines should be numbered, but in order that the reading of the numbers may be easy, the stylus with which they are engraved in the wax must not have a too fine point. If the wax has been scraped from the glass in places by the metallic FIG. 17 strips, the injury may be repaired with the aid of a warmed knife blade or with a piece of hot glass. The arrangement which has been described is the one usually employed in graduating ordinary eudiometers (Fig. 17). When smaller tubes are to be graduated, they must be raised above the groove by notched blocks which should have a length equal to the width of the board. These blocks should be provided with two holes or slots for the brass posts. If tubes attached to bulbs are to be graduated, notched metallic strips which are shorter than those mentioned will probably be required. In the place of the grooved and hinged board a half dozen notched blocks may be used. These should have a length of about 2 decimeters. The proper depth and also the size of the notch will be determined by the form and size of the apparatus to be graduated. Each block is provided with two threaded posts, 96 QUANTITATIVE EXERCISES one upon either side of the notch, and with screws by which it may be fastened to a table top. To hold the apparatus in place and to guide the graduation, the metallic strips previously described may be used. It is desirable that the distances between the points of the compass should be adjustable. Some of the recent forms of the extension-beam trammels used by mechanics fulfill this condition most satisfactorily. The graduation may be etched into the glass with a very con- centrated solution of hydrofluoric acid, which is best applied with a swab of cotton wool attached to the end of a wire. If the graduated portion of the instrument is kept thoroughly wet with fresh quantities of the acid, an exposure of about two minutes is required for the proper etching of the scale. A some- what better effect is obtained by using the acid in the dry, gas- eous condition. A suitable bath for this purpose is easily made by lining a narrow wooden trough or box with sheet lead. A quantity of ground fluor spar is spread over the bottom of the trough and covered with concentrated sulphuric acid. The tube is placed on top and the part to be etched covered with a curved piece of sheet lead. To determine the length of time during which it is necessary to expose the apparatus in order to secure a satisfactory result, it is well, if practicable, to place a trial tube in the bath at the same time, which may be removed at intervals for the purpose of examining the lines t ^ with the finger nail. Tubes to be etched by the gaseous acid must be closed with corks, and the whole of the exposed exterior must be covered with wax. If it is required to divide a fixed arbi- trary length of tube into a given number of equal spaces, as happens when the grad- uation of burettes and similar apparatus is undertaken, Bunsen's arrangement represented in Fig. 18 a may be substituted for the standard millimeter scale. It consists of a system of converging lines etched on a plate of hard glass. Measured on the line ab, APPARATUS FOR MEASUREMENT OF LIQUIDS 97 or any line parallel to it, the converging lines are equidistant. Suppose now it is required to divide a length of 20 mm. into 15 equal spaces. A straight edge would be placed upon the plate parallel to ab and moved towards the apex until the distance between the first and the fifteenth line, measured on the straight edge, is equal to 20 mm., when it would be clamped to the glass. The straight edge would next be placed in line with the piece to be marked and the grad- uation transferred in the usual manner. It is somewhat difficult to secure and main- tain the right relation between the straight edge and the base line ab ; it is therefore better to employ in the place of the Bunsen system of conver- ging lines a system of equidistant parallel lines (Fig. 18 b ). The intersections will then be equidistant whatever the position of the straight edge on the ruled plate. It is sometimes necessary to prepare for a special purpose a burette or other liquid-measuring apparatus which differs in some way from the instruments usually kept in stock. As a rule, the graduation of such pieces presents no great difficulty. We will suppose that the bulb tube represented in Fig. 19 is to be so graduated that the bulb, together with a short section of the upper and lower tubes, will deliver 100 cc. at 20, while the remainder of the lower tube will deliver cubic centime- ters at the same temperature. The directions for the operation would be as follows : Mark the point above the bulb at which it is desired to have the graduation begin and put the tube in the place of the burette in the arrangement represented in Fig. 16. Substitute for the pipette in the figure a 100-cc. calibrating pipette and find in the table which goes with the instrument how many stem divi- sions must be added to the capacity of the bulb if the instru- ment is to deliver 100 cc. at 20. Fill both instruments with water and empty the pipette to the zero mark under the bulb. 93 QUANTITATIVE EXERCISES Now allow the water to flow from the burette into the pipette until it has risen to the right height in the stem. Mark the tube under the bulb on a level with the meniscus. This will- com- plete the graduation of the bulb. A little preliminary measuring may be necessary before commencing such a graduation in order to determine at what point it is best to locate the mark above the bulb. For the graduation of the tube substitute for the pipette used in graduating the bulb a 5- or 10-cc. calibrating pipette, and find, as before, how many stem divisions must be filled for the delivery by the instrument of 5-cc. (or 10-cc.) volumes at 20. Draw off exactly the required quantities and mark the tube after each withdrawal. Cover the tube with wax and with the aid of one of the systems of lines previously described graduate the spaces between the marks into tenths of a cubic centimeter. Finally, determine by a calibration of the instru- ment the errors of the graduation. The marks made upon the tube during the graduation must lie, as nearly as possible, in the same vertical line. They should be very short also, and at the same time so distinct that after- wards they may be readily identified under the wax. -The tube may be waxed before graduation, but in that case the covering must be thin or the tube will not be sufficiently translucent. In using apparatus graduated to deliver certain volumes of liquids, it is assumed that a given area of glass surface always retains the same quantity of liquid when the apparatus is emptied, whereas the quantity retained may vary somewhat according to the character of the liquid and the condition of the surface. Instruments of this kind should be thoroughly cleansed, first with an alcoholic solution of potassium hydroxide and then with distilled water. Grease of any kind upon the glass causes that portion of the liquid which should remain uni- formly distributed over the surface to collect in drops, and it is APPARATUS FOR MEASUREMENT OF LIQUIDS 99 by no means certain that the quantity of liquid in these will be equal to that which would normally cling to the clean glass. Hence the interior of burettes and of other liquid-measuring apparatus should not be wiped with cloths, paper, or other material likely to contain any oily matter. The practice of rinsing with ether is likewise unsatisfactory because the ordi- nary commercial ether often contains in solution fats or gums which, after evaporation of the ether, are left upon the glass. Sometimes, in spite of the most thorough cleansing, the liquid film persists in breaking and collecting in drops. In such cases the difficulty cannot be remedied since it is apparently due to the character of the glass surface and not to any deposit of foreign material upon it. Care should be taken, when measuring from a burette, not to allow it to deliver too rapidly, otherwise more than the normal quantity of liquid will be left temporarily upon the glass, and the reading, if taken immediately, will be erroneous. If there is any reason to fear an error from this cause, the correctness of the reading should be confirmed by a later one. The correct reading of burettes is greatly facilitated by the use of the Erdmann float. The float should be neither so large as to stick in any part of the tube, nor so small that it can assume any other than a vertical position in the liquid. Standard and Normal Solutions A standard solution is one whose concentration has been regulated with a view to its convenient use in determining other substances. For example, a solution of potassium per- manganate of such concentration that one cubic centimeter of it will convert five milligrams of iron from the ferrous to the ferric condition is a standard solution ; likewise a solution of sodium chloride for the determination of silver, one cubic centi- meter of which will precipitate ten milligrams of silver. Any solution used in volumetric work whose concentration is known 100 QUANTITATIVE EXERCISES or whose equivalence, with respect to the substances which may be determined by it, has been ascertained, is a standard solution. Normal solutions are standard solutions which are peculiar in this respect, that the standard determining their concentration is of such a character that equal volumes of different solutions are chemically equivalent. The definitions for normal solutions which are now generally accepted are the following : 1. A normal solution of an acid is one which contains in a liter-volume one gram of replaceable hydrogen. 2. A normal solution of a base is one which contains in a liter-volume that quantity of the basic metal which will replace one gram of acid hydrogen. 3. A normal solution of a salt is one which contains in a liter- volume that quantity of salt which is formed by the replace- ment of one gram of acid hydrogen by the metal of a base. A liter- volume of a normal mono-basic acid, or of a normal mono-acid base, contains the number of grams of the dissolved substance which is equal to the molecular weight of the sub- stance ; while a normal solution of a bi-basic acid, or of a bi-acid base, contains in a liter the number of grams of the dissolved substance which is equal to one-half the molecular weight of the substance; etc. Standard solutions of certain salts for example, potassium permanganate and ferrous sulphate are employed in volu- metric work for purposes of oxidation and reduction ; as when iron is determined in accordance with the reaction 2 KMn0 4 + 10 FeS0 4 + 8 H 2 SO 4 = 5 Fe 2 3 S0 4 + 5 H 2 O + K 2 SO 4 + 2 MnSO 4 ; and chromic acid in accordance with the reaction 6 FeSO 4 + 2 CrO 3 + 6 H 2 SO 4 = Cr 2 3 SO 4 + 3 Fe 2 3 SO 4 + 6 H 2 O. The question arises, What are to be considered as normal solu- tions in such cases? According to the definitions previously given, a normal solution of potassium permanganate regarding APPARATUS FOR MEASUREMENT OF LIQUIDS 101 the substance as a salt of the mono-basic acid HMnO 4 would contain in a liter-volume the number of grams of the substance which is equal to its molecular weight. But a liter of such a solution, acting as an oxidizing agent, would be equivalent to 5 grams of hydrogen. Again, since ferrous sulphate is a salt .of a bi-basic acid, a normal solution of it, according to the defi- nition, would contain in a liter-volume the number of grams of the substance which is equal to one-half its molecular weight. But as a reducing agent, a liter of such a solution would be equivalent only to one half gram of hydrogen. On the whole, it appears more rational to emphasize the purpose for which such solutions are used rather than their classification as salts ; and to adopt, therefore, the following definitions with reference to them: 1. A normal solution of any substance employed as an oxidiz- ing agent is one containing in a liter-volume the quantity of active oxygen which is required to convert one gram of hydrogen into water. 2. A normal solution of any substance employed as a redu- cing agent is one having in a liter-volume a reducing power equal to that of one gram of hydrogen. According to the definitions here given, a normal solution of potassium permanganate would contain in a liter-volume the number of grams of the salt which is equal to one-fifth its molecular weight ; while a normal solu- tion of ferrous sulphate would contain in the same volume the number of grams of the salt which is equal to its molecular weight. The principal advantage in using normal solutions in volu- metric work lies in the fact that a general system based on the atomic and molecular weights of the substances employed greatly simplifies the computation of the quantitative results of all chemical reactions in which those substances take part. In using standard solutions for the determination of other sub- stances, the effect of unavoidable errors of measurement upon the correctness of the results is proportional to the concentration 102 QUANTITATIVE EXERCISES of the solutions. It is therefore customary in work requiring any considerable degree of accuracy to employ very dilute solu- tions. Normal solutions are diluted to one-tenth, arid in some instances to one-hundredth, of their concentration. The decimal plan of dilution is adopted because it does not sensibly diminish the advantage of the normal system. Normal solutions are to be carefully distinguished from the gram-equivalent solutions which are much used in the determi- nation of molecular weights by certain modern methods. A gram-equivalent solution always contains in a liter the number of grams of the dissolved substance which is equal to the molec- ular weight of the substance. Such solutions are equi-molec- ular or molecular-equivalent, that is, equal volumes of them contain the same number of molecules ; but the equal volumes are not, as in the case of normal solutions, necessarily chem- ically equivalent. Some confusion has arisen from the practice of calling gram-equivalent solutions normal solutions. Perhaps the distinction between the two classes of solutions could be emphasized with advantage by calling the one volume-normal, and the other molecular-normal. The Correction of Standard Solutions for Temperature All volumetric apparatus should be graduated or calibrated for the particular temperature which usually prevails in the laboratory in which the instruments are to be used. The stand- ard solutions also should be so made up as to be correct at the standard temperature ; and they should be used, as far as prac- ticable, at that temperature. But, since the temperature of every laboratory is subject to considerable variations, it is often neces- sary both to make and to use the standard solutions at other than the standard temperature. The errors which arise from this source are usually tolerable in ordinary volumetric work, but they require attention whenever any considerable degree of accuracy is sought. Such corrections, though seeming to AI'I'AU.VITS FOll MKASI'IIKMKNT OK UQl IDS 103 involve laborious computations, can be easily and expeditiously made with the aid of a very simple device which will now be explained. In estimating the magnitude of the errors which result from measuring standard solutions at other than standard tempera- tures, two things must be taken into account, the expansion or contraction of the liquids and the expansion or contraction of the measuring instruments. The errors of the measurements are equal to the differences between the two. We will suppose, for purposes of explanation, that the standard temperature is 20, and that water is the liquid to be dealt with. The reason for selecting water instead of a solution will appear hereafter. The problem is to devise some expeditious method of finding what volumes quantities of water measured at other tempera- tures would have if measured at the standard temperature of 20 ; or, if need be, for finding what volumes quantities of water measured at 20 would have if measured at other tem- peratures. We will suppose that the extreme limits to be pro- vided for are 10 on the one side and 30 on the other. The following table gives the volumes of water at 10, 15, 25, and 30 as compared with its volume at 20. TABLE I 10 15 20 26 30 0.998511 0.999098 1.000000 1.001142 1.002503 Table II gives the volumes which a liter of water, measured at 20, would have at 10, 15, 25, and 30, and the amounts of the contraction or expansion. TABLE II 10 ir> 20 25 .10 8.511 cc. MM. 098 cc. 1000.000 cc. 1001.142 cc. 1 002.503 cc. 1.489 cc. 0.!M)2 cc. 0.000 cc. 1.142 cc. 2.503 cc. Suppose a graduated glass vessel holding exactly one liter at 20 is filled with water also having a temperature of 20. The 104 QUANTITATIVE EXERCISES volume of the water will be 1000 cc. If now the temperature of the water falls to 10, its volume will be 998.511 cc. (see Table II). But the water will not measure that amount by the graduation of the vessel because the latter has also diminished in size by 1000 ^ AAAOC? that is, by 0.25 cc. It will appear to 998.511 have a volume of 3 - ~, or 998.761 cc.; and 1000 -998.761, _L . or 1.239 cc., is the value of the correction which must be added to the apparent volume to find what the volume of the water would be at 20, the standard temperature. If, on the other hand, the temperature* of the water rises to 30, its true volume will be 1002.503 cc. ; but it will measure less than that in a graduated vessel which is correct at 20 because the vessel has also suffered expansion. Its apparent volume will be ' , or 1002.252 cc.; and 1002.252-1000, Ji.OOO^iO or 2.252 cc., is the correction which must be deducted from the apparent volume of the water at 30 in order to find what its volume at 20 would be. Table III gives the values of the cor- rections for one liter of water at 10, 15, 25, and 30. We should obtain values sufficiently near the truth for all ordinary purposes by simply subtracting the contraction or expansion of a liter measuring flask from the absolute contraction or expan- sion of a liter of water as given in Table II. TABLE III 10 15 25 30 + 1.239 cc. + 0.777 cc. - 1.017 cc. - 2.253 cc. For convenience of use in practice a curve of corrections is to be made for each degree between 10 and 20 on one side and between 20 and 30 on the other. To prepare the curves a horizontal line upon the cross-ruled paper is made to represent cubic centimeters of liquid from cc. to 100 cc. A vertical line at the 100 cc.-end of the horizontal one, and extending above THE UNIVERSITY RN\^ OF LIQUIDS 105 and below it, is employed for the corrections to be applied to a 100 cc. -volume at different temperatures ; the upper portion being reserved for positive quantities and the lower one for negative quantities. Each space on the vertical line is made to represent 0.01 cc. Hence we cut off on the upper portion of it 12.4 spaces to represent the contraction from 20 to 10, and on the lower portion 22.5 spaces to represent the expansion from 20 to 30. Each of these two intervals is then divided into ten equal parts labeled 19, 18, 17, . . . , 10 from the base line upwards, and 21, 22, 23, . . . , 30 from the base line downwards. Finally, the temperature points upon the vertical line are joined by straight lines to the zero end of the horizontal line. With the aid of such a figure one can determine by a simple inspection how much is to be added to or subtracted from any volume of water not exceeding 100 cc., when measured at any temperature between 10 and 30, in order to find what volume it would occupy at 20 ; or he may ascertain with equal ease what volume water measured at 20 would appear to have if measured at any other temperature within the given limits. Correction curves prepared in accordance with the plan here developed are not rigidly accurate. The expansion of water has been assumed to be uniform between 10 and 20 on the one hand, and between 20 and 30 on the other, which is not in accordance with the truth. Again, the expansion of glass has been assumed to be regular between 10 and 30, which is also not strictly correct. The errors resulting from the former assumption are not large and they may be easily avoided by dividing the vertical or temperature line of the correction figure in accordance with the known irregularities of the expansion of water. The effect of the irregularities of the expansion of glass is of no significance since it never amounts to quantities which can be measured by ordinary volumetric apparatus. The figures employed for the correction of liquid volumes for temperature may, of course, be drawn upon a larger scale 106 QUANTITATIVE EXERCISES than that proposed above, and for larger volumes of the liquid, e.g. a liter instead of 100 cc. The expansion of glass and of water, the usual solvent, has been investigated with care, but the expansion coefficients of solutions of the concentration usually employed in volumetric analysis have not, unfortunately, been determined to any great extent. It is often assumed for purposes of correction that these dilute solutions expand and contract with changing tem- peratures to about the same extent as water itself. But, judging by the results of an investigation by Alfred Schulze (ZeitscTirift fur analytisclie Chemie, 21, 167), the assumption is justified only in the case of very dilute solutions, solutions, for example, of -j 1 ^ normal concentration. Schulze determined the expansion of T ^ normal solutions of sodium chloride and silver nitrate from to 30. His results, together with the corresponding figures for water, are given for certain intervals of temperature in the following table. TABLE IV 10 15 20 25 30 Water 1.000000 1.000124 1.000712 1.001615 1.002759 1.004123 XT 1.000000 1.000360 1.001030 1.001965 1.003160 1.004630 8 1.000000 1.000398 1.001075 1.002032 1.003240 1.004690 In the next table the volumes of the three liquids at 10, 15, 25, and 30 are compared with their volume at 20. Water N TABLE V io; 15 20 25 30 0.998511 0.999098 1.000000 1.001142 1.0X)2503 0.998398 0.999066 1.000000 1.001192 1.002659 0.998369 0.999044 1.000000 1.001205 1.002652 If we subtract the numbers in the above table from unity and multiply the differences by 1000, and then deduct the expansion APPARATUS FOR MEASUREMENT OF LIQUIDS 107 of a liter flask from 10 and 15 to 20, and from 20 to 25 and 30, we shall obtain the quantities which would be used in constructing for a liter-volume of each of the three liquids a correction figure like that already explained. Table VI gives these quantities. TABLE VI 10 15 25 30 Water + 1.239 cc. + 0.777 cc. - 1.017 cc. - 2.253 cc. ^ NaCl 1.352 0.809 1.067 2.409 ^ AgNO 3 1.381 0.831 1.080 2.402 Judging by the evidence afforded by this table, it is probably safe to employ the known expansion of water for the correction of solutions of tenth-normal concentration ; for with a standard temperature of 20, the maximum error which could result from so doing would amount in measuring a liter-volume of ^ silver nitrate to only 0.142 cc. at 10, 0.054 cc. at 15, 0.063 cc. at 25, and 0.149 cc. at 30 ; while the error in measuring an equal volume of ^ sodium chloride solution would amount to only 0.113 cc. at 10, 0.032 cc. at 15, 0.05 cc. at 25, and 0.156 cc. at 30. The maximum error in the correction for a measurement of 50 cc. of either liquid would amount to less than 0.01 cc. Schulze also determined the expansion of six normal solutions from to 30. The results for several intervals of tempera- ture, together with the corresponding volumes of water, are given on the following page. 108 QUANTITATIVE EXERCISES Water Oxalic acid Hydrochloric acid Nitric acid Sulphuric acid Sodium car- "1 bonate j Sodium ") hydroxide j TABLE VII 10 15 20 25 30 1.000000 1.000124 1.000712 1.001615 1.002759 1.004123 1.000000 1.000993 1.001940 1.003125 1.004560 1.006168 1.000000 1.001010 1.001905 1.003013 1.004328 1.005850 1.000000 1.001800 1.003050 1.004490 1.006120 1.007933 1.000000 1.001720 1.002945 1.004385 1.005990 1.007820 1.000000 1.001880 1.003130 1.004565 1.006165 1.007955 1.000000 1.002050 1.003365 1.004848 1.006510 1.008330 The expansion of the six normal solutions included in the table diverges more from that of water at temperatures below 10 than above. This will appear more clearly if we select 20 instead of as our standard temperature, as is done in the following table. Water Oxalic acid Hydrochloric acid Nitric acid Sulphuric acid Sodium carbonate Sodium hydroxide If the quantities in Table VIII are treated as were those in Table V in order to secure the data required for the construction of a correction figure for each of the liquids, we obtain the following results. Water Oxalic acid Hydrochloric acid Nitric acid Sulphuric acid Sodium carbonate Sodium hydroxide 10 0.998511 0.997874 0.998003 0.997322 0.997346 0.997327 0.997215 TABLE VIII 15 0.999098 0.998818 0.998895 0.998566 0.998566 0.998571 0.998524 20 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 25 1.001142 1.001430 1.001311 1.001622 1.001598 1.001592 1.001653 30 1.002503 1.003033 1.002828 1.003427 1.003420 1.003374 1.003465 TABLE IX 10 15 25 30 + 1.239 cc. + 0.777 cc. - 1.017 cc. - 2.253 cc. 1.876 1.057 1.305 2.783 1.747 0.980 1.186 2.578 2.428 1.309 1.497 3.177 2.404 1.309 1.473 3.170 2.423 1.304 1.467 3.124 2.535 1.351 1.528 3.215 APPARATUS FOR MEASUREMENT OF LIQUIDS 109 It appears from the values recorded in Table IX that the known expansion of water cannot be employed for the correction of standard solutions of normal concentration. Up to the pres- ent time we have the necessary data for the temperature correc- tion of only the six normal solutions included in the above table. As a temporary expedient, however, it is probably safe to employ for normal solutions of unknown expansion the mean values of the corrections in Table IX. For a liter-volume these are : TABLE X 10 15 20 25 30 + 2.236 cc. + 1.218 cc. 0.000 cc. - 1.409 cc. - 3.008 cc. We have to consider now the course to be followed when a standard solution is to be made at some other than the standard temperature. We will suppose that the standard temperature is 20 and that a tenth-normal solution of sodium chloride is to be made at 15 in a liter flask, which is correct, of course, only at 20. At 15 the flask will hold not a liter, but 1.000 -=- 1.000125, or 999.875 cc., and this will be the true volume of the solution when made up at the given temperature. We wish now to find what its volume at 20 will be. For this purpose we assume that the expansion of tenth-normal solutions is about equal to that of water. If the volume of water at 20 is 1.0, its volume at 15 is 0.999098 (see Table I); therefore 999.875 cc. of the solution measured at 15 will become 999.875 --- 0.999098, or 1000.778 cc., at 20. A liter of the solution should contain at the standard temperature 5.806 grams of the salt, and a cubic centi- meter 0.005806 gram. The weight of the salt to be dissolved at 15 is therefore 0.005806 x 1000.778, or 5.8105 grams. Suppose, on the other hand, that the temperature at which the solution is to be made is 25. The flask will then have a capacity of 1.000 x 1.000125, or 1000.125 cc., and this will be the volume of the solution when made. Its volume at 20 will be 1000.125 -=-1.001142, or 998.98 cc. The quantity of the salt to be weighed out is therefore 998.98 x 0.005806, or 5.8001 grams. CHAPTER V THE PREPARATION OF STANDARD SOLUTIONS OF ACIDS AND ALKALIES INDICATOES When a standard solution of potassium permanganate is allowed to flow from a burette into a solution of ferrous sul- phate to which a little sulphuric acid has been added, the fol- lowing reaction takes place : 2 KMn0 4 + 10 FeS0 4 + 8 H 2 SO 4 = K 2 SO 4 -f 2 MnSO 4 + 5 Fe 2 3S0 4 + 8 H 2 O. As long as there remains any ferrous salt in the solution, the permanganate is reduced and loses, in consequence, its charac- teristic color. As -soon, however, as the reaction with the irpn is finished, the reduction ceases, and an additional drop of the permanganate or even a fraction of a drop if the volume of the liquid is not large imparts a distinct rose color to the solu- tion. The sudden appearance of the color is so striking that one is always able to determine with great precision the point at which the reaction between the permanganate and the ferrous iron is finished. If a standard solution of silver nitrate is added in the same way to a solution of any chloride, the chlorine is precipitated as silver chloride, AgN0 3 + NaCl = NaNO 3 + AgCl. But since the solution of silver nitrate is colorless, and the freshly formed silver chloride is slow in subsiding, it is diificult to determine when the precipitation is completed. If, however, in the beginning, there are added to the solution of chloride a 110 STANDARD SOLUTIONS OF ACIDS AND ALKALIES 111 few drops of a solution of neutral potassium chromate, the pre- cipitation of silver chloride will proceed as before, and there will be no permanent reaction between the silver nitrate and the chromate until the precipitation of the chlorine is finished. There will then appear in the solution a permanent red color due to the formation of silver chromate, which is a sufficient indica- tion that enough of the standard solution has been added. Again, if a solution of sodium arsenite is added to one of bleaching powder, the arsenite will be converted into arseniate, Na 3 A sO 3 + CaCl 2 O = Na 3 AsO 4 + CaCl 2 . But nothing will occur in the solution to indicate when the reaction is finished. If, however, a drop of the liquid is removed upon the end of a glass rod from time to time, and applied to a piece of filter paper which has been dipped in a solution of starch and potassium iodide and then tlried, it is easy to ascer- tain when the last trace of hypochlorite disappears ; for as long as any of it is present a blue spot will appear whenever the paper is touched with a drop of the liquid. Substances which, like potassium chromate in the determina- tion of chlorine by a standard solution of silver nitrate, and like the mixture of potassium iodide and starch in the determination of a hypochlorite by sodium arsenite, are employed to indicate the completion of reactions are called indicators. Only those which are most frequently used in connection with the neutral- ization of acids and bases need be considered in this place. 1. LITMUS Preparation. The crushed commercial litmus is repeatedly extracted with fresh quantities of boiling 85 per cent alcohol for the purpose of removing a violet coloring matter which is reddened by acids but not made blue by alkalies. The residue, consisting mainly of calcium carbonate, carbonates of the alka- lies, and the substance to be isolated, is washed with more hot 112 QUANTITATIVE EXERCISES alcohol upon a filter, and then digested for several hours with cold distilled water. The filtered aqueous extract has a pure blue color and contains an excess of alkali, a part of which is in the form of carbonate and a part in combination with the litmus. To remove the alkaline reaction, the solution is heated to the boiling point and cautiously treated with very dilute sul- phuric acid until it becomes distinctly and permanently red. The boiling must be continued until the carbonic acid which is liberated in the solution has been expelled, otherwise the blue color may reappear after a time. The red solution, after expul- sion of the carbonic acid, is treated with a dilute solution of barium hydroxide until the color changes to a violet, and is then filtered. In this state the solution is very sensitive to acids or alkalies, changing to red with the former and to blue with the latter. In closed vessels the 'solution soon loses color and acquires an offensive odor. But if a solution which has been thus altered is exposed to the air in shallow vessels, it soon regains its original color. Solutions of litmus should therefore be kept in open and only partly filled bottles. Paper caps placed over the necks of the bottles will protect the solutions from dust and at the same time admit the air which is necessary for their preservation. In neutralizing an acid with an alkali, the quantity of the lat- ter which must be added is somewhat more than equivalent to the quantity of the former, since a small amount of the alkali is required to give the litmus a blue color. For the same reason, when an alkali is neutralized, a slight excess of the acid must be added. Hence the importance of making the indicator as sensitive as possible in the beginning. There are two reme- dies for the difficulty. The litmus solution may be divided into two parts, one of which is changed to a red color with the least possible quantity of acid, and the other to a blue with the least possible quantity of alkali. When now an acid is to be neutral- ized with a standard alkali, the blue solution is employed as the STANDARD SOLUTIONS OF ACIDS AND ALKALIES 113 indicator and vice versa. Or, one may apply a so-called color correction. The magnitude of this correction is ascertained by adding to a quantity of neutral water, equal in volume to the solution of acid or alkali, the same amount of the indicator that is to be used in the neutralization experiment, and then finding how much of the standard solution is required to produce the required color. If preferred, the litmus may be precipitated and preserved in solid form. For this purpose the solution, prepared as described above, is evaporated to a small volume and then treated with strong alcohol. The precipitate is collected on a filter, washed with alcohol, and dried over calcium chloride. Litmus is a satisfactory indicator with the following sub- stances : 1. Hydrochloric, hydrobromic, sulphuric, nitric, and oxalic acids. 2. The hydroxides of the alkaline and alkaline earth metals and ammonia. 3. The arsenites and silicates of the alkalies. 4. The carbonates and sulphides of the alkalies and alkaline earths in boiling solutions. Its conduct is unsatisfactory : 1. With sulphurous, phosphoric, arsenic, boric, and chromic acids. 2. With most organic acids. 3. With carbonates and sulphides in cold solutions. 2. PHENOLPHTHALEIN Preparation. Half a gram of the solid material is dissolved in 100 cc. of neutral 95 per cent alcohol. If the alcohol is found to have an acid reaction, as it often has, it should be boiled for a short time. If its acid reaction does not disappear after boiling, the alcohol should be agitated with dry calcium hydroxide (slaked lime) and redistilled. 114 QUANTITATIVE EXERCISES Phenolphthalein is nearly colorless in neutral and acid solu- tions and red in those containing the least excess of alkali. It is a delicate indicator: 1. For the hydroxides of the alkaline and alkaline earth metals. 2. For most mineral acids. 3. For most organic acids. Its conduct is unsatisfactory : 1. With ammonia and in solutions containing ammonium salts. 2. With arsenious, silicic, and boric acids. Phenolphthalein is exceedingly sensitive to carbonic and sulphhydric acids, but exhibits a neutral reaction as soon as their acid salts have been formed. With phosphoric and arsenic acids it exhibits a neutral reaction when two-thirds of their acid hydrogen has been replaced. In this respect it differs from litmus, toward which the mono-hydrogen phosphates and arseni- ates of the alkaline metals are alkaline, and the di-hydrogen salts neutral. 3. METHYL ORANGE Preparation. One part of the dyestuff is dissolved in a thousand parts of cold distilled water. Ordinarily not more than two or three drops of this dilute preparation should be added to a solution in which a determination is to be made. In very dilute neutral or alkaline solutions methyl orange has a yellow color which changes to a pink in the presence of the least excess of one of the stronger mineral acids. It owes its great value as an indicator not to any superior sensitive- ness, but principally to the fact that it is almost wholly indif- ferent to carbonic and sulphhydric acids, and to certain salts which give an acid reaction with litmus and some other indi- cators. It is also indifferent to arsenious, boric, silicic, and hydrocyanic acids, which makes it practicable to determine vol- umetrically the bases in combination with these weak acids. STANDARD SOLUTIONS OF ACIDS AND ALKALIES 115 Methyl orange may be used as an indicator in the determina- tm of the following substances : 1. The stronger mineral acids. 2. The hydroxides of the alkaline and alkaline earth metals. 3. Ammonia. 4. The bases in such carbonates, sulphides, arsenites, silicates, ad borates as are decomposed by dilute nitric, hydrochloric, or alphuric acid. 5. Phosphoric and arsenic acids which become neutral to lethyl orange when one-third of their hydrogen has been ^placed. 6. Sulphurous acid which becomes neutral to the indicator *ith the formation of its acid salt. Methyl orange cannot be used for the determination of organic cids, or in solutions containing nitrous acid or nitrites which estroy it. Moreover, it cannot be employed in hot solutions. 4. TKOP^OLIN The dyestuff known as tropseolin No. 00 conducts itself owards acids and alkalies like methyl orange. 5. COCHINEAL Preparation. Commercial cochineal is reduced to a coarse powder and digested with from 10 to 20 parts of 25 per cent alcohol. In neutral and acid solutions cochineal has a yellowish-red color, which changes to a violet in the presence of alkali. Towards the stronger mineral acids and the hydroxides of the alkaline and alkaline earth metals it is quite sensitive. It is of little value in the titration of organic acids, and cannot be used in solutions containing acetates, salts of copper, or any traces of iron or aluminium. It can be used by gaslight with very satisfactory results. 116 QUANTITATIVE EXERCISES EXERCISE X THE PREPARATION OF STANDARD SOLUTIONS OF ACIDS AND ALKALIES I. BY MEANS OF OXALIC ACID a. Preparation of Pure Oxalic Acid Agitate commercial oxalic acid in a closed bottle with a mix- ture of equal parts of ether and 95 per cent alcohol until the liquid is fully saturated with the acid. Filter into a flask through a plaited paper. Partly immerse the flask in a water bath, connect it with a condenser and receiver, and then heat as long as a copious distillate is obtained. To the distillate, which consists mainly of ether, add more alcohol, and with the mixture extract more of the acid. Filter and distill as before. When enough of the acid has been extracted, and its solution freed from ether, add to the residue an equal volume of distilled water which is free from ammonia and concentrate upon the water bath in a porcelain dish until the odor of ethyl oxalate and alcohol disappears and the solution is ready to crystallize on cooling. If the odor of ethyl oxalate or alcohol has not wholly disappeared when the solution becomes sufficiently con- centrated for crystallization, more water must be added and the evaporation repeated. Stir the solution while the crystals are forming. Collect the acid in a funnel in the bottom of which a perforated porcelain disk or a platinum cone has been placed. Remove as much as possible of the mother liquor with the aid of a filter pump, and spread the acid to dry upon a clean unglazed porcelain plate. Burn a quantity of the acid upon the lid of a platinum crucible, or in a dish of the same material, to find whether or not it leaves a weighable residue. Commercial oxalic acid contains acid oxalates from which it cannot be readily freed by the ordinary process of recrystalliza- tion from water. The difficulty in removing the salts by this STANDARD SOLUTIONS OF ACIDS AKD ALKALIES 117 method is due to the fact that the acid oxalates, though readily dissolved by hot water, are only very moderately soluble in cold water. Hence they are reprecipitated from cooling saturated solutions of the acid. A partial removal of the salts may be effected by saturating cold water with the acid and then evap- orating to the point of crystallization. The air-dried acid is neither deliquescent nor efflorescent in air containing the usual amount of moisture. It cannot be dried in a desiccator, since in an atmosphere devoid of moisture it loses water of crystallization. Its solutions are not altogether stable. b. Preparation of a Tenth-Normal Solution of Oxalic Acid Oxalic acid is bi-basic and has a molecular weight of 125.08. It would therefore be necessary, in order to prepare a liter of 125 08 the normal solution, to weigh out ^ , or 62.54 grams of the A pure acid. To prepare a liter of a tenth-normal solution, one- tenth of this quantity, or 6.254 grams, would be required. One half-liter of the latter solution will suffice for the present exercise. This will require 3.127 grams of the acid. The weighing of fixed quantities, however, consumes much time. It is therefore better to proceed as follows : Weigh out a few milligrams more than the required amount of the acid. Dis- solve it in distilled water, free from ammonia and carbonic acid ; transfer the solution to a half-liter flask, taking care not to wet the neck ; rinse the vessel in which the solution was made sev- eral times with water and pour the rinsings into the flask. Add more water, a little at a time, mixing the contents of the flask after each addition, without wetting the neck, until the flask is nearly full. Now fill to the mark, close the flask, and mix the liquid thoroughly. The solution will be somewhat too concentrated. Divide the weight of acid required for a half- liter, i.e. 3.127 grams, by the weight of the acid in one cubic centimeter of the solution. This will give the number of cubic 118 QUANTITATIVE EXERCISES centimeters which must be diluted to half a liter, and the differ- ence between that number and 500 will be the volume of water required for the dilution. With a pipette remove a quantity of the solution, add the required volume of water, and then fill the flask to the mark with a portion of the solution which was removed to make room for the water. The plan here proposed for making solutions of definite con- centration from weighed quantities of substances has various advantages over that of weighing out exactly the required amounts of the substances to be dissolved. The most important of these are the saving of time and the avoidance of long expo- sure of the material to the atmosphere at the time of weighing. Such exposure at the balance of powdered materials, or of those which absorb water or carbonic acid, is a serious obstacle in the way of obtaining correct weighings. There is one error in the process which requires attention when the solutions to be made are of considerable concentra- tion. It is assumed that the final volume of the liquid is equal to the sum of the volumes of the solution diluted and of the water which is added to it, whereas, in the case of aqueous solutions, dilution is usually attended by contraction. The effect of the error upon tenth-normal solutions is unimportant, and in the case of more concentrated solutions it may be reduced to insignificance by weighing out only very little more than the required amount of the substances to be dissolved. Distilled water usually contains ammonia and carbonic acid, both of which must be removed before it is used in making standard solutions of acids. Therefore the water which is to be employed for this purpose should be vigorously boiled for 20 or 30 minutes and then allowed to cool to the standard temper- ature. Carbonic acid in the water with which standard solu- tions of acids are made increases the acidity and interferes with the normal conduct of such indicators as litmus and phenol- phthalein ; while ammonia, under the same conditions, weakens the acids and strengthens the standard alkalies. If only those STANDARD SOLUTIONS OF ACIDS AND ALKALIES 119 indicators are used which are indifferent to carbonic acid, the presence of that acid is, of course, unobjectionable. But stand- ard acids which are made up with water containing consider- able carbonic acid will exhibit different concentrations when neutralized with an alkali, according as litmus or phenolphthal- ein on the one hand, or methyl orange on the other, is used as the indicator. It is therefore advisable to expel the carbonic acid and ammonia from all water which is to be used in connec- tion with neutralization experiments. The boiling of the water for this purpose should take place in porcelain vessels, since hot water extracts alkali from all varieties of glass which are used in a chemical laboratory, and from some of them with astonishing rapidity. This source of error in acidimetric work should not be overlooked. Beakers, flasks, and other glass vessels should be 'tested with regard to their fitness for use in such experiments. This may be done by boiling in them for an hour or more water having, in the beginning, a neutral reac- tion ; and then determining with the aid of phenolphthalein and a very dilute standard acid whether an appreciable amount of alkali has been dissolved. The common practice of employing compressed air from the lungs to force from a wash bottle the water which is required for dilution or other purposes is, of course, inadmissible in .vol- umetric work with acids and bases. c. Preparation of a Tenth-Normal Alcoholic Solution of Potassium Hydroxide Dissolve two or three grams of sodium hydroxide in a liter and a half of 95 per cent alcohol and redistill. This treatment will free the alcohol from carbonic and other acids which the commercial material usually contains, and also from 'alde- hydes and a substance extracted from the oak barrel staves, both of which when treated with alkali give a yellow color to the alcohol. 120 QUANTITATIVE EXERCISES Dissolve about 3.3 grams of the purest obtainable potas- sium hydroxide in a half-liter of the redistilled alcohol, and set the solution aside in a glass-stoppered bottle. At first the solution will be cloudy from the presence in it of insoluble potassium carbonate, but this soon subsides and becomes firmly attached to the glass, leaving the solution of hydroxide quite clear. With the room and the solutions at very nearly the standard temperature, fill one burette with the tenth-normal oxalic acid, and another with the alcoholic caustic potash. Cover both burettes with inverted test tubes. Measure into an Erlenmeyer flask 25 cc. of the standard acid and add to it a few drops of a solution of phenolphthalein which has also been made with the redistilled alcohol. Titrate the acid with the alkali until the red color appears and then determine whether a measurable quantity of the acid is required to destroy it. Titrate back and forth with the two solutions until a point is reached where the quantities of alkali and acid required to produce and destroy the color cannot be measured upon the burettes. Repeat the experiment. If the first and second results agree, calculate from the ascertained relation of the two solutions how many cubic centimeters of the alkali will be required to make a half- liter of a tenth-normal solution. Measure into a 500-cc. flask the volume of alcohol necessary for dilution, and fill to the mark with the alkali. Compare the diluted solution with the standard oxalic acid. They should be found equivalent, vol- ume for volume. The principal objection to the use of phenolphthalein as an indicator is its extreme sensitiveness to carbonic acid. Solu- tions containing it which have been reddened by the addition of a slight excess of an alkaline hydroxide soon lose their color in the air in consequence of the absorption of carbon dioxide. Even the breath of the operator is often a source of difficulty in a titration when this indicator is used. The evil is partially remedied by using flasks instead of beakers, STANDARD SOLUTIONS OF ACIDS AND ALKALIES 121 and by titrating, whenever practicable, into hot instead of cold solutions. Alcoholic solutions of the alkaline hydroxides are not stable and must therefore be frequently restandardized. They soon turn yellow and then reddish-brown in consequence, apparently, of the absorption of oxygen and the formation of aldehyde resin. Any moderate development of color does not, however, interfere with their use in neutralizing acids. The principal advantage in using an alcoholic rather than an aqueous solution of an alkaline hydroxide lies in the fact that the alkaline carbonates, being nearly insoluble in concentrated alcohol, separate from the former as fast as they are formed in consequence of unavoid- able exposure of the solutions to the air. In other words, alco- holic solutions of the caustic alkalies keep themselves free from carbonates and therefore in fit condition for use with indicators which, like litmus and phenolphthalein, are sensitive to car- bonic acid. Aqueous solutions of the alkaline hydroxides which are prac- tically free from carbonates may be prepared by saturating so- called absolute alcohol with. the solid caustic alkalies and then diluting the alcoholic solutions, after subsidence of the insol- uble matter, with water. In such solutions any carbonate which may be subsequently formed in consequence of exposure to the air will, of course, remain in solution. Aqueous solutions of the caustic alkalies may be freed from carbonates by adding to them a little hydroxide of calcium or of barium. But such solutions, as will be explained hereafter, cannot, under certain conditions, be used in conjunction with oxalic acid. The great change in volume which alcohol suffers when its temperature is raised or lowered constitutes an objection to the employment of alcoholic solutions in volumetric work. Care must be taken both to make and to use such solutions at the standard temperature. Otherwise corrections must be applied to the measurements. 122 QUANTITATIVE EXERCISES If the volume of alcohol (96 to 97 per cent) at is repre- sented by unity, its volume at any higher temperature t will be found by the formula 1 + at + bt 2 + ct 8 , in which a = 0.00104139 b = 0.0000007836, c = 0.000000017618. The following table gives the volumes of alcohol, also those of water at several temperatures. TABLE I Alcohol Water 1.000000 1.000000 10 1.010510 1.000124 15 1.015857 1.000712 20 1.021282 1.001615 25 1.026799 1.002759 30 1.032423 1.004123 The next table gives the volumes of alcohol and of water at 10, 15, 25, and 30 as compared with their volumes at 20. TABLE II 10 15 20 25 30 Alcohol 0.989452 0.994688 1.000000 1.005403 1.010908 Water 0.998511 0.999098 1.000000 1.001142 1.002503 Table III gives, in cubic centimeters, the decrease in volume of a liter of alcohol and of a liter of water when their tempera- ture falls from 20 to 15 and 10 ; and their increase in vol- ume when the temperature rises from 20 to 25 and 30. TABLE III 10 15 20 25 30 Alcohol 10.55 cc. 6.31 cc. 0.00 cc. 5.40 cc. 10.91 cc. Water 1.49 cc. 0.90 cc. 0.00 cc. 1.14 cc. 2.50 cc. If we deduct from the volumes given in the first horizontal line of the table the contraction of a liter flask from 20 to 15 and 10 and its expansion from 20 to 25 and 30, we shall obtain the data required for the preparation of a correction figure (see page 104) to be used in connection with strong alcohol STANDARD SOLUTIONS OF ACIDS AND ALKALIES 123 or with weak solutions of alkalies in concentrated alcohol. Table IV gives these differences. TABLE IV 10 15 20 25 30 10.3 cc. 6.185 cc. 0.00 cc. 5.275 cc. 10.66 cc. d. Preparation of a Tenth-Normal Solution of Hydrochloric Acid Dilute 25 cc. of concentrated chemically pure hydrochloric acid to a liter volume with boiled distilled water. Determine the acid in measured portions of the solution with the standard alcoholic caustic potash, using phenolphthalein as the indicator, and then, without lurther dilution, proceed to determine the strength of the acid as directed under II. II. BY MEANS OF CARBONATES Dissolve about 6.5 grams of potassium hydroxide in a liter of distilled water. The solution will be somewhat more than decinormal. It is not necessary to know its exact strength, nor is it necessary to boil the water with which it is made. Weigh into beakers or Erlenmeyer flasks two portions of pure calcium carbonate of about 0.2 gram each. Add to each portion 50 cc. of the hydrochloric acid whose strength was determined as directed under I, d, and cover the beakers or flasks with watch glasses. When the solution of the carbonate which may be hastened by the application of a very gentle heat is complete, rinse the covering glasses into the solutions with distilled water, add a few drops of a dilute solution of methyl orange, and titrate the excess of hydrochloric acid with the water solution of potassium hydroxide. Having found how much of the latter is required to neutralize the former, measure out an equal volume of the alkali and titrate it with the hydrochloric acid whose strength is to be determined. The difference between the volume of the acid required to neutralize 124 QUANTITATIVE EXERCISES the alkali and that added to the carbonate in the first place is, of course, the volume of the acid which has been neutralized in dissolving the carbonate. From this and from the known weight of the carbonate it is easy to calculate the concentration of the hydrochloric acid. The two results should agree very closely with each other and with those obtained by proceeding as directed under I, d. Dilute the acid to the decinormal standard (using boiled distilled water for the purpose) and compare the diluted solu- tion with the decinormal oxalic acid, using for this purpose the standard alcoholic solution of potassium hydroxide and phenol- phthalein. Equal volumes of the two acids should neutralize the same volume of the alkali. Saturate a small quantity of so-called absolute alcohol with potassium hydroxide, and when the liquid has become clear dilute 10 cc. of the solution to a liter with recently boiled water. With the aid of this solution compare again the two decinormal acids, using at one time phenolphthalein and at another litmus as the indicator. Calcium carbonate for the standardization of acids may be prepared in the following manner: Calcium chloride, such as is usually employed for drying gases, is dissolved in water; the solution is treated with a little calcium hydroxide, boiled, and filtered; the calcium is then precipitated as oxalate with ammonium oxalate and a little ammonia. After standing in a warm place for several hours the oxalate is collected on a filter, washed with water, dried, and converted into carbonate by heat- ing it in a platinum dish. The carbonate is dissolved in hydro- chloric acid and the calcium reprecipitated as oxalate ; and from the oxalate the carbonate is obtained in the same manner as before. The carbonate thus obtained will probably have a gray color in consequence of the separation of carbon. It is dissolved in hydrochloric acid and the solution, if not perfectly clear, is filtered. The calcium is now precipitated as carbonate with ammonia and ammonium carbonate. The precipitate is collected, STANDARD SOLUTIONS OF ACIDS AND ALKALIES 125 thoroughly washed with boiling water, dried, transferred to a platinum dish, moistened with a solution of ammonium carbon- ate, and heated to constant weight at a temperature below a red heat. The treatment with ammonium carbonate and the subse- quent heating to constant weight should be repeated until such repetition is found to produce no change in the weight of the material. The crystallized calcium carbonate known as Iceland spar is often pure enough to be used in determining the strength of acids, but much of the material now sold under that name con- tains magnesium carbonate. It is therefore unsafe to employ a specimen of the mineral for this purpose until its purity has been demonstrated. OTHER METHODS OF STANDARDIZING ACIDS AND ALKALIES In general, any substance of pronounced acid or basic charac- ter which can be obtained in pure condition and is stable in the air may be employed to standardize alkalies and acids. Of the acids which satisfy these conditions, none are superior to oxalic acid. There are, however, several acid salts which may be used with advantage for the purpose, such as the acid oxalates of the alkali metals and acid potassium tartrate. The compound of this class which is most frequently employed is potassium tetroxalate. Of the basic substances suitable for the determination of the strength of acids, the carbonates of sodium and of the alkaline earths are probably the best, though certain oxides, e.g. the oxide of zinc, may be used. The concentration of acids may be determined by precipi- tating and weighing their insoluble salts, such as barium sul- phate, silver chloride, and silver bromide. There are also certain reactions which are attended by the liberation or the consumption of definite quantities of acid, and some of these may be utilized to produce an acid of known strength, or to ascertain the 126 QUANTITATIVE EXERCISES strength of an acid of unknown concentration. An example of such reactions is furnished by the following equation : Na 2 S0 3 + H 2 + I 2 = Na 2 S0 4 + 2 HI. If the quantity of the iodine which takes part in the reaction is known, the quantity of the resulting hydriodic acid can be cal- culated, and this may be employed to determine the neutraliz- ing power of any solution of an alkali. A few of the methods of standardizing alkalies and acids will be given in greater detail. 1. By Means of Potassium Tetroxalate Potassium tetroxalate, KHC 2 O 4 H 2 C 2 O 4 - 2 H 2 O, may be used with advantage instead of oxalic acid. The salt is stable in the air at ordinary temperatures ; but, like oxalic acid, it cannot be dried in a hot-air bath or in a desiccator. It is best prepared in the following manner: A concentrated solution of oxalic acid is divided into two parts, one of which is slightly less than a fourth of the whole. The smaller portion is heated to the boiling point, treated with a little litmus, and carefully neutral- ized with pure potassium carbonate. The larger portion is then heated and the solution of potassium oxalate stirred into it. If any tetroxalate separates during the mixing of the liquids, the heating is continued, with addition of more water if neces- sary, until a clear solution is obtained. The solution is stirred while crystallizing to prevent the formation of large crystals, which are much more apt than the smaller ones to include mother liquor. The product should be recrystallized once or twice from pure distilled water. The crystals are collected in a funnel, in the b6tto,m of which a platinum cone or a perforated porcelain disk has been placed, and freed to the greatest possi- ble extent, with the aid of a filter pump, from mother liquor. Finally, they are washed with a little cold water and dried in the air upon unglazed porcelain plates. STANDARD SOLUTIONS OF ACIDS AND ALKALIES 127 The tetroxalate is a tri-basic acid with a molecular weight of 252.22 ; a normal solution of it would, therefore, contain in a liter- volume 84.0733 grams of the salt. 2. By Means of Sodium Carbonate The substance which has been longest and probably most frequently employed for the standardization of acids is the neutral anhydrous carbonate of sodium. It is prepared for use either from the acid salt or from the crystallized neutral car- bonate by heating in a platinum vessel until everything volatile has been expelled. The product is hygroscopic and must there- fore be preserved in closed bottles. The portion of the material which is to be used in any experiment should be reheated in a small platinum crucible or boat, cooled in a desiccator, and pro- tected from the moisture of the air while weighing by inclosing it in a weighing glass. If an indicator is used which, like lit- mus and phenolphthalein, is sensitive to carbonic acid, the neu- tralization of the carbonate must take place in a boiling solution. 3. By Means of Sulphuric Acid derived from Copper Sulphate If an aqueous solution of copper sulphate is subjected to electrolysis, it is quantitatively decomposed into metallic copper and free sulphuric acid. It is evident that if the sulphate is pure and the weight of it is known, the quantity of the acid which will be liberated can be calculated ; also that this known quantity of acid may be utilized to determine the strength of any alkaline solution, which may in turn be employed to standardize other acids. The sulphate should be purified by repeated crystallizations. It is stable in the air at ordinary temperatures, but cannot be dried in a desiccator or in a hot-air bath. The electrolysis may be effected in a platinum dish with precipitation of the copper upon the platinum, or in a beaker glass with use of any of the ordinary forms of platinum electrodes. CHAPTER VI THE DETERMINATION OF SPECIFIC GRAVITY DENSITY AND SPECIFIC GRAVITY The terms density and specific gravity, as they are ordinarily employed, have the same significance, though the former is usually applied to gases and the latter to liquids and solids. Both are used to signify the amount of matter in an object, or its mass, as compared with the mass of an equal volume of some standard substance. If any distinction between the terms is to be attempted, we might define density as the mass of a unit volume of any object, and specific gravity as the weight of a unit volume of the same; in which case density = -, , and volume specific gravity = p^ But this distinction is immaterial volume since in all the practice of the chemist the terms mass and weight have fundamentally the same significance. In a certain sense the term specific gravity is misleading, for it suggests the erroneous idea that the density of an object is in some way dependent on the force of gravity, which is a variable quantity. Water at 4 C. has been selected as the standard for the comparison of liquids and solids with respect to specific gravity or density. If the cubic centimeter and the gram are employed as the units of volume and mass, the unit of specific gravity and that of weight are in all respects identical, since both are the cubic centimeter of water at 4. The specific gravity of any liquid or solid may then be defined as the weight in a vacuum of one cubic centimeter of the substance, and conversely, the 128 THE DETERMINATION OF SPECIFIC GRAVITY 129 specific volume of any liquid or solid may be defined as the volume of one gram of the substance. Owing to the lightness of gases as compared with other forms of matter and also to the simple relation existing between their weights and those of the molecules of which they are made up, it is more convenient to employ some gas as the standard of density for this class of bodies. Hydrogen is usually made the standard for comparison. Accordingly the density of a gas may be defined as its weight in a vacuum as compared with the weight of an equal volume of hydrogen when measured under the same conditions of temperature and pressure. The molecu- lar weight of any gas may then be found by doubling its density, since hydrogen with a density of 1 has a molecular weight of 2, and the molecular weights of all gases are proportional to their densities. Air is also employed as a standard for the comparison of gases with respect to density. It is, however, ill adapted to the purpose owing to the variability of its composition. The density of an object changes with its volume and its volume varies with its temperature. It is therefore necessary to fix upon a standard temperature not only for the standard substance but also for all of those substances which are to be compared with it. As stated already, the standard temperature for water (the standard substance) is 4, the temperature of its maximum density. The standard temperature for other sub- stances is 0. A strict adherence to the latter standard is, how- ever, practicable only in the case of those substances whose cubical expansion coefficients are known. Hence in many instances it is possible only to give the specific gravity of a liquid or solid for the particular temperature at which it was experimentally determined. The temperature at which all gases are compared with respect to density is 0. Owing to their compressibility there is required for gaseous bodies a second standard, that of pressure. The standard pressure is that which will, at 0, support a vertical 130 QUANTITATIVE EXERCISES column of mercury 760 mm. in length. But, since the pressure required to support such a column of mercury varies with the intensity of the earth's attraction, it is necessary to define the latitude and altitude at which it shall be valid as a standard. The latitude and altitude agreed upon are 45 and sea level. EXERCISE XI DETERMINATION OF THE SPECIFIC GRAVITY OF SOLIDS I. DETERMINATION OP THE SPECIFIC GRAVITY OF A SILVER COIN There are required: 1. A thoroughly cleansed silver dollar or half dollar. 2. A fine platinum wire long enough to suspend the coin at the proper distance above the balance pan. 3. A beaker glass of recently boiled distilled water which has cooled to the temperature of the balance room. 4. A bridge to place over the balance pan as a support for the beaker. Weigh the coin and then suspend it in a loop on the end of the wire at the proper height above the pan. Remove the coin from the loop, leaving the wire in its place on the hook. Place the beaker of water on the bridge over the pan and weigh the wire with the loop submerged in the water. Remove the wire, replace the coin in the loop, suspend it in a beaker of hot water, and then boil until all air is expelled from the surface of the coin. Immerse the coin for a few minutes in cold water, and then transfer it, still wet, to the water on the bridge. Weigh the coin submerged in the water and note the temperature of the latter. The difference between the last weight and that of the wire with its loop submerged is the weight of the coin in water. The difference between the weight of the coin in air and in water is the weight of a volume of the water equal to that of the coin. THE DETERMINATION OF SPECIFIC GRAVITY 131 Correct the weight of the coin and that of the water displaced by it to a vacuum, using 0.0012 gram as the weight of a cubic cen- timeter of air; 8.4 and 21.5 as the specific gravities of the brass j i *. i A i.- i weight of coin and platinum weights respectively; r- j weight of displaced water as a sufficiently close approximation to the specific gravity of the coin ; and the proper value, to be found in the tables, as the density of the water. Divide the corrected weight of the coin, by the corrected weight of the water. The quotient is the specific gravity of the former as compared with water at the temperature of the experiment. To find the specific gravity of tlie coin as com- pared with water at 4, the result must be multiplied by the density of the water at the time of weighing the coin in it. An exact determination would also involve a correction for the expansion of the coin from to the temperature of the water at the time of the experiment; but since its expansion coeffi- cient is unknown, this correction cannot be applied. II. DETERMINATION OF THE SPECIFIC GRAVITY OF GLASS IN FRAGMENTS There are required : 1. A specific-gravity flask with a perforated stopper (Fig. 20). 2. From 10 to 15 grams of broken glass. Cleanse the flask first with an alcoholic solution of caustic potash and then with distilled water. Drain it thoroughly and wipe the outside with filter paper. Insert a cork through which have been passed a filled calcium chloride tube and a small glass tube which reaches nearly to the bottom of the flask. Aspirate air through the flask until it is dry. Weigh the flask by the method of Borda or Gauss, first empty and then with the glass whose specific gravity is to be determined. Cover the glass with distilled water. Place the flask under a bell jar which is connected with an air pump and exhaust until the 132 QUANTITATIVE EXERCISES air has been removed from the surface of the glass. Fill the flask with recently boiled distilled water and insert the stopper. Place it in a water bath having a temperature a few degrees above that of the balance room. Stir the water in the bath and keep it for a long time at a constant temperature, still above that of the balance room, by adding water of a higher temperature whenever neces- sary. Remove the flask from the bath, carefully cleanse the out- side with filter paper, and then allow it to stand for an hour or more in the balance case. Weigh by the same -method as before. Remove the broken glass, fill the flask with distilled water, heat in the bath to the same temperature as before, remove the flask, cleanse, cool and weigh it as in the first instance. Let P represent the weight of the flask, P, the weight of the flask and the glass, W the weight of the flask when filled with glass and water, and W, the weight of the flask when filled with water alone. Then P,-P is the weight of the glass a, and (P, -P ) + W W is the weight of the water displaced by the glass b. Reduce a and b to their weights in a vacuum, using - as the specific gravity of the glass, and divide the corrected value of a by the corrected value of b. The quotient will be the den- sity of the glass as compared with that of water when both have the temperature of the bath. We wish, however, to compare glass at with water at 4. For the purpose of explaining the method of applying the temperature corrections, we will assume that the temperature of the bath was 25 and let a and b represent the corrected weights of the glass and of the dis- placed water. The commonly accepted cubical-expansion coef- ficient of glass is 0.000025. Accordingly a unit volume of glass at becomes 1.000625 volumes at 25. A unit volume of water at 4 becomes 1.002868 volumes at 25. Now if we sup- pose the volumes of the glass and of the water to be kept constant by the addition of more material while the temperature of the THE DETERMINATION OF SPECIFIC GRAVITY 133 former falls from 25 to 0, and that of the latter from 25 to 4, the final weight of the glass will be a, x 1.000625 grams, and that of the water displaced will be b t x 1.002868 grams. Hence the specific gravity of the glass at as compared with , ... , a, 1.000625 water at 4 will be - x ' The student should familiarize himself with the use of Jolly's balance and of Nicholson's hydrometer for the determination of the specific gravity of solids. He should also work out in detail : 1. A method for determining, by weighing in water, the specific gravity of a substance which is lighter than water. 2. A method for determining, by weighing in benzene (sp. gr. 0.88), the spe- cific gravity of a substance which is soluble in water. 3. A method of determining the specific gravity of a substance by measuring the water, or other liquid, which it displaces. EXERCISE XII DETERMINATION OF THE SPECIFIC GRAVITY OF LIQUIDS I. WITH THE PYCNOMETER There are required: 1. An Ostwald (Fig. 21) or Sprengel (Fig. 22) pycnometer. 2. A quantity of pure benzene. Wet the outside of the instrument with distilled water and then dry it with filter paper. Suspend it by a platinum wire from the hook over the balance pan, and weigh. Attach to b a rubber tube, which is in turn connected with a full pipette, or with any other arrange- ment to prevent the entrance of saliva into the rubber tube, and immerse the end a in recently boiled distilled water which has cooled to the temperature of the room. Fill the apparatus by moderately diminishing the pressure within and Tl 0=t if FIG. 21 FIG. 22 134 QUANTITATIVE EXERCISES suspend it by the platinum wire in a bath of distilled water hav- ing a temperature slightly above that of the air. Maintain the bath for a considerable time at a constant temperature as directed in Exercise XI under II. Just before removing the instrument from the bath, touch the point a with filter paper until the liquid in the tube recedes to the mark c. If, by accident, too much liquid is withdrawn, the difficulty may be remedied by touching the end of the tube a with a drop of water on a glass rod. Remove the pycnometer from the bath, dry it with filter paper, and weigh when its temperature has fallen to that of the balance room. Empty the pycnometer, rinse with successive small por- tions of strong alcohol, then with ether which leaves no residue on evaporation, and dry by aspirating air through it. Fill the apparatus with benzene and proceed in exactly the same manner as when it was filled with water, being very care- ful to maintain the bath at the same temperature as before. Having found the relative weights (reduced to a vacuum) of equal volumes of water and benzene at the temperature of the bath, calculate the specific gravity of the latter at as com- pared with the former at 4, using 0.00138 as the cubical expansion coefficient of benzene. II. BY WEIGHING AN OBJECT IN Two LIQUIDS Construct a glass sinker, Fig. 23, with a little mercury in the bottom to increase its weight and to keep it in a vertical position when submerged in a liquid. The instrument should have a volume of from 10 to 15 cc. Place in the balance case two well-covered cylinders, one containing distilled water and the other pure benzene. Suspend IG ' the sinker by a platinum wire from the stirrup hook and weigh it, first in the air, next in the water, and finally in the hydrocarbon, taking care that the same length of wire is sub- merged in both liquids. Note the temperature of the water and of the benzene, which, of course, should be the same. THE DETERMINATION OF SPECIFIC GRAVITY 135 Let W represent the weight of the sinker in air, W w its weight in water, W b its weight in benzene. Then W W w is the weight of the water displaced by the sinker, and W W b is the weight of an equal volume of benzene. Reduce the weights to their values in a vacuum and find the density of benzene at as compared with that of water at 4. III. BY THE MOHR-WESTPHAL BALANCE The principle employed in the preceding experiment is util- ized in a convenient manner in the construction of the Mohr- Westphal balance, Fig. 24. There are several modifications of the instrument, but in its usual form it consists essentially of a beam without pans. One arm is shorter and heavier than the other and serves only as a counterpoise. The longer and lighter arm is graduated into ten equal divisions. At the end of the graduated arm is suspended by a platinum wire a thermometer which serves as a sinker. The adjustment is such that the balance is in equi- librium when the sinker is sus- pended in air. The weights are of three or four denominations in decimal order. The heaviest one is just equal to the loss in weight which the sinker suffers when it is immersed in water having a temperature of 15. Hence if the sinker is submerged in water of that temperature and one of the heaviest weights is placed upon the hook from which the sinker is suspended, the balance will again be in equilibrium. FIG. 24 136 QUANTITATIVE EXERCISES To determine at the same temperature the specific gravity of a liquid heavier than water, one of the heaviest weights is placed upon the hook, the sinker is immersed in the liquid, and other weights are then distributed along the arm until equilib- rium is obtained. Suppose we represent the weights in their descending order by A v A%, B, and (7, and that in a given experiment the distribution along the arm, when the balance is in equilibrium, is as follows: A l on the 10th division (i.e. on the hook), A l on the 5th, A 2 on the 3d, and B on the 9th. The specific gravity of the liquid is 1.539. When the specific gravity of a liquid lighter than water is to be determined, the weight A 1 is removed from the hook. Care must be taken that the depth to which the platinum wire is submerged in the different liquids is always the same. HYDROMETERS (AREOMETERS, DENSIMETERS) Instruments of this kind are constructed in accordance with the principle that a body will sink in a liquid which is specific- ally lighter than itself until it has displaced its own weight of the liquid. There are two classes of hydrometers. In one of these the immersion of the instrument is constant, and in the other vari- able. As examples of the first class, we have the hydrometers of Fahrenheit and of Nicholson ; and of the second, the volu- meter of Gay-Lussac, the ordinary specific-gravity spindles, the hydrometers of Beaume and of Twaddell, alcoholometers, etc. Of these two classes of hydrometers, examples of which are described in the following pages under A and B, only instru- ments of the seconoT variety, i.e. those of variable immersion, are employed by the chemist. Instruments belonging to the first class, i.e. those of constant immersion, are, however, of interest to him from the standpoint of the principles which are involved in their construction. THE DETERMINATION OF SPECIFIC GRAVITY 137 CLASS A B Instruments of Constant Immersion 1. FAHRENHEIT'S HYDROMETER This instrument, Fig. 25, is made wholly of glass. It con- sists (1) of a small bulb #, which is filled with mercury to keep the apparatus in a vertical position when swimming in a liquid ; (2) of a larger bulb 5, which gives to the instru- ment the necessary volume ; (3) a narrow tube LK< '( ! LAK WEIGHTS 157 will serve to illustrate the application of the chemi- cal method of determining molecular weights to substances which are neither acids nor bases. An analysis shows that in it C : II :: 1 : 1. The simplest formula which the compound can have is, therefore, CH. It is found, however, on treating ben- zene with chlorine that the hydrogen in it is replaced in several different stages, and that in the compound containing the least chlorine only one sixth of the hydrogen has been replaced. The molecule of benzene cannot, therefore, contain less than six atoms of that element. Moreover, since the quantities of hydrogen replaced by chlorine, or any other element or group of elements, always vary by one or more sixths of the whole and never by any smaller fraction, it is extremely improbable that the molecule contains more than six atoms of hydrogen. Hence the formula C 6 H must be assigned to benzene. PHYSICAL METHODS The so-called " physical methods " of determining molecular weights are all based on what are called by Ostwald the colr ligative properties of matter. Under certain conditions equal numbers of molecules produce equal effects, regardless of the chemical constitution and character of the molecules. Thus the volumes of gases under equal conditions of temperature and pressure are proportional to the number of gaseous mole- cules, and wholly independent of the composition of the mol- ecules. The pressures exerted by equal volumes of gases at the same temperature are likewise proportional to the number of molecules which they contain. The occupation, under the same conditions of temperature and pressure, of equal spaces by equal numbers of gaseous molecules, without regard to their weight or chemical character, is a " colligative " property of gases. If equal volumes of different gases, when measured under like conditions, contain the same number of molecules, the weights of such equal volumes are related to each other as 158 QUANTITATIVE EXERCISES are the molecular weights of the gases, and the determination of the density of a gas is equivalent to a determination of its molecular weight. Other colligative properties of matter on which may be founded methods of determining molecular weights are observed in cer- tain effects which are produced by substances in solution. The effects known as osmotic pressure, the lowering of the vapor tension of the solvent, and the depression of its freezing point are all proportional not to the weight of the different substances dissolved but to the number of the molecules contained in a unit volume of their solution. Under the same conditions equal numbers of molecules in a unit volume of a solution produce equal osmotic pressure, an equal lowering of the vapor tension of the solvent, and an equal depression of its freezing point. Hence we may determine the relative molecular weights of dif- ferent substances by finding what quantities of them will pro- duce these effects to the same degree; since these quantities are related to each other as are the molecular weights of the substances themselves. I. Dumas' Method At the present time the method of Dumas is rarely resorted to by chemists ; it will therefore not be described in great detail. By this method, which is applicable to easily volatilized liquids and solids, the molecular weight of a substance is deduced from the weight of a known volume of its vapor. The principle on which it is based is precisely the same as that which is employed in determining the densities and the molecular weights of gases by weighing. It is, in fact, a method for the determination of the densities of the vapors of substances at temperatures somewhat above their boiling points. A glass balloon, Fig. 30, having a capacity of from 100 cc. to 250 cc., is carefully cleansed, and dried internally by attaching to it a calcium chloride tube through which air is alternately DETERMINATION OF MOLECULAR WEIGHTS 159 pumped out and readmitted. The balloon is weighed, with a closed vessel of the same form and size as counterpoise, and the temperature of the air within the balance case and the height of the barometer are noted. The balloon is then warmed and its outlet is immersed in the liquid whose density is to be determined. On cooling, the liquid ascends into the balloon. After the introduction of several grams of the material, the balloon is placed in a bath which can be heated to a temperature considerably higher than the boiling point of the substance. Only the outlet is allowed to project above the liquid in the bath. The bath is heated to the re- quired temperature and constantly stirred. When nearly all of the liquid has distilled out of the balloon, the tem- perature of the bath is kept as constant as possible until no more vapor issues from the apparatus. The outlet is then closed with a blowpipe, and a record is made of the temperature of the bath and of the height of the barometer. The balloon is removed from the bath, cleansed, and weighed, and the temperature within the balance case at the time of weighing and the height of the barometer are again recorded. To determine the capacity of the balloon, a file mark is made on the small tube near the end ; the end of the tube is then immersed in mercury or recently boiled water, and the tip broken off. The liquid rises in the balloon, and should fill it completely, excepting, of course, the space occupied by the liquefied or solidified substance under investigation. As a rule, however, a bubble of gas remains in the top of the bulb, showing that the air was not all expelled by the vapors of the substance. The space occupied by the sub- stance is so small that it may safely be neglected, but the volume of the residual air must usually be determined. The pro- cedure by which the capacity of the apparatus and the volume of the air bubble are both ascertained is as follows : The balloon is submerged in the liquid until the air within is under atmos- pheric pressure, i.e. until the liquid within and that without are 160 QUANTITATIVE EXERCISES on the same level. The outlet is then closed with the finger and the bulb removed from the bath. The bulb is inverted and the air allowed to escape. If mercury has been used, the quantity of that metal required to complete the filling of the vessel is determined either by weighing or by measuring. The volume of the mercury thus introduced is equal to that of the air bubble. Finally, the capacity of the vessel is found by measuring or weighing the mercury which now completely fills it. If, on the other hand, water has been used, the vessel, after the escape of the air, is dried externally and weighed. It is then completely filled and again weighed. The difference between the two weights is the weight of the water whose volume is equal to that of the air bubble. The capacity of the vessel is calculated from the weight of the water which fills it. Having found the capacity of the balloon at the temperature of the last experi- ment, its capacity at the temperature of the bath when it was closed with the blowpipe is calculated in the usual manner. But there must be deducted from this the volume, at the same temperature, of the air which was not expelled by the vapors of the substance. The difference is the volume of the vapor at the temperature of the bath. As both the temperature of the bath and the height of the barometer were recorded at the time of closing the balloon, the theoretical volume of the vapor under standard conditions can be calculated. The weight of the vapor is found by deducting from that of the closed apparatus both the weight of the bulb and that of the air which remained in it at the time of closing. Having found the weight of the vapor and its theoretical vol- ume under standard conditions of temperature and pressure, the former is divided by the weight of an equal volume of hydrogen under the same conditions. The quotient is the density of the vapor as compared with that of hydrogen. To find the molecular weight of the substance, its vapor density must be doubled. The weight of the balloon enters twice into the calculation first in finding its capacity, and secondly in finding the weight DETERMINATION OF MOLECULAR WEIGHTS 161 of the vapor. But when the balloon was weighed in the first instance it was filled with air. To find its true weight, there- fore, we must deduct that of the air which was weighed with it. For the determination of the molecular weights of substances whose boiling points are too high to permit the use of glass, porcelain balloons have been employed. To close these, the flame of the oxy-hydrogen blowpipe is required. The materials used in the bath must be such as to permit the raising of the temperatures of the vapors several degrees above the boiling points of the substances, since at temperatures near their boiling points the vapors of substances do not sufficiently obey the laws of Boyle and of Gay-Lussac. II. The Method of Gay-Lussac (Hofmann's Modification) The method of Gay-Lussac is the converse of Dumas', since by it the molecular weight is deduced not from the weight of a known volume of the vapor but from the volume of the vapor of a known weight of the substance. The procedure of the author of the method was as follows : A gas-measuring tube about 400 mm. in length was filled with mercury and inverted in an iron bath half full of the same metal. A thin glass bulb completely filled with a known weight of the substance was introduced by placing it under the open end of the tube. A glass cylinder, open at both ends, also wider and somewhat longer than the measuring tube, was placed in the bath and the space between the eudiometer and the cylinder was filled with water, oil, paraffin, glycerin, or some other liquid which could be heated to a sufficiently high temperature. The bath was then heated to the desired temper- ature and kept as nearly constant as possible until the volume of the vapor no longer increased. Finally there were recorded (1) the volume of the vapor, (2) the length of the mercury col- umn within the measuring tube, (3) the temperature of the bath, 162 QUANTITATIVE EXERCISES and (4) the height and temperature of the barometer. From these data the theoretical volume of the vapor under standard conditions could be calculated ; and the weight of the substance divided by the weight of an equal volume of hydrogen gave the theoretical density of the vapor under the same conditions. The method in its original form is no longer in use. The principal objections to it are (1) the mercury bath, the vapors of which are poisonous ; (2) the difficulty of obtaining liquids to place between the measuring tube and the cylinder, which will remain transparent at high temperatures ; and (3) the shortness of the measuring tube. The method could be used only for the determination of the molecular weights of substances having comparatively low boiling points. Most of these diffi- "~~Jl culties were overcome by a modification of the method which was proposed by Hofmann. Hofmann's Method In the apparatus of Hofmann, Fig. 31, the measuring tube has a length of one meter. The advantage of the greater length is in the effect of diminished pressure on the boiling points of the substances whose molecular weights are sought. By enlarging the closed end of the tube and thus increasing the vacant space into which the substance evaporates, or by using very small quantities FIG 31 ^ ma t er ial it is practicable to determine the molecular weights of substances at temperatures several degrees below their boiling points under ordinary atmospheric pressure. A glass jacket 40 mm. wide and 90 cm. long is placed over the measuring tube in the position shown in the figure, and connected at the top with a vessel containing a liquid of suit- able boiling point. The vapor of the boiling liquid enters the jacket and passes out through the small tube at its lower end, heating the tube to the boiling point of the liquid. The sub- stance is inclosed in a minute flask (with a ground-glass stopper), DETERMINATION OF MOLECULAR WEIGHTS 163 which is just large enough to contain the quantity of material required for the determination. The experiment is made in the following manner : The meas- uring tube is filled with mercury, inverted, and its open end immersed in a dish of the same metal. The height and temper- ature of the barometer and of the mercury column in the tube are recorded. The little flask containing the weighed quantity of the substance, which must completely fill it, is brought under the open end of the tube and allowed to ascend into the vacuum above. As it reaches the top of the mercury column, the stopper usually flies out of the flask. It is, however, imma- terial whether it does so or not, since, unless the flask has been too tightly closed, it is soon expelled by the expanding material. The jacket is connected at the top with a flask or other vessel containing the liquid whose vapor is to heat the substance, and the exit tube at the bottom is attached to a condenser if nec- essary. The liquid employed depends on the temperature required. The liquids most frequently used are water, aniline (183), naphthalene (217), ethyl-benzoate (213), and amyl- benzoate (261). The liquid in the vessel connected with the jacket is boiled until the volume of the vapor in the measuring tube no longer increases. There are then recorded (1) the vol- ume of the vapor, (2) the length of the mercury column above the lower end of the jacket, (3) the length of the mercury column below the jacket, i.e. that portion of the column which is not heated by the vapor of the boiling liquid, (4) the tem- perature, as nearly as it can be determined, of the mercury in the tube at a point halfway between the lower end of the jacket and the surface of the metal in the dish, and (5) the height and temperature of the barometer. In finding the pressure under which the vapor was measured (by subtracting the corrected height of the mercury column in the measuring tube from the corrected height of the barom- eter) the two portions of the mercury column, having different temperatures, must be separately reduced to their length at 164 QUANTITATIVE EXERCISES 0. It will be seen that the correction of the height of the mercury column is at best only approximate, owing to the lack of uniformity in the temperature of its different parts. Several plans for overcoming this difficulty have been proposed. Of these, the most obviously practicable one is to make the mer- cury cistern narrower and so to lengthen the jacket that it will inclose both the eudiometer and the cistern. The correc- tion for the tension of the mercury vapor is made by subtract- ing from the corrected pressure the tension of the metal for the given temperature as found in the tables. The measuring tube should be calibrated, and if any considerable degree of accuracy is required, a correction for the expansion of glass must be applied. The use of the Gay-Lussac method and of the Hofmann modi- fication of it is necessarily limited to substances whose boiling points are considerably below that of mercury. At temperatures above 300 it cannot be employed with advantage owing to the great tension of the mercury vapor. Determination of the Volume of a Vapor by Means of the Pressure which it Exerts The volume which a gas would have under standard condi- tions of temperature and pressure may be deduced from the pressure which it is found to exert when confined, at any given temperature, in a space of known volume. Hence the molecular weight of a volatile substance may be ascertained by determining the pressure exerted by a known weight of its vapor in a vessel of known capacity. Modifications of the Gay-Lussac method, which are based upon this principle, have been proposed by Bell and Teed (Journal of the Chemical Society, 1880, 1, 576), and by Malfatti and Schoop (Zeitschrift fur physikalische Chemie, 1887, 159). . DETERMINATION OF MOLECULAR WEIGHTS 165 Determination of the Volume of a Vapor by measuring the Liquid or the Gas which it Displaces Methods of this kind are identical in principle with that of Gay-Lussac, since they differ from it only in the manner of determining the volume of the known weight of vapor. This is ascertained indirectly by measuring the volume of a liquid (usually mercury) or of a gas (air, hydrogen, or nitrogen) which the vapor displaces. The best known and most useful of these methods is that of Victor Meyer. EXERCISE XIII DETERMINATION OF THE MOLECULAR WEIGHT OF CHLOROFORM BY THE METHOD OF MEYER The simplest form of the Meyer apparatus is shown in Fig. 32. It consists of three parts : (1) a glass tube in which a weighed quantity of the substance is converted into a vapor ; (2) a glass, or better, in many cases, a metallic, mantle or bath, in the bottom of which is placed the liquid to be heated for the purpose of producing the required temperature ; and (3) a graduated tube in which is collected the air or other gas displaced by the vapor of the substance. The total length of part 1 is about 800 mm. Its lower and larger end b has a capacity of about 100 cc. The narrower portion, between b and the cuplike enlargement at the top, has an internal diameter of about 6 mm. The side tube a, through which the displaced gas passes into the measuring tube, is joined to the main tube at a point about 100 mm. from the upper end of the latter. Its internal diameter should not much exceed 1 mm. The mantle has a diameter of 40 mm. and a length of 520 mm., exclusive of the bulblike enlargement at \HJ the lower end, the capacity of which is about 80 cc. FIG. 32 166 QUANTITATIVE EXERCISES Thoroughly cleanse the apparatus by washing it with alcohol, and then with ether which leaves 110 residue 011 evaporation. Attach a calcium chloride tube to a, insert a stopper through which is passed a long glass tube reaching to the bottom of 6, and aspirate air through the apparatus until it is dry. Place a quantity of ignited asbestus in the bottom of b. Fill the bulb c nearly full of distilled water, and clamp the mantle in an iron stand at such a height that when the stand is upon the floor, the tube a will be a little above the top of the work table. Arrange all parts of the apparatus as indicated in the figure. Select a tightly fitting, singly perforated rubber stopper for d. Pass through it, from the upper end, a short glass tube provided with a ground stopcock. The tube need not have an external diameter of more than 5 mm. The channel through the stopcock should, however, be relatively large. Blow a bulb with a capacity of 0.3 or 0.4 cc. on the end of a thin small glass tube, Fig. 33. Weigh the bulb, immerse the open end of the stem in pure chloroform, and, by alternately warming and cooling the bulb, introduce from 0.2 to F 33 0.3 cc. Dry the wet end of the stem with filter paper and close it in the flame. Weigh again. Pass the stem of the bulb through the stopcock, as shown in Fig. 33, and fix it in position by turning the latter until it presses lightly against the stem. Insert a stopper in d. Boil the water in c vigorously. Immerse the outlet of a in the dish of water e. When no more air issues from the apparatus, fill the gas-measuring tube with water and invert it over the outlet of a. Replace the stopper in d by the arrangement represented in Fig. 33, and, after about one minute, close the stopcock. The stem will be cut and the bulb containing the chloroform will fall upon the asbestus in the bottom of b. The chloroform is converted into vapor, and a volume of air equal to that of the vapor is transferred from the upper part of the apparatus to the measuring tube. The air in passing through the water is cooled, and its volume when measured is therefore OF MOLECULAR WEIGHTS 167 smaller than that of the vapor of the chloroform. This, how- ever, is not a source of error, since, if the air transferred and the chloroform vapor were of the same temperature, the latter would theoretically have suffered the same contraction in con- sequence of an equal lowering of temperature. The condition that the air forced out of the apparatus shall have the same temperature as the vapor whose density is to be determined is an essential one, for if its temperature is lower, the contraction in passing through the water will be too small, and the volume of the air collected in the measuring tube will therefore be too large. It cannot, however, be fully realized, since the air in the outlet tube, which is the first to be forced into the eudiometer, has a temperature very near that of the outside atmosphere. It is for this reason that the bore of a is made as small as is practicable. The heating is to be continued until, for a space of two min- utes, no more air is expelled. The air is then measured and its volume under standard conditions is found in the usual way. The weight of the chloroform divided by the weight of an equal volume of hydrogen is the theoretical density of the chloroform, and its density is one-half its molecular weight. The original apparatus of Meyer was closed with a simple rubber stopper, which was removed at the time of introducing the substance and then quickly replaced. The compression pro- duced by the insertion of the stopper caused the expulsion of a few bubbles of air which were allowed to escape before placing the eudiometer in position over the outlet. Under these con- ditions the success of the determination depended very much upon the good judgment and the alertness of the experimenter. Hence a number of modifications of the apparatus were soon proposed, which obviate the necessity of opening it at the time of dropping the substance into the heated chamber below. The accompanying Fig. 34, A, B, and (7, represents some of the 168 QUANTITATIVE EXERCISES modifications which are now in common use. In -4, the tube containing the substance is released by turning the bent wire which passes through the stopper ; in B, by turning the stop- cock; and in C, by drawing to the left the wire in the hori- zontal tube. A distinct disadvantage in all of these devices is the necessity of introducing the substances in open tubes, and of leaving them for some time exposed to a more or less elevated temperature. If tubes with ground-glass stoppers are substi- tuted for the open ones, the determinations are often lost in consequence of their failure to release the stoppers even when heated above the boiling points of the substances. These difficulties are obviated in the case of liquids by using the arrangement prescribed in the preceding exercise. If the fe A V substance is a solid, a narrow tube is closed at one end and then drawn out at a point near the closed end, leaving a pas- sage just large enough for the introduction of the material. The tube is weighed^ the substance introduced, and its weight ascertained. The tube is then fused off at the proper distance from the substance, leaving a stem which is passed through the stopcock in the manner already described. When a substance is liable to be attacked by oxygen at the temperature required for the determination of its molecular weight, the air in the apparatus is displaced by some other gas, such as nitrogen or hydrogen. And when the temperatures are DETERMINATION OF MOLECULAR WEIGHTS 169 too high to permit the use of glass vessels, an apparatus of platinum or of porcelain is employed. The following list con- tains the names and boiling points of some of the substances which are used in the bath of the Victor Meyer apparatus. Water (100), amyl-alcohol (130), xylene (137 to 143), aniline (182.5), ethyl-benzoate (213), amyl-benzoate (261), diphenyl amine (310), mercury (357.25), sulphur (448.4), phosphorus pentasulphide (518), stannous chloride (606). For the deter- mination of molecular weights at still higher temperatures, a gas or a coal furnace is employed. THE FREEZING-POINT METHOD When a substance is dissolved in a liquid the freezing point of the latter is lowered, and the observed depression is, in gen- eral, very nearly proportional to the concentration of the solu- tion. In other words, if one gram of sugar is dissolved in 100 grams of water, the latter will no longer freeze at 0, the freez- ing point of pure water, but at some lower temperature ; if two grams of sugar are dissolved in the same quantity of water, the observed depression of the freezing point will be double that of the solution containing one gram, etc. The depression of the freezing point which is observed in a one-per-cent solution of a substance in any given liquid, i.e. when one gram of the substance is dissolved in 100 grams of the liquid, is called the specific depression of the freezing point of the liquid for the particular substance. If different substances, in quantities proportional to their respective molecular weights, are dissolved in equal weights of any given liquid, the different solutions will as a rule be found to have the same freezing point. From this fact is drawn the conclusion that the extent of the depression in the case of any given liquid is determined solely by the numerical ratio of the molecules of the dissolved substance and of the solvent. In other words, equal numbers of molecules, when dissolved in 170 QUANTITATIVE EXERCISES equal quantities of any given liquid, produce an equal lowering of the freezing point whether the molecules are of the same kind or of different kinds. The depression of the freezing point which results from dis- solving in 100 grams of a liquid a number of grams equal to its molecular weight is called the molecular depression of the freez- ing point of the liquid for that substance. The molecular depression is equal to the product of the specific depression and the molecular weight of the substance. For any given liquid the molecular depressions for different substances have a nearly con- stant value. This constant may be determined experimentally by dissolving in a known weight of a liquid a weighed quantity of some substance of known molecular weight, and ascertaining the depression of the freezing point ; or it may be calculated, when the requisite data are at hand, by the equation of Van't Hoff : T 2 C= 0.02 , in which C is the constant to be found, T the absolute freezing point of the liquid, and W its latent heat of fusion. The following table gives the molecular depression of the freezing point of several liquids as found by experiment and by calculation. BY EXPERIMENT BY CALCULATION Water 18.8 18.7 Acetic acid 39.0 38.8 Formic acid 28.0 28.4 Benzene 50.0 53.0 Nitrobenzene 70.0 69.5 Phenol 74.0 77.0 Naphthalene ., 69.0 69.4 If the molecular depression of the freezing point of any solvent is divided by the molecular weight of the same, the quotient is the depression which one molecule of any substance, behaving normally in solution, will produce in 100 molecules of DETERMINATION OF MOLECULAR WKKJIITS 171 the solvent. This value is, of course, constant for any given solvent, but, contrary to the conviction of Raoult, it varies with different solvents. There are many exceptions to the rule that equi-molecular quantities of different substances produce, in a fixed quantity of any given solvent, an equal lowering of the freezing point. For example, when water is used as a solvent, molecular-equiv- alent quantities of the class of bodies known as electrolytes acids, bases, and salts produce a much greater depression of the freezing point than equivalent quantities of indifferent sub- stances, such as the sugars and urea. Hydrochloric, hydrobromic, hydriodic, and nitric acids, also the hydroxides and the halogen salts of the metals of the alkalies, produce in dilute aqueous solutions nearly twice the normal depression of the freezing point. This conduct on the part of electrolytes is not regarded as invalidating the law that equal numbers of molecules pro- duce equal effects. It is supposed, rather, to indicate that, in aqueous solutions, the molecules of the bodies in question suffer a certain kind of dissociation. In benzene, nitrobenzene, and ethylene bromide, on the other hand, the alcohols and the organic acids produce only about one-half the normal depres- sion of the freezing point. This conduct is supposed to be due to the existence in such solutions of double molecules, e.g. (C 2 H 4 O 2 ) 2 , instead of C 2 H 4 O 2 , since the same substances in other solvents produce normal depressions. To determine the molecular weight of any substance by the freezing-point method, a small weighed quantity of it (g} is dis- solved in a weighed quantity of some solvent (G) in which it is supposed to behave normally, and whose molecular depression (c) is known. The freezing point of the solvent is determined before (t) and after (,) the introduction of the substance. The depression (t 1 1 ) is represented by d. Having found the depres- sion d, which g grams of the substance produce in G grams of 172 QUANTITATIVE EXERCISES the solvent, it is necessary to find how much of it would produce an equal depression in 100 grams of the solvent, since the con- stant c is calculated for that weight of the liquid. This is done by means of the proportion xslOO ::*:(?. x G If 100 grams of the substance produce the depression d in G 100 grams of the solvent, the quantity (m) which will produce the molecular depression is lOOc ^-, since Gd . G Gd The process by which c is obtained is such that m is equal to the molecular weight of the substance. The formula m = 10 c - Gd is general, and to obtain the molecular weight of any substance it is necessary only to substitute in it the proper numerical values of (7, #, (7, and d. The method is applicable only to quite dilute solutions, and appears, in general, to give the most satisfactory results in those which are about one-tenth normal. The thermometer which is used both in the freezing-point and in the boiling-point methods of determining molecular weights was devised by Beckmann, Fig. 35. Its characteristic feature is the reservoir at the top to which a portion of the mercury in the bulb may be transferred. The scale is divided into hundredths and has a total range of only five or six degrees. It is practicable, by transferring portions of mercury from the bulb below to the reservoir above, or from the reser- voir to the bulb, to adjust the instrument for use at widely different temperatures. Suppose, for instance, that it is required to measure changes of temperature between 34 and 38, and that the range of the scale is nominally 6. The bulb is placed in water having a temperature of about 40. If the mercury DETERMINATION OF MOLECULAR WEIGHTS 173 FIG. 35 rises to the top of the scale or slightly above it, there is no need of readjustment, since, in that case, the upper end of the mercury column will be within the scale both at 34 and 38. If the mercury rises and flows over into the reservoir, the column, when the mercury ceases to expand, is broken off at its highest point by striking the bulb against the palm of the hand. The thermometer will then register any temperature between the desired limits. If, on the other hand, the mercury on being heated to 40 does not enter the scale, or ascends only part way through it, a portion of the metal in the reservoir must be trans- ferred to the bulb. This transference is accom- plished in the following manner : The mercury above is forced into the upper end of the res- ervoir by striking the top of the thermometer against the hand. The bulb is then heated until the mercury in it rises and joins that in the reservoir. Finally, the bulb is placed in water of 40, and the column broken in the manner previously described. It is to be observed that the divisions upon the scale of the Beckmann thermometer have a somewhat variable value owing to the fact that the quantity of mercury in the bulb varies according to the temperatures for which the thermometer is adjusted. In other words, the value of the scale as a measure of changes of temperature (of depressions and elevations) depends on the quantity of the contracting or expanding mer- cury in the bulb. If the quantity is diminished, as it must be for the higher temperatures, the value of the scale is correspond- ingly increased ; if, on the other hand, a portion of the mercury is transferred from the reservoir to the bulb to prepare the instrument for use at lower temperatures, the value of the scale FIG. 36 174 QUANTITATIVE EXERCISES is diminished. Errors from this source may require attention when a thermometer is used for widely separated temperatures ; as, for example, when the same instrument is employed for the determination both of freezing and of boiling points. The method which is here suggested for the correction of such errors is as follows : The value of the scale, when the mercury in the bulb is in the vicinity of 0, is determined by comparing the instrument with a standard thermometer. If now the ther- mometer is used at a higher temperature, requiring a transfer to the reservoir of a portion of the mercury in the bulb at 0, the observed depressions or elevations, in terms of the value which the scale has at 0, are to be multiplied by 1 -f- 1% in which t is the higher temperature, and 7 the apparent expansion of mercury in glass, i.e. the dif- ference between the cubical expansion of mercury and of glass. If, on the other hand, the instrument is used at a lower tem- perature, , requiring a transfer of some of the mercury in the reservoir to the bulb, the observed depressions or elevations are to be multiplied by 1 ^7. The determination of the value of the scale, when the mer- cury in the bulb is in the neighborhood of 0, is made in the following manner: The mercury above is forced into the end of the reservoir nearest the bulb, and the mercury in the bulb is warmed until it rises and forms a junction with that in the reservoir. The bulb is placed in water having a temperature of 7 or 8, and, when the mercury comes to a standstill, the thread is broken off at its highest point. The bulb is now placed in ice water. The top of the thread should recede nearly to the zero mark of the scale. If it does not, or if it descends below that point, the experiment is repeated, using warmer or colder water for the first immersion, as the case may require. The following considerations will serve to explain the pro- posed method of correcting the Beckmann thermometer. Sup- pose an instrument of this'kind is so adjusted that the end of the thread is within the scale when its bulb is in ice water. DETERMINATION OF MOLECULAR WEIGHTS 175 Depressions and elevations of temperature in the vicinity of can now be measured in terms of the scale. Suppose, however, it is desired to measure changes of temperature around some higher temperature t. A portion of the mercury in the bulb must be transferred to the reservoir, and the value of each scale division is thereby increased in the same proportion as the quantity of the mercury in the bulb is diminished. If we let m represent the quantity of mercury in the bulb when the instru- ment is adjusted for 0, then the quantity in the bulb when it is adjusted for the higher temperature t will be m mty. The values of a scale division are, of course, inversely propor- tional to the quantities of mercury forced into the stem from the bulb in consequence of a given rise of temperature, and these are directly proportional to the quantities in the bulb. If we repre- sent by unity the quantity of mercury which will enter the stem in consequence of a given rise of temperature when the instru- ment is adjusted for 0, then the quantity #, which will enter when it is adjusted for t c , will be found by the proportion m : m mty : : 1 : x. x = l- ty. That is, if we know the value of the scale when the temperature is in the vicinity of 0, we can find its value in the vicinity of any higher temperature t by multiplying by 1 4- ty. In the same way it may be shown that, knowing its value in the vicinity of 0, we can find its value at any lower tempera- ture t by multiplying by 1 ty. The mercury exhibits a strong inclination to stick in the capillary tube of the Beckmann thermometer. This tendency manifests itself more strikingly with a falling than with a rising temperature. It should be overcome, as far as possible, when- ever a reading is to be made, by tapping the thermometer near the top with some hard object. A device for this purpose, which has been used with advantage, is a minute vibrating electrical hammer attached to the top of the instrument. 176 QUANTITATIVE EXERCISES Figures 36 and 37 represent the forms of the Beckmann apparatus which are in common use for the determination of molecular weights by the freez- ing-point method. The tube A, Fig. 36, which contains the sol- vent whose freezing point is to be determined both before and after the introduction of the substance, is separated from the freezing mixture in C by the wider tube B. The substance to be investigated is intro- duced through the side tube Z>. The stirrers E and F, the for- mer of which is best made of stout platinum wire, are em- ployed to equalize the temper- ature of the liquid in A and of the freezing mixture in C. The apparatus represented in Fig. 37 is used when the sol- vent, like glacial acetic acid, is hygroscopic. The only essen- tial difference between it and that in Fig. 36 is the arrangement , through which dry air is passed during an experiment. The tube G is of such internal diameter that the stirrer which passes through it can be worked up and down without friction. To its side is attached the bulb tube H, in which a small quantity of concentrated sulphuric acid is placed. The acid is prevented from spattering into the solvent by a disk which is fastened in a horizontal position to the wall of the larger bulb. The air is dried before entering H by passing it over pumice stone which has been moistened with sulphuric acid. FIG. 37 FIG. 38 DETERMINATION OF MOLECULAR WEIGHTS 177 Solid substances which dissolve readily are best introduced in the form of compressed tablets. These are easily prepared by stamping the requisite quantity of the loose material in a small pastil press such as is used in making medicinal tablets. Liquids are introduced by means of the pipette shown in Fig. 38. EXERCISE XIV DETERMINATION OF MOLECULAR WEIGHTS BY THE FREEZING-POINT METHOD 1. UREA Bring into the tube A a weighed quantity of distilled water which will somewhat more than suffice to cover the bulb of the thermometer, and into C a mixture of broken ice, coarse salt, and water. Remove A from B and immerse it for a time in the freezing mixture. Return it, after drying the outside, to its place in B. Let the water in it cool somewhat below the freez- ing point, and then stir vigorously until ice begins to form, tak- ing care not to let the stirrer rub against the bulb of the ther- mometer. The thermometer will rise a little and then become stationary. The highest temperature is the true freezing point of the water. Remove the tube A after considerable ice has formed, and continue to stir until the mercury in the ther- mometer is observed to rise. Repeat the experiment several times. Remove A and introduce through the side tube in com- pact form a quantity of pure urea which is calculated to give a nearly one-twentieth molecular-normal solution. Stir until the urea is dissolved and the ice has nearly, but not quite, all melted. Return A to its place in B. Let the solution cool for a short time and then stir until ice again forms. The thermometer will rise, become stationary for a few moments, and then begin to fall. The highest temperature reached is the one to be recorded. Remove J, stir vigorously, and observe the thermometer while the ice is melting. Repeat the experiment several times. 178 QUANTITATIVE EXERCISES Add three other small quantities of urea, each about equal to the first, and determine the freezing point after each addition. Calculate the molecular weight of urea from the depression of the freezing point, which was observed for each concentra- tion, using 18.9 as the molecular depression of water. Deduce also from the observed depressions and the known molecular weight of urea the molecular depression of the freezing point of water. If stirring the under-cooled solution fails to induce freezing, the difficulty may be overcome by introducing a minute frag- ment of ice. The effect of so doing upon the concentration of the solution is, of course, insignificant. The same course is to be followed when other solvents than water are used. If no crystals of the solvent are at hand, they may be prepared by freezing a little of the pure liquid in a small test tube. A con- venient method for the preparation of crystals to be used in starting the freezing of the solvent has been described by Beck- mann (ZeitscJirift fur physikalisehe Chemie, 7, 329). The concentration of the solution is, of course, increased by the freezing of a portion of the solvent. This explains the falling of the thermometer which is observed to follow its rise when freezing begins. Since the quantity of ice which will be formed is determined by the amount of the under-cooling, the error due to such an increase in concentration may be dimin- ished by cooling the solution only slightly below its freezing point. The increase in concentration may be calculated by the formula r = in which A r is the fraction of the solvent which solidifies in consequence of the under-cooling, the degree of the under-cooling which preceded solidifica- tion, c the specific heat of the solvent, and X the heat of solidification of a unit quantity of the solvent. DETERMINATION OF MOLECULAR WEIGHTS 179 2. CANE SUGAR Proceed as directed under 1, using water as the solvent and " rock candy " as the material to be experimented upon. 3. CHLOROFORM The glacial acetic acid which is used as the solvent in this experiment must be carefully protected from the moisture of the air. It is advisable to use the apparatus represented in Fig. 37, and to conduct air dried by sulphuric acid through G. Glacial acetic acid, when pure, melts at 16.75. It is, however, hygroscopic and is therefore usually found to fuse at a lower temperature. The presence in it of a small quantity of water does not interfere with its use as a solvent, provided the same is not acquired during the course of an experiment. Glacial acetic acid gives normal results with nearly all sub- stances which dissolve in it without chemical action. The molecular depression of its freezing point is 39. THE BOILING-POINT METHOD If a nonvolatile substance is dissolved in a volatile liquid, the vapor tension of the latter is diminished and its boiling point is therefore raised. The effects produced by substances in solution upon the vapor tension and boiling points of liquids are in all respects analogous to those produced upon their freezing points. In the case of a given solvent and soluble substance, the lowering of the vapor tension at any given temperature and the consequent elevation of the boiling point are proportional to the concentration of the solution. Again, equi-molecular quantities of different substances, when dissolved in the same weight of any given liquid, produce an equal lowering of the vapor tension, and consequently an equal elevation of the boiling point of the solvent. No practicable method has yet been devised for the determi- nation of molecular weights by measuring directly the effect of 180 QUANTITATIVE EXERCISES substances in solution upon the vapor tension of the solvents. It has been found easier to utilize for this purpose the temperatures of equal- vapor tension, i.e. the boiling points of the solvents. The definitions employed are similar to those which were given in connection with the freezing-point method. 1. The specific elevation of the boiling point of any liquid is that which is observed when 1 gram of a substance is dissolved in 100 grams of the solvent. Obviously the specific elevations produced by different substances are inversely proportional to the molecular weights of the substances. 2. The molecular elevation of the boiling point of a liquid is that which is produced when a number of grams of a substance equal to its molecular weight is dissolved in 100 grams of the solvent. In the case of any given substance, the molecular ele- vation is equal to the product of the specific elevation and the molecular weight of the substance. It is a constant for any given solvent in the same way and with the same limitations as the molecular depression of the freezing point. Like the latter, it may be determined experimentally by operating with weighed quantities of the liquid and of some substance of known molec- ular weight, or it may be calculated by means of the formula 7^2 (7=0.02 , in which C is the constant to be found, T the absolute boiling point of the liquid, and W its latent heat of vaporization. The following table gives the molecular elevation of the boil- ing points of several liquids. Ether 21.1 Benzene 26.7 Acetone 16.7 Water 5.2 Chloroform . . . . 36.6 Acetic acid .... 25.3 Carbon bisulphide . 23.7 Ethylene bromide . 63.2 Alcohol 11.5 Phenol 30.4 Ethyl acetate . . . 26.1 Aniline 32.2 Methyl alcohol . . 9.2 Isopropyl alcohol . . 12.9 DETERMINATION OF MOLECULAR WEIGHTS 181 If the molecular elevation of any solvent is divided by the molecular weight, the quotient is the elevation of the boiling point which one molecule of any substance, not dissociating in solution, will produce in 100 molecules of the solvent. The method of deducing the molecular weight of a substance from the effect which it produces on the boiling point of a liquid is the same as that employed in the freezing-point process. If g grams of the substance produce an elevation e in G grams of the solvent, then the quantity of the substance which will produce" the same elevation in 100 grams of the solvent is 100 g ; for x : 100 : : g : G. Again, if 100 $- grams of the G G substance produce the elevation e in 100 grams of the solvent, the quantity which will produce the molecular elevation is 100 C-&-, since Ge G Ge m represents the molecular weight of the substance, and its value is found by substituting in the formula the numerical values of (7, #, G, and e. As might be expected from their behavior when tested by the freezing-point method, the class of bodies known as electro- lytes gives, when dissolved in water, abnormal elevations of the boiling point. In benzene, chloroform, and carbon bisulphide, certain bodies, especially hydroxyl compounds, give less than the calculated elevation of the boiling point. This is supposed to be due to the existence in such solutions of complex molecules, consisting either of the dissolved substance and the solvent, or of the former only. The results, however, become more nearly nor- mal with increasing dilution. When a substance of unknown molecular weight is to be investigated, it is safer to test its effect upon the boiling points of several liquids. 182 QUANTITATIVE EXERCISES With reference to the selection of a solvent for any particu- lar determination, it is to be observed that the liquid chosen should be one in which the substance is very readily soluble, also that its boiling point should be, in general, not less than 130 or 140 lower than that of the substance to be investi- gated. If the boiling points of the substance and of the avail- able solvents are too near together, the freezing-point rather than the boiling-point method should be employed. As a rule, the best results are obtained when ether, alcohol, ethyl acetate, acetone, acetic acid, formic acid, thymol, and phenol are used as solvents. A number of forms of apparatus for the determination of molecular weights by the boiling-point method have been devised and ~ recommended. Only one of them, that of H. C. Jones, Fig. 39, will be described here. It consists of a glass tube A, 180 mm. in length and 40 mm. in diameter, to the side of which is attached the smaller tube a. It is contracted at the top to a diameter of about 27 mm. arid ground to receive a light glass stopper, which is inserted when the apparatus is to be weighed. The tube is filled with glass beads to a height of 30 or 40 mm., and into these is pressed to a depth of 15 or 20 mm. the platinum cylinder P, which has a length of 80 mm. and a diameter of 25 mm. The space within the platinum cylinder, under and around the bulb of the thermometer, is filled with scraps of platinum foil whose corners have been bent in different directions to prevent too close packing and whose edges have been serrated to facilitate the escape of vapor. The condenser tube which enters at a is provided at the top with a U-tube containing some drying agent. The apparatus is surrounded by a jacket of asbestus Jf, 120 mm. FIG. 39 DETERMINATION OF MOLECULAR WEIGHTS 188 in height and 15 mm. in thickness, which rests on an asbestus board having a hole in the center. The hole is covered with a piece of wire gauze. EXERCISE XV DETERMINATION OF MOLECULAR WEIGHTS BY THE BOILING-POINT METHOD 1. IODINE Adjust the thermometer so that the upper end of the mer- cury column will be in the lower part of the scale at the boiling point of ether. Carefully cleanse and dry the apparatus, especially those parts which will afterwards come in contact with the solvent, and arrange the beads, platinum cylinder, and platinum scraps as indicated in the description of the apparatus. Close A with the ground-glass stopper and the side tube a with an ether-tight cork and weigh. Introduce somewhat more anhydrous ether than is necessary to cover the bulb of the thermometer when in place and weigh again. If a balance of sufficient capacity to permit the weighing of so heavy a load is not available, the solvent must be weighed separately. Arrange everything as shown in the figure; heat cautiously and determine the boiling point of the ether. Several observa- tions should be taken at considerable intervals of time, and the height of the barometer should be recorded with each observa- tion of the temperature. The thermometer must be vigorously jarred just before reading, and the reading should be made after a rise rather than after a fall of temperature. This may always be done by allowing the liquid to cool a little and then reheat- ing it to its boiling point. Introduce through the side tube, when the ether is cold, from 0.5 to 0.7 gram of dry resublimed iodine, and again deter- mine the boiling point, recording, as before, the height of the barometer. Afterwards introduce several other small weighed 184 QUANTITATIVE EXERCISES portions of iodine, from 0.1 to 0.2 gram, determining the boil- ing point after each addition. Finally, when the apparatus has cooled, weigh again in order to ascertain whether any ether has been lost during the experiment. Calculate the molecular weight of iodine from the results of the individual determinations and from the total observed ele- vation of the boiling point, using 21.1 as the molecular eleva- tion of the boiling point of ether. Calculate also from the observed elevation and the known molecular weight of iodine the molecular elevation of the boiling point of the solvent. 2. NAPHTHALENE Proceed exactly as directed under 1. The boiling solution has something more than its calculated concentration, owing to the absence of a portion of the solvent in the form of vapor and of returning liquid. Errors from this cause are reduced to a minimum by carefully regulating the rate of boiling, which should not be more rapid than is neces- sary for the maintenance of a constant temperature and to prevent the overheating of the liquid. The temperature indicated by the thermometer varies some- what according to the depth to which the bulb is submerged in the boiling liquid. It is therefore well to maintain the same degree of submergence through the whole course of any single determination of a molecular weight. The most serious difficulty which is encountered in the use of the boiling-point method is the variability of atmospheric pressure. A rise or fall of one millimeter in the barometer is followed by a change of boiling point amounting in the case of most liquids to nearly .03. It is obvious that the real results of a determination may be wholly masked in consequence of such barometric fluctuations as frequently occur within the time required for an experiment. This difficulty may be met more or less successfully in various ways. DETERMINATION OF MOLECULAR WEIGHTS 185 1. A second apparatus containing the solvent only may be placed beside that in which the determination is made. If the liquids in both are boiled under the same conditions, as nearly as possible, and if the two thermometers are read simultane- ously, the observed fluctuations of the boiling point of the pure solvent may be applied as corrections to the observed elevations of the boiling points of the solution. 2. A pressure regulator may be employed (see Zeitschrift fur physikalische Chemie, 11, 25). 3. All observed boiling points may be corrected to standard pressure by means of the formula To Correction = n , in which oO T is the absolute boiling point of the liquid under standard pressure, c a constant depending upon the chemical nature of the solvent, and n the difference in millimeters between 760 and the observed height of the barometer. The value of c for several different liquids, also the meaning of the formula and the manner of using it, will be found on page 191 of the second edition of Landolt and Boernstein's Physikalisch- Chemische Tabellen. CHAPTER VIII THE PURIFICATION OF SUBSTANCES The preparation of substances in pure condition and the maintenance of their purity are obviously matters of the highest importance in quantitative chemistry ; nevertheless, but little of a comprehensive character which is likely to be useful to the student can be said upon these subjects. The processes of purification and the measures adopted to prevent contamination must be constantly modified to suit the conditions, i.e. the char- acter of the substances to be purified and the nature of the impurities to be removed or guarded against. Hence a minute knowledge of the reactions of the substances concerned, rather than of general rules, and vigilance are essential to a judi- cious selection of methods and a successful execution of them. There are, however, a few operations, such as evaporation, recrys- tallization, filtration, washing upon filters, etc., which are so frequently employed in the preparation of materials in pure condition that some observations regarding them may be of advantage. 1. EVAPORATION OF LIQUIDS When a solution is to be evaporated for the purpose of increasing its concentration or for the purpose of purifying a substance by recrystallization, attention should be paid to the possible action of the solvent and the dissolved matter upon the material of the containing vessel. In general, a porcelain vessel is less readily attacked by reagents than one of glass, and platinum resists their action still better than porcelain. Glass and porcelain are much more readily attacked by alkaline than by neutral or acid solutions, and less readily by those which 186 THE PURIFICATION OF SUBSTANCES 187 are moderately acid than by those which are neutral. Hence, as a rule, if such a course is practicable, an alkaline or even a neutral solution which is to be concentrated in glass or porcelain should be slightly acidified. This may often be done without disadvan- tage when the substance whose purity is an object of concern is a salt, since the presence in a solution of a slight excess of the same acid as that in the salt is frequently unobjectionable. Most of the glass used in a chemical laboratory is essentially a silicate of the alkali metals, potassium and sodium, and of cal- cium. The character of the glass, especially as regards its power to resist the action of reagents, depends upon the ratio of these three constituents, and apparently more upon the ratio of the alkaline and alkaline-earth bases to each other than upon that of the silica to the sum of the bases. An increase in the pro- portion of the calcium improves the glass in respect to its ability to resist the action of reagents, but at the same time increases the difficulty of working it in the flame. An increase in the pro- portion of the alkalies produces precisely the opposite effects ; that is, glass containing a relatively high percentage of the alka- lies is easily worked, and is also readily attacked by reagents. The injurious effect of a large proportion of the alkalies may however be diminished to some extent by increasing the propor- tion of the silica. A soda glass is said to resist the action of reagents better than a potash glass of analogous composition. Two varieties of glass of established excellence for chemical purposes have been put upon the market. One of these, the so- called Stas glass, is characterized by its great resisting power, and also, unfortunately, by the difficulty of working it in the flame. Its composition is represented by the ratio (K 2 0, Na 2 0) : CaO : SiO 2 : : 1 : 1 : 7. The second variety, known as Weber's glass, has also a considerable resisting power and is worked with a fair degree of ease. Its composition is represented by the ratio (K 2 0, Na 2 0) : CaO ; SiO 2 : : L37 : 1 : 7.3, 188 QUANTITATIVE EXERCISES A third variety of glass known as " the Jena utensil and tube glass for chemical and physical uses " has within recent years entered into competition with the long-known and highly valued Bohemian or "hard" glass. According to one certificate of official examination, this glass was found to excel the best Bohemian in the following ratios : 4 to 5 : 1, when treated with water at 20, 11 to 12 :1 " " " " " 80, 3:1" " " 2-normal soda solution. When treated for 6 hours with a normal solution of sulphuric acid at 100, neither glass was sensibly attacked. On the other hand, as regards resistance to the action of a 2-normal solution of sodium hydroxide, the Bohemian was found to exel the Jena glass in the ratio of 3 : 2. The Jena glass is said to be greatly superior to the Bohemian in respect to its power to withstand sudden changes of temperature. The question of the composition of the glass employed for chemical purposes, and the relation of its qualities, good and bad, to composition is worthy of much more general and systematic attention in the laboratory than has hitherto been given to it. The following references to published communications may be of use to those who wish to learn what observations upon this subject have already been made public. R. Fresenius, Quantitative Analyse, 2, 796. A. Emmerling, Liebig's Annalen, 150, 257 (Zeitschrift fur analytische Chemie, 8, 434). W. Fresenius, Zeitsch. anal. Chem., 22, 397. E. Bohlig, Zeitsch. anal. Chem., 23, 518. Kreusler and Henzold, Berichte der deutschen chemischen Gesellschaft, 17, 34 (Zeitsch. anal. Chem., 23, 532). V. Wartha, Zeitsch. anal. Chem., 24, 220. Marshall and Potts, American Chemical Journal, 10, 425 (Zeitsch. anal. Chem., 28, 613). Stas, Chemical News, 17, 1. R. Weber, and R. Weber and E. Sauer, Annalen der Physik und der Chemie (N.F.), 4, 431. Zeitschrift fur angewandt Chemie, 1891, 662. Ber. d. d. chem. Ges., 25, 70, 1814. Zeitsch. anal. Chem., 31, 425, 672. F. Mylius, Ber. d. d. chem. Ges, 22, 310. THE PURIFICATION OF SUBSTANCES 189 F. Mylius, Zeitsch. anal. Chem., 30, 247. O. Schott, Zeitschrift fur Instrumentenkunde, 9, 81; 11, 331 (Zeitsch. anal. Chem.); 30, 317; 31, 419. F. Mylius and F. Foerster, Zeitsch. fur Instrumentenkunde, 9, 117 (Zeitsch. anal. Chem., 30, 317). Zeitsch. anal. Chem., 31, 24. F. Kohlrausch, Ann. der Phys. und Chem. (N.F.), 44, 577 (Zeitsch. anal. Chem., 31, 421). Ber. d. d. chem. Ges., 24, 3560; 26, 2998 (Zeitsch. anal. Chem., 34, 591). E. Pfeiffer, Ann. der Phys. und Chem. (N.F.), 44, 239. F. Foerster, Zeitsch. anal. Chem., 33, 299, 322, 381. A. Winkelmann and 0. Schott, Zeitsch. fur Instrumentenkunde, 14, 6 (Zeitsch. anal. Chem., 34, 591). The danger that exposed solutions will become contaminated by the dust in the air and by the volatile reagents which are used in the laboratory is too obvious to require more than a passing mention. There is, however, one source of contamina- tion which is not so generally recognized as it deserves to be. It is the sulphur in the illuminating gas. Any aqueous solu- tion or basic substance which is heated in an open vessel over a lamp burning illuminating gas is in danger of becoming con- taminated with sulphuric acid unless precautions are taken to divert the products of combustion. For this reason it is often better to evaporate liquids and to heat strongly basic substances over an alcohol lamp rather than over a Bunsen burner. The so-called bumping of evaporating solutions is frequently a source of trouble. The cause of the phenomenon is the superheated condition of the liquid in that part of the vessel to which the heat is applied, usually the bottom, which in- creases to a certain degree, when a large amount of vapor suddenly forms and escapes through the liquid above with explosive violence. In the case of actively boiling liquids it is frequently helpful to introduce scraps of platinum foil with serrated edges, or bits of broken glass, or anything in fact which, owing to its numerous sharp edges and points, facilitates the escape of vapor from a hot liquid. The disturbance usually ceases if the vessel is placed in a bath of any kind so that the 190 QUANTITATIVE EXERCISES liquid is heated uniformly upon all sides. Hence the utility of flasks surrounded with a net of woven wire, and of metallic vessels for the evaporation of liquids which exhibit this propen- sity. If a liquid is to be rapidly evaporated in an open metallic vessel, e.g. a platinum crucible or dish, the vessel should be tilted to one side and the flame applied to it above the surface of the liquid instead of below it. Any arrangement is advan- tageous which enables one to apply the heat principally to the upper portions of an evaporating liquid, or at least as much to the upper as to the lower portions. A bath which is service- able when a liquid of not too high boiling point is to be evapo- rated in a beaker or other vessel of similar form is quickly made in the following manner: A long strip of copper wire gauze, whose width is somewhat greater than the height of the vessel, is tightly wound several times around the beaker and fastened with wire. The lower edges are turned inward until they meet, and hammered into a flat and compact bottom. The bath is filled to a depth of 10 or 15 mm. with loose asbestus, and its vertical outside covered with several thicknesses of asbestus paper. It is best heated on an iron plate. A simple but often useful device for applying heat to a low-boiling liquid at any desired point is a copper wire which is wound around the con- taining vessel. The ends of the wire are allowed to extend to a safe distance from the apparatus and, singly or twisted together, are heated with a lamp or by other suitable means. The arrangement is more effective if the surface to be wound with the wire is first covered with copper foil. , 2. RECRYSTALLIZATION When a hot saturated solution of a substance is cooled for the purpose of purifying the substance by recrystallization, the liquid should be stirred while the crystals are forming. In this way small crystals are obtained which are less likely to inclose mother liquor than the large ones which form in tranquil solutions. THE PURIFICATION OF SUBSTANCES 191 Crystals collected upon paper filters are. liable when removed to become contaminated with shreds of the paper. It is there- fore better, as a rule, to collect the product of a recrystalliza- tion in a funnel in the bottom of which only a platinum cone or a perforated porcelain disk has been placed. If the nitrate is found to contain too many crystals, it may be again passed through the filter. It is important, after each recrystallization, to remove from the crystals as completely as possible the adhering mother liquor. To this end a filter pump should be employed, and the mass in the funnel should be made as compact as possible by pressing and stamping with a pestle or other hard object. Finally, when no more liquid can be extracted by means of the pump, the crystals should be immediately transferred to a clean unglazed porcelain plate and then stirred until they are thor- oughly dry. If the substance is not too soluble, the crystals, after removal of the mother liquor by the pump, may be mois- tened with pure water, allowed to stand for a short time, and again freed from mother liquor by pumping. In some cases the adhering mother liquor may be removed by washing the crystals with a liquid, e.g. alcohol, in which they are insoluble, or only slightly soluble. Many substances containing water of crystallization, such as CuSO 4 .5H 2 O, C 2 O 4 H 2 .2H 2 O, etc., which appear to be stable in the air, really exert a vapor tension at ordinary temperatures, as is proved by their efflorescence when placed in desiccators. Such substances can only be air-dried, and that only at ordinary temperatures, or dried over desiccating materials which have a vapor tension equal to or greater than their own. The handling, in quantitative operations, of substances hav- ing water of crystallization or capable of acquiring it from a moist atmosphere requires intelligent management. One gen- eral rule, however, may be given with respect to their treatment, namely, that substances which contain water of crystallization, but are not hygroscopic, must at all times be surrounded by an 192 QUANTITATIVE EXERCISES atmosphere in which the tension of water vapor is sufficient to prevent their dissociation, while substances which are capable of absorbing water must be kept in an atmosphere in which the tension of water vapor is just equal to their own. It will be readily understood that it is not often practicable to conform to the latter condition if the hygroscopic substances contain any water whatsoever; hence such materials, as a rule, must be completely freed from water and preserved thereafter in a dry atmosphere. This course, however, often leads to difficulties, especially in the case of salts, many of which, when heated to the temperatures requisite for their complete dehydration, decompose with loss of acid and formation of more or less of basic salts.* 3. DESICCATION In drying substances to a constant weight we have to deal with hygroscopic moisture, i.e. the water which condenses on the surfaces of all solids which are exposed to a moist atmosphere ; with the water which adheres to the outside of bodies when they are separated from liquids, as by filtration ; with water of crystallization ; and, less frequently, with so-called water of con- stitution, or chemically combined water. In all of these cases the desiccation is effected by means of drying agents or by heat, or by means of both drying agents and heat. To desiccate a substance by means of a drying agent, it is placed with the absorbent in a closed vessel (a desiccator), care being taken to provide for the greatest possible freedom of dif- fusion between them. Since the evaporation of the water upon or within the substance to be dried must precede its absorp- tion, anything which promotes its volatilization is of advantage. * It is unfortunate that we have not, at the present time, a more extensive and systematic knowledge of the aqueous vapor tension exerted at different temperatures by substances containing water, whether of crystallization or of constitution, and by aqueous solutions of varying concentration, since such knowledge, aside from its value in other directions, would be of the greatest utility in many quantitative operations. THE PURIFICATION OF SUBSTANCES 193 Hence desiccators are often attached to filter pumps for the purpose of diminishing the pressure within them. Sometimes, with the same end in view, they are heated. This is permis- sible in some cases but not in all. If the absorbent, like cal- cium chloride, has a considerable vapor tension of its own at elevated temperatures, the desiccators must be kept cool. The drying agents which are commonly employed in desiccators are those that were mentioned in connection with the drying of gases, such as calcium chloride, sulphuric acid, and phosphorus pentoxide ; and since there is no essential difference between the drying of a gas when it is passed over an absorbent and the drying of a solid when it is inclosed with the absorbent in a desiccator, whatever was said of them in the former connec- tion is equally applicable to them in the latter. It may, how- ever, be well to recall one caution, namely, that when sulphuric acid is used as a drying agent, care must be taken to exclude organic matter and all other substances which act upon it with formation of sulphur dioxide. The evaporation of liquids at temperatures below their boil- ing points is greatly facilitated by constantly replacing the sat- urated atmosphere about them by one which is unsaturated with the vapor of the liquids. This principle can often be utilized with great advantage, not only in the evaporation of masses of liquids, but also in the desiccation of solids both at ordinary and at more elevated temperatures. The most effi- cient of all desiccators is one through which a current of dry gas, e.g. air, is passing. Conditions which retard the diffusion of the water vapor away from the drying materials should, of course, be avoided. For this reason substances to be dried, like liquids to be evaporated, should be placed in shallow ves- sels rather than in those with high sides. It will be seen, too, that advantage is to be gained by increasing the area of the evaporation, i.e. by spreading the material to be desiccated. The removal of liquids from the surfaces of solids by evapo- ration, as in the drying of precipitates, is much slower at any 194 QUANTITATIVE EXERCISES given temperature than could be anticipated from the known volatility of the liquids at that temperature. This is due to the fact that the vapor tension of a liquid, when in the form of a film upon the surface of a solid, is less at a given tem- perature than in other situations ; also, in many instances, to the fact that such films are, in reality, concentrated solutions of the material of the solids which they surround. It is there- fore well, if practicable, when a wet substance is to be rapidly dried, to heat it to a temperature several degrees above the boiling point of the liquid to be removed. Hot-Air Baths The ordinary rectangular copper hot-air bath is too familiar an object in the laboratory to require description. This form of bath, though convenient and in universal use, is sometimes a unsuited to the > dry ing of materials, owing to the readiness with which it is entered by the prod- ucts of combustion from the lamp beneath. In this respect the cylindrical bath with its tight bottom and removable cover is superior to the usual form. The maintenance of constant temperatures in baths is a matter of great importance, and a large number of automatic gas regulators have been devised for this purpose. The best of these for general use is probably the Reichert regulator shown in Fig. 40. The gas enters the hollow O O stopper at a and passes through b to the lamp under the bath, one portion escaping from the stopper through the small hole r water THE UNIVERSITY 198 QUANTITATIVE EXERCISES motor. In many cases a sufficient amount of agitation may be secured in the manner recommended by Ostwald, who employs an arrangement similar to a windmill, which is attached in a horizontal position to the upper end of the shaft and kept in motion by placing a burning lamp beneath. Since the amount of power obtained in this way is very small, the agitator must be constructed of light materials throughout, and pains must be taken to reduce as much as possible the friction upon the wearing parts. The arms of the windmill may be made of aluminium, or of wire bent into the proper form and covered with paper. As a means of propulsion, a small water air blast is more efficient than a lamp. 4. PRECIPITATION Some judgment must be exercised with respect to the concen- tration of solutions from which precipitations are to be made. The fact that nearly all precipitates, especially when they are first formed, are somewhat soluble in their mother liquors sug- gests the propriety of avoiding unnecessary dilution previous to precipitation. On the other hand, it should not be forgotten that a moderate degree of dilution is advantageous and, in many cases, necessary. Rapidly forming precipitates inclose portions of the adjacent liquid and protect them, for a time at least, from the action of the precipitating agent. It is obvious that the incompleteness of the precipitation due to this cause, and also the slowness with which the precipitation will be completed in consequence of diffusion through the protecting layers of pre- cipitated material, must increase with the concentration of the solution. It is obvious, too, that precipitates which inclose con- centrated mother liquors must be difficult to cleanse by subse- quent washing upon filters. It is always necessary to add an excess of the precipitating agent, and the more soluble the precipitate, the larger should be the excess of the precipitant. If a solution of any silver THE PURIFICATION OF SUBSTANCES 199 salt, e.g. silver nitrate, is mingled with one containing an exactly equivalent quantity of a chloride, e.g. sodium chloride, and the resulting silver chloride is separated from the liquid by nitration, the filtrate, though perfectly clear, will be found to contain both silver and chlorine; for if it is divided into two parts, and silver nitrate is added to one and sodium chloride to the other, both portions will give precipitates of silver chloride. Again, if a solution of any barium salt, e.g. the chloride, and one of any sulphate, e.g. sulphuric acid, are brought together in equivalent quantities and the precipitated barium sulphate is removed by filtration, the filtrate will give a further precipi- tation of sulphate when treated either with barium chloride or with sulphuric acid. It is not necessary, in order to obtain the further precipitation, to employ silver nitrate or sodium chloride in the first case, and barium chloride or sulphuric acid in the second. Any soluble silver salt or soluble chloride in the one instance, and any soluble barium salt or soluble sulphate in the other, will produce the same result. In other words, it is neces- sary only that the substance added and the precipitate shall have a constituent (ion) in common. This principle is of great utility in quantitative, separations by precipitation. Most precipitates, when first formed, are so finely divided that portions of them remain suspended for a time in the mother liquors. If immediate filtration is attempted, the filters become clogged and frequently cloudy filtrates are obtained. On stand- ing, in contact with the mother liquors, the finer particles dis- appear while the larger ones grow to greater size ; that is, the precipitates become coarser in time and therefore much easier to filter and to cleanse by washing. The change in a precipi- tate from the finer to the coarser condition is greatly facilitated by heat. These observations have given rise to the following rules : (1) Whenever practicable, precipitate from hot solutions ; (2) continue to heat for some time after precipitation ; (3) never attempt to filter until the supernatant liquid has become per- fectly clear. 200 QUANTITATIVE EXERCISES 5. FILTERS The filter paper which is now in common use for quanti- tative purposes, known as the ashless paper, consists almost entirely of cellulose and leaves a scarcely weighable residue when burned. It differs from the paper formerly used in that, in addition to a treatment with hydrochloric acid for the pur- pose of extracting inorganic bases, it has been subjected to the action of hydrofluoric acid for the purpose of eliminating silicic acid. These filters can be employed with safety without further purification and the weight of the ash may usually be neglected. If other filter papers must be employed, they should be cleansed and the ash which they leave when burned should be deter- mined. To purify them, they are soaked, a large number at a time from 24 to 48 hours, in quite dilute hydrochloric acid, and then washed with distilled water until the washings give no reaction for chlorine with silver nitrate. Owing to their tenderness while wet, some care must be exercised in manipu- lating them, or they will be torn and more or less disintegrated. To determine the ash, a number of the papers (from 5 to 15) are completely incinerated in a weighed platinum crucible and the weight of the residue ascertained. A filter paper should be carefully fitted to the walls of its funnel at all points. This is easily accomplished if the walls of the funnel make the correct angle with its axis. The paper is folded symmetrically, opened in the funnel, and formed, as well as may be, to the sides. It is then wet with distilled water, allowed to drain, and again fitted to the sides of the fun- nel, care being taken not to rend the paper by rough handling. If the funnel is not of correct form, the last folding of the paper is made somewhat unsymmetrically, and the longer or shorter side is opened according as the angle of the sides is too great or too small. The funnels selected for papers of given sizes should be only slightly larger than the folded filters, since when the edges of the funnels are high above those of the papers, it is THE PURIFICATION OF SUBSTANCES 201 much more difficult to introduce without loss the materials to be filtered and the liquids which are employed in washing the precipitates. In filtering under diminished pressure, the portion of the paper which extends into the stem of the funnel requires sup- port. The platinum cones devised by Bunsen are usually employed for this purpose. They are made in the following manner: A disk of platinum foil is cut in the form represented in Fig. 42, and a mold for it is made by allowing plaster of Paris to harden about the steel cone-model represented in Fig. 43. The platinum disk is softened in the flame, FIG. 42 wrapped about the apex of the steel model, and then formed in the gypsum mold. If the platinum cone opens when removed from the mold, it is made a little too small by pressing the opposite sides with the fingers ; it is then grasped with the forceps, reheated, and again formed in the mold. When finished it should perfectly maintain its shape and present no visible opening at the apex. If greater firmness is desired, the overlapping edges may be soldered at a single point by melting at the proper place a little borax and a fragment of gold. Any change in form due to the last operation is easily remedied by reshaping the cone in the mold. Instead of a platinum cone, one made by folding a small disk of the so-called hardened paper may be used to support the apex of the filter. The Gooch filter, which is often used with advan- FIG. 43 tage in quantitative work, requires a platinum cru- cible, in the bottom of which a considerable number of minute holes have been made. The sides of the crucible are straight, and the bottom, which is flat, is provided with a closely fitting platinum cap, which is removed for filtering and replaced when the crucible and its contents are to be heated. The filter proper is made by depositing upon the perforated bottom of the crucible a layer of finely divided asbestus. The depth of the 202 QUANTITATIVE EXERCISES layer and also the fineness of the asbestus used in making it may vary somewhat according to the coarseness of the material to be filtered. To prepare the asbestus for use in this filter, a quantity of the material, of good quality, is macerated with water in a por- celain mortar until it is reduced to a sufficiently fine condition. It is then stirred up in a larger quantity of water and the por- tion which remains suspended for some time after the water has come to rest is floated out. The residue is soaked for several hours in moderately strong hydrochloric acid, filtered, washed with distilled water, dried, and finally ignited in a platinum dish over the blast lamp. . In addition to the perforated crucible and the pre- L J pared asbestus, there are required for the completion of the Gooch filter the cylindrical glass funnel a, Fig. 44, and the rubber band b which serves to hold the crucible in place. When a filter is to be made, a quantity of the prepared asbestus suspended in water is introduced into the crucible (arranged as shown in the figure), FIG. 44 and the water is drawn off under moderately dimin- ished pressure. Other portions of asbestus are after- wards introduced and treated in the same manner until a filter of sufficient thickness has been obtained. Finally, the filter is washed two or three times with water (to remove any material which would be likely to become dislodged and lost in subse- quent operations), dried, and heated to constant weight at the temperature to which the precipitate which it is proposed to collect upon it is to be heated. It sometimes happens, during the collection and washing of a precipitate upon an asbestus filter, that some of the shreds of the filter are carried into the filtrate; the latter should always, therefore, be examined. If it is found to contain fragments of asbestus, these should be col- lected upon a filter of ashless paper and the loss to the filter determined by burning the paper and weighing the residue. THE PURIFICATION OF SUBSTANCES 203 An asbestus filter which is of service in some cases is pre- pared by placing a perforated porcelain disk in the bottom of a cylindrical funnel, similar to that represented in Fig. 44, and depositing upon it a layer of prepared asbestus in the same manner as in making the Gooch filter. The Monroe filter, which may often be used with advantage as a substitute for one of asbestus, is made in the following manner: A perforated Gooch crucible is placed upon filter or blotting paper and its bottom covered to a depth of 4 or 5 mm. with moist ammonium-platinum chloride. The crucible is cleansed externally, dried, covered, and placed in its cap. The double salt is then gradually decomposed by heat. If cracks appear in the filter, as they are likely to do, they are filled with a fresh portion of the double salt and the crucible is again heated. Finally, the upper surface of the filter of spongy platinum is made smooth by gently rubbing it with the end of a glass rod which has been rounded in the flame. All precipi- tates which can be dissolved in any reagent which does not attack platinum may be collected and washed upon such a filter. There is one danger, however, which is not to be overlooked. If the pores of the filter are filled with air, and a liquid containing free hydrochloric acid is passed through it, a little platinum will be dissolved. 6. FILTRATION Liquids are filtered while hot, if practicable, because in that condition they pass through the filters much more rapidly than when cold. In quantitative separations, however, it is necessary to take into account the effect of temperature upon the solubil- ity of the material to be collected on the filters. In transferring a liquid and precipitate to a filter, it is best to introduce the greater portion of the former as free from the latter as may be ; in other words, it is well not to stir up the precipitate unnecessarily until nearly all of the liquid has been passed through the filter. The purpose of this is, of course, to 204 QUANTITATIVE F.XKIIUSKS postpone as long as possible the clogging of the filter which is sure to follow the introduction of a finely divided precipitate. When only a little of the liquid remains with the precipitate, the latter is stirred up and as much of it as possible is intro- duced into the filter with the residue of the former. A small quantity of the filtrate always less than a filterful is then returned to the vessel and more of the precipitate is brought upon the filter in the same manner. This procedure is repeated until but little of the precipitate remains except that which is attached to the sides and bottom of the vessel. To complete the transference of the precipitate, a small quantity of the fil- trate (3 to 5 cc.) is poured into the vessel and the whole interior surface is washed down with a feather or with a rubber on the end of a glass rod. The detached material is then stirred up with the liquid and brought upon the filter. This last operation must be repeated until no particles of the precipitate can be detected upon the sides or bottom of the vessel, and until the wash liquid is entirely free from any appearance of cloudiness. There are two good reasons for the practice of employing the filtrate, rather than water or some other liquid, to bring the precipitate upon the filter. In the first place, the filtrate, being already saturated, exerts no solvent action on the precipitate; in the second place, the volume of the filtrate is not increased by its use for this purpose as it would be if another liquid were employed. To prepare a feather for use in detaching precipitates from the interior surfaces of vessels, it is trimmed in the following manner: At a point near the free end where the rachis is judged to be sufficiently stiff and elastic the feather is cut off transversely at an angle of about 30 to its axis. The barbs on either side are then cut away for a distance of about 15 mm. in lines parallel to the rachis and at a distance of 2-4 mm. from it. The remainder of the rachis is entirely denuded of barbs and made very smooth by scraping with the edge of a sharp knife blade. TIIK I'UMFICATIOX OF SUISTA NCKS 205 A substitute for the feather, which is in common use, is familiarly designated as the "policeman." It is made from a rectangular piece of sheet rubber by covering one side except a narrow strip through the center with cement and then once folding the piece through the middle at right angles to the uncovered strip. A long pocket is thus provided, into which the end of a glass rod may be crowded. This arrangement, though not superior to the feather, is to be preferred to a glass rod with a short piece of rubber tubing drawn over the end, which is sometimes used hi cleansing beakers, since the uncov- ered condition of the end of the rod in the latter affords the pre- cipitate an opportunity to become lodged between the rubber and the glass. 7. THE WASHING OF PKECIPITATES It is important that the washing of precipitates should be accomplished with the least possible quantity of liquid: 1st, because of the solvent action of the wash liquid upon the pre- cipitate ; 2d, in order to avoid an unnecessary increase in the volume of the filtrate; and 3d, for the purpose of saving time. To this end the filter pump, or some other means of securing diminished pressure, should always be employed in the washing of precipitates, and before introducing a fresh portion of the wash liquid as much of the liquid already in the filter should be withdrawn as it is possible to extract with its aid. How irrational a different course would be will appear from the fol- lowing illustration. We will suppose that in washing a given precipitate 25-cc. portions of water are introduced into the filter, and that after each addition all but 0.5 cc. is withdrawn with the aid of the puuip. Theoretically the impurities would be reduced by the first washing to 0.02 ; by the second, to 0.00039 ; by the third, to 0.0000077 ; and by the fourth, to 0.00000015. Suppose, on the other hand, that the successive 25-cc. portions of water are added while 5 cc. of liquid remain in the filter. Theoretically the impurities will then be reduced by the first 206 QUANTITATIVE EXERCISES washing to 0.2; by the second, to 0.0333; by the third, to 0.00556 ; and by the fourth, to 0.000926. A comparison of the two sets of figures will convince one of the immense advantage to be gained in washing precipitates by drawing off, as completely as possible, the liquid already in a filter before adding a fresh portion of the wash liquid. The above estimate of the rate at which the impurities will be reduced under the given conditions is based on the supposition that when a quantity of wash liquid is introduced into the filter, the impurities will distribute themselves uniformly through the whole body of the liquid, and that the portion which passes through the filter into the filtrate is therefore of the same con- centration as that which remains behind in immediate contact with the precipitate and the material of the filter. As a matter of fact, however, the portion of the solution which remains behind and cannot be extracted by the pump is always more concentrated than the filtrate. It is for this reason that the cleansing of a precipitate by washing is found in practice even under the best management to be much slower than is, indicated by the computations just given. Nevertheless, the argument in favor of thoroughly extracting the liquid already in a filter before introducing a fresh portion of the wash liquid holds good. The tendency of solutions to become more concentrated in the immediate vicinity of solids, e.g. around precipitates and the material of filters, is known as adsorption. A familiar effect of adsorption is that which is observed when a standard solution is passed through a dry filter; the first portion of the 'filtrate is well known to be weaker than the original solution, and it is therefore always rejected. Precipitates which owing to their fine state of subdivision work themselves into the interstices of the filter and clog it to such an extent as seriously to interfere with filtration are often partially washed by decantation before bringing them upon the filter ; that is, they are stirred up with portions of the THE PURIFICATION OF SUBSTANCES 207 wash liquid, which, when the precipitates have subsided, are poured into the filter. This method of cleansing precipitates is, however, exceedingly ineffective, owing to the large fraction of the liquid which must each time be left with the precipitate. The objection to it is identical with that to the practice of introducing wash liquid into filters before removing as much as possible of the liquid already in them. It has been stated that if a saturated solution of a compound is treated with a soluble substance containing one of the con- stituents into which the compound dissociates in solution, some of the dissolved material will be precipitated, and that, for this reason, it is customary to add an excess of the precipitating agent. The same principle may be utilized with great advantage at times to diminish the solubility of precipitates in the liquids with which they are washed ; for example, if a precipitate of barium chromate is to be washed with water containing a little acetic acid or an acetate in which it is sensibly soluble, its solu- tion may be almost entirely prevented by adding a little ammo- nium chromate to the wash liquid. The quantity of the salt required for this purpose is very small, and when the other impurities have been washed out of the precipitate the little ammonium chromate introduced with the wash liquid may be sufficiently eliminated by a very moderate washing in pure water in which barium chromate is only slightly soluble. If freshly precipitated silver chloride is collected upon a filter and is then washed for a long time with pure water especially with cold water it will be noticed that the filtrate remains perfectly clear as long as any of the liquid in which the precipi- tation was made is still in the filter, and for some time after the beginning of the washing with water ; that later, however, the upper portions of the filtrate become cloudy from the pres- ence of precipitated silver chloride. If the receiving vessel is exchanged for an empty one, and the washing with water is continued, a clear filtrate will be obtained, which, nevertheless, becomes cloudy when any acid or soluble salt is added to it. On 208 QUANTITATIVE EXERCISES the other hand, if a little acid or a small quantity of some salt is added to the water before beginning the washing of the precipi- tate, the nitrate will remain clear to the end. The explanation of this conduct is as follows: Silver chloride, when freshly precipitated, belongs to a class of bodies known as colloids, a characteristic of which is the tendency to form with pure water so-called pseudo solutions, from which they are reprecipitated by the addition of acids or salts. The solution of the silver chloride, therefore, does not begin, in the case just cited, until these substances have been removed from the filter by washing, and a reprecipitation follows because of their presence in the filtrate. Familiar examples of precipitates which behave in a similar manner are the hydroxides of iron and aluminium and the sulphides of the metals. Such substances are difficult to cleanse by washing, owing to their voluminous and sometimes gelatinous character and their tendency to clog the filters. On standing and when heated, they usually become more compact and therefore easier to wash upon filters. In the more compact condition they are also less inclined to redissolve to " run through" the filter on continued washing. In dealing with them it is well to precipitate from hot solutions and to keep the liquid hot for some time after precipitation ; to allow them to stand a long time before attempting filtration ; and to add to the wash water some substance which will prevent a return to the pseudo-soluble condition. It appears to make but little dif- ference what substance is employed for the last purpose so long as it does not affect the composition of the precipitate ; it is therefore well, when permissible, to select ammonium salts, since these can afterwards be expelled from the precipitates by heat. CHAPTER IX SILVER AND THE HALOGENS EXERCISE XVI DETERMINATION OF CHLORINE AND SILVER . I. GRAVIMETBICALLY AS SILVER CHLORIDE Weigh into a beaker preferably one having a " lip " about 0.2 gram of pure potassium chloride. Dissolve the salt in 75 or 100 cc. of water and add slowly, with constant stirring, a dilute solution of silver nitrate, to which have been added a few drops of nitric acid, until it is believed that the silver nitrate is slightly in excess. Let the precipitate subside and then add to the nearly clear supernatant liquid a little more of the silver nitrate. If the cloudiness does not increase, warm the contents of the beaker for half an hour upon a sand bath or a wire gauze, stirring vigorously from time to time, and then set the beaker aside in a dark place. When the liquid above the precipitate has become perfectly clear, rub the under side of the beaker lip with a minute quan- tity of vaseline or with some kind of grease. This is intended to prevent the liquid from working its way over the edge and running down the outside of the beaker while being transferred to the filter. The precaution, though customary, is hardly necessary, since with proper manipulation there is no need of loss from this cause. Bring the precipitate upon a small ash- less filter which is arranged for use with the filter pump. In transferring the contents of the beaker to the filter, a glass rod is held vertically with its lower end reaching nearly to the 209 210 QUANTITATIVE EXERCISES bottom of the filter, and against this is laid the edge of the beaker at the point over which the liquid and precipitate are to pass. In this way the liquid is made to glide quietly down the rod and enter the filter without spattering. When the filter has been sufficiently filled, the beaker is tilted backwards, but the rod should not be removed as long as any liquid remains between it and the edge. If a little becomes lodged at the point of contact, as is usually the case, it may be made to flow in the one direction or the other by changing the angle of the rod and by sliding it up and down over the edge of the beaker. If the rod is removed prematurely, the liquid and precipitate which are entangled between it and the beaker will run over the edge and down the outside of the latter; and when the out- side has once become wet, it is difficult to avoid a repetition of the accident. The precipitate which adheres to the beaker is brought into the filter with the aid of small portions of the filtrate and a trimmed feather or a " flag," as described in the preceding chapter. To wash the precipitate, first remove the mother liquor as completely as possible with the aid of the filter pump, and then, after having detached the pump, moisten the precipitate and paper with a small quantity of cold water containing a little silver nitrate. Give the impurities to be removed by the wash- ing a little time for diffusion, and then, as before, draw off the liquid with the pump as completely as possible. Continue washing the precipitate in this manner with water containing silver nitrate until the potassium nitrate has been removed, and then wash it two or three times in the same way with small portions of cold water containing a very little nitric acid. The silver nitrate is added to the first wash water to diminish the solubility of the silver chloride and also to prevent its return to the colloidal condition. The nitric acid in the water which is employed in the last stage of the washing process does not directly affect the solubility of the chloride, but it effectually corrects the tendency to revert to the colloidal state. SILVER AND THE HALOGENS 211 Dry the filter at 100 or slightly above that temperature. Open it on a piece of glazed paper and transfer the silver chlo- ride to a weighed porcelain crucible which is also placed upon the paper. If necessary, a piece of stiff platinum wire or a small platinum spatula may be employed to detach the chloride which adheres to the paper, in which case the wire or spatula is afterwards to be wiped clean upon the paper. Fold the paper in the form of a square by turning in the edges, and roll it together tightly, but in such a way that the half of the paper which has been in contact with the precipitate is all at one end. Beginning in the middle of the roll, wind a platinum wire spi- rally about the half which contains no chloride. The wire should be so long that about 75 mm. of its length will not be required in the winding. With the unused end of the wire in one hand, hold the roll over the crucible in a vertical position with the free end upward, and with a lamp burning with a small but good oxidizing flame in the other hand light it at the top. If, as the flame descends, portions of the paper are incompletely burned, touch the parts which are only charred with the edge of the flame as often as may be necessary to com- plete the incineration. When the roll has been completely burned down to the point where the wire begins, turn it into a horizontal position and burn the part inclosed by the wire. It is important that no incompletely burned matter should drop from the wire, since the combustion cannot be finished in the crucible. The roll must therefore be held very steadily, and to this end it is well to support the hand by resting it on the table or on a block. If the column of ash outside of the wire curls over and appears to be in danger of breaking off and falling before the burning is completed, its position should be so changed as to diminish the strain. Transfer to the crucible anything which may have fallen upon the glazed paper, add a few drops of dilute nitric acid, and evaporate it at a very mod- erate temperature. Repeat the treatment with nitric acid and the evaporation, and then add a few drops of hydrochloric acid. 212 QUANTITATIVE EXERCISES Evaporate to dryness and heat the crucible until the chloride in it begins to fuse around the edges'. Cool the crucible in a desiccator and weigh. To remove the chloride from the crucible, introduce a piece of zinc and a little hydrochloric or sulphuric acid. Silver chloride melts at about 450. It is perceptibly soluble even in cold water, but less so, as explained already, in water containing a small quantity either of a soluble silver salt or of a chloride. The presence of a considerable quantity of chlo- rides or of the nitrates of the metals of the alkalies and alkaline earths increases its solubility. It is easily dissolved in solu- tions of potassium cyanide, sodium thiosulphate, and ammonia. The method just given suffices in the case of most soluble chlorides for the separation of chlorine from the metals. Stan- nic, mercuric, antimony, platinic, and chromic chlorides are exceptions to the rule. In solutions of the first four, silver nitrate precipitates, in addition to the chlorine, some of the metal with which it was previously combined. In solutions of chromic chloride the precipitation is incomplete. The deter- mination of chlorine in these salts must be preceded by a sepa- ration of the metals. The tin is best precipitated by ammonium nitrate ; the antimony and mercury, by hydrogen sulphide ; and the chromium, by ammonia. Solutions of platinic chloride are evaporated to dryness with sodium carbonate and the residue is heated to the fusing point in a platinum crucible. The sul- phides of some of the metals, when precipitated from solutions of their chlorides by hydrogen sulphide, are inclined to carry down with them a portion of the chlorine. In such cases the solution should be dilute and fully saturated with the gas. It should also be allowed to stand for some time after saturation in a closed vessel before filtration. If practicable, the sulphide should be redissolved and again precipitated. Lead, silver, and mercurous chlorides, because of their insol- ubility, also require special preliminary treatment. The first is SILVER AND THE HALOGENS 213 decomposed by digestion with acid sodium or potassium carbon- ate ; the second, by fusion with an alkaline carbonate ; and the third, by digestion with caustic soda or potash. Bromine and iodine are determined as silver salts in the same manner as chlorine. Care must be taken, however, not to treat solutions of their salts with nitric acid until after an excess of silver nitrate has been added. This precaution is especially necessary in the case of the iodides, which, with the exception of silver iodide, are quite readily decomposed by nitric acid with liberation of iodine. Bromine and iodine are separated from the various metals by the same methods as chlorine. There are also certain special methods which may be employed to separate iodine from some of the metals. To determine silver as chloride, the solution containing it is treated, at a temperature somewhat below the boiling point, with a few drops of nitric acid and then with a very moderate excess of hydrochloric acid, or of sodium or potassium chloride. The precipitate is washed on the filter, first with cold water containing a little nitric acid, and then two or three times with pure water. In all other respects the procedure is the same as in the determination of chlorine. It is customary to state the results of quantitative determi- nations in the form of percentages, not of the constituents determined, but of the whole material or compound employed in the analysis ; for example, the result of a determination of chlorine in potassium chloride would be expressed as follows : Theoretical percentage of Cl in KC1 = 47.53 Found " " " " " = Error = per cent 214 QUANTITATIVE EXERCISES If the quality of the work is to be judged, it is fairer to state the results in the form of weights, as follows : Theoretical weight of Cl in .... grm. KC1 = . . . . grm. Found " " " " " " " = " Error = . . . . " It will be seen that when the results are expressed in the customary form, the effect of the algebraic sum of the errors of the analysis is inversely proportional to the quantity of the material operated upon. In other words, if large quantities of material are employed, one may work somewhat carelessly and nevertheless obtain seemingly good results. This fact is of course a strong argument in favor of using only small quanti- ties. Another sufficient reason for the employment of only moderate quantities of material is to be found in the fact that small precipitates are much more easily and rapidly cleansed by washing than large ones. Much of the time which is usually spent in making computa- tions may be saved by preparing, before beginning a piece of quantitative work, a table of equivalent weights which includes all of the substances involved in the calculations to be made. A table of this kind including nearly all the substances employed in the present chapter will be found on the following page. In the horizontal lines are given the quantities of various sub- stances which are equivalent to unit quantities of the substances designated in the first vertical column. They are found, of course, by dividing the atomic or molecular weights or the proper multiples of them of the substances whose symbols stand at the head of the several columns by the atomic or molec- ular weights of those whose symbols are given in the first column. For example, to find the weight of bromine which is equivalent to any unit weight of chlorine, we divide 79.35, the atomic weight of the former, by 35.18, the atomic weight of the latter, and obtain 2.2555, which is the number under Br SILVER AND THE HALOGENS 215 $3 . o So 00 * cq to co o "* co co 05 rH rH CO O O QO O rH CO t rH rH rH O O l>- O t- O "^ O G<1 rH rH t co "* ^ i>- t>- oo OrHOOOOOrHC^rH CO "<* CO O5 * t^ Tti (M rHOOOOOOOOOOOrHO ^ O P3 i i O PQ h-t bC bD bO r A ^bcOPQhHbcM'bJD^^^ 216 QUANTITATIVE EXERCISES and opposite Cl in the table. Again, if K 2 O 2 O 7 acts upon an iodide in an acid solution, there are liberated six atoms of iodine for each molecule of the bichromate, and to find the weight of the former, which, in such a reaction, is equivalent to a unit weight of the latter, we divide six times the atomic weight of iodine (6 x 125.89) by 292, the molecular weight of the bichro- mate. The result is 2.5867, which is the number in the table under I and opposite K 2 Cr 2 O 7 . The manner of using such a table is obvious, but its usefulness will be illustrated by a few examples. Suppose a quantity of potassium chloride, IF, has been weighed out, and it is desired to know what weight of silver chloride it should yield, we find in the table opposite KC1 and under AgCl the number 1.9228 ; the weight of the silver salt is W x 1.9228. Suppose a weight of silver chloride, W f , has been obtained, and we desire to find the weight of the chlorine in it ; under Cl and opposite AgCl is given the equiva- lent 0.2472, and the weight of the chlorine is W, x 0.2472. Suppose again that we have a given weight of arsenious oxide, W n , and are required to ascertain how much potassium bichro- mate will be needed for its oxidation to arsenic acid ; by refer- ring to the table we find the weight to be W n x 0.9904. II. VOLUMETBICALLY BY' MOHR's METHOD One-tenth normal solutions of potassium chloride and of silver nitrate are required. To prepare the former, weigh out about 7.5 grams of pure potassium chloride. The quantity must not be less than 7.4, and should not exceed 7.6 grams. Dissolve the salt and dilute the solution in a liter measuring flask to the mark on the neck. Divide the weight of the salt in solution by the capacity of the flask in cubic centimeters to find the amount of the salt in one cubic centimeter, and then divide 7.4, the weight of the salt in one liter of a tenth-normal solution, by the quotient. The second quotient will be the number of cubic centimeters of the SILVER AND THE HALOGENS 217 solution which must be diluted to one liter, and the difference between this and 1000 will be the volume of the water required for the dilution. Remove from the flask with a pipette a quan- tity of the solution which is somewhat greater than that of the water to be introduced. Measure in the required volume of water and fill the flask to the mark with the solution which was withdrawn. Close the flask and thoroughly mix its contents. The solution should have, at the time of its dilution, very nearly the standard temperature. To prepare the solution of the silver salt, dissolve about 21 grams of neutral silver nitrate in 1200 cc. of water. Fill one burette with the tenth-normal potassium chloride solution, and another with the solution of silver nitrate. Measure into a beaker 10 cc. of the chloride solution. Add about 50 cc. of water and a few drops of a solution of neutral potassium chro- mate which is free from chlorine. The liquid in the beaker, after the addition of the chromate, should have a distinct but not a deep yellow color. Titrate the solution of the chloride, stirring it constantly, with the solution of silver nitrate until a slight but permanent red color is obtained. Repeat the experi- ment several times with fresh portions of the chloride. Having found the number of cubic centimeters of the silver solution which are equivalent to ten of the chloride, multiply by 100. The product will be the number which must be diluted to a liter. Measure the water required for the dilution into a dry liter flask, and fill to the mark with the solution of silver nitrate. The two solutions should be equivalent; determine whether they are so. Weigh off from 0.1 to 0.2 gram of pure potassium chloride, and determine the chlorine in it by means of the standard solution of silver nitrate. Barium and lead form nearly insoluble chromates ; therefore to determine chlorine in combination with these metals it is neces- sary to add a slight excess of the chromate, i.e. somewhat more than is required for their precipitation. The titration 218 QUANTITATIVE EXERCISES may then be made without removal of the insoluble chromates. Or the metals may be precipitated as sulphates with sodium sulphate. Silver chromate does not form in the presence of acids, and silver oxide is precipitated by the alkalies; hence all the solu- tions employed in connection with the method of Mohr must be neutral, and the presence of reducing substances is, of course, inadmissible. Silver chromate is soluble in 6666 parts of water at 17.5, and in 3704 parts at 100 ; if, therefore, potassium chromate is added to a solution of silver nitrate, a red precipitate is obtained, which disappears rather slowly on titrating with a solution of a chloride. For this reason it is not advisable, when silver is to be determined, to treat its solution with the chromate and then to titrate with a standard solution of some chloride until the red color is destroyed. It is much better to add at once an excess of the chloride, and then to determine the amount of the excess by means of a standard solution of silver nitrate. Bromine and iodine may also be determined by the method of Mohr. III. VOLUMETRICALLY BY VOLHARD J S METHOD Dissolve about 10 grams of ammonium sulphocyanate in 1200 cc. of water. Fill one burette with the solution, and another with the tenth-normal solution of silver nitrate. Meas- ure 10 cc. of the latter into a beaker. Add 5 cc. of a cold satu- rated solution of ferric ammonium sulphate and about 50 cc. of water. Stir in dilute nitric acid, drop by drop, until the solution becomes nearly colorless. Titrate with the solution of sulpho- cyanate until a faint but permanent red color appears. Repeat the experiment several times. Having found the relation of the two solutions, dilute that of the sulphocyanate to the tenth- normal standard, proceeding as directed under II. If the ammonium sulphocyanate is quite wet at the time of weighing, the preliminary solution of it may be found to be top SILVER AND THE HALOGENS 219 weak ; it is therefore well, in such a case, to weigh out some- what more than the prescribed quantity of the salt. But if the required additional quantity has been considerably overesti- mated, giving a much too concentrated solution of the sulpho- cyanate, it should be diluted before making the determinations on which the final dilution to the standard is to be based. As a rule, solutions which are to be diluted to any fixed standard should have, at the time of determining their strength, very nearly their final concentration. The nitric acid (specific gravity 1.2) which is used to decol- orize the indicator should be boiled to free it from nitrous acid and oxides of nitrogen. Dissolve a weighed silver ten-cent piece in dilute nitric acid and evaporate nearly all the excess of the acid. Dilute with water and boil the solution to remove nitrous acid and oxides of nitrogen. Pour the solution, when cold, into a 100-cc. meas- uring flask, add the washings, and dilute to the mark with water. Determine the silver in measured portions of the solution. According to Volhard, silver may be determined in the pres- ence of copper without difficulty provided the ratio of the latter to the former does not exceed that of 7 to 10. In the presence of nickel and cobalt the determination is satisfactory, but requires some practice. Mercury and palladium, on the other hand, must be removed before the silver can be estimated. Weigh out from 0.1 to 0.2 gram of pure potassium chloride and dissolve it in about 100 cc. of water. Add 5 cc. of the iron solution and decolorize with nitric acid. Measure in an excess of the standard solution of silver nitrate about twice the quantity required to precipitate the chlorine and then titrate with the solution of sulphocyanate, stirring constantly, until the liquid assumes a light yellowish-brown color. The difference between the quantity of silver added in the first place and that found by the subsequent titration with the sul- phocyanate is the quantity which was required to precipitate the chlorine. 220 QUANTITATIVE EXERCISES The end-reaction when chlorine is determined in the manner prescribed above is much less striking than when silver is pre- cipitated by sulphocyanate in the absence of silver chloride, and the color due to the formation of ferric sulphocyanate is not per- manent if the excess of sulphocyanate is small. This is due to a reaction between the coloring substance and silver chloride : Fe(CNS) 3 + 3 AgCl = 3 AgCNS + FeCl 3 . A little experience, however, enables one to determine with ease and certainty when the precipitation of the silver is complete. It is well, when this method of determining chlorine is employed for the first time, to continue adding the sulphocyanate until a deep color is developed, and then to add silver nitrate until it is destroyed. A few such titrations, back and forth, in the same solution, with close observation of the changes in color, will prepare one sufficiently for accurate work. The difficulty resulting from the reaction between the ferric sulphocyanate and the silver chloride may be avoided in the following man- ner: The solution of the chloride, the indicator, and the excess of silver nitrate are placed in a small measuring flask and well shaken. The flask is filled to the mark with water, the contents thoroughly mixed, and then quickly filtered through a dry paper, the first portions of the filtrate being discarded. The excess of silver is then determined by titrating meas- ured portions of the filtrate with the standard solution of sulphocyanate. When the quantity of .chlorine to be determined is not even approximately known, it is recommended to add a drop or two of the sulphocyanate solution from time to time while measur- ing in the silver nitrate. As long as any chlorine remains unprecipitated, the color produced by the sulphocyanate will disappear slowly, but when the silver is in excess, it disappears instantly. The quantity of sulphocyanate introduced in this way must, of course, be added to that which is subsequently used in determining the excess of silver. SILVER AND THE HALOGENS 221 When the silver is standardized in the manner prescribed under II, and afterwards used for the determination of chlorine by the method of Volhard, the results are, as a rule, somewhat low in consequence of the reaction between the ferric sulpho- cyanate and the silver chloride. It is therefore recommended that a solution of silver nitrate which is to be used principally for the estimation of chlorine by this method be especially stand- ardized for chlorine. For this purpose a solution of a weighed quantity of a pure chloride is treated with the indicator and an excess of the preliminary solution of silver nitrate, and then titrated with any very dilute solution of ammonium sulphocy- anate. Having found in this way the volume of the sulpho- cyanate solution required to precipitate the excess, the relation of the silver and sulphocyanate solutions to each other is ascer- tained. The difference between the volume of the silver nitrate added to the chloride and that found to be equivalent to the sulphocyanate which was used in precipitating the excess of silver is the volume of the silver nitrate which is equivalent to the weighed quantity of chloride. A solution which is stand- ardized in this manner will give correct results when employed for the estimation of chlorine by the method of Volhard, but it must be restandardized as directed under II when the method of Mohr is to be used. Bromine is determined by the method of Volhard in precisely the same manner as chlorine. The end-reaction, however, is more distinct and permanent, owing to the fact that silver bro- mide is decomposed by ferric sulphocyanate much more slowly than silver chloride. To determine iodine, the iodide dissolved in two or three hundred times its weight of water is placed in a bottle having a ground-glass stopper. The silver nitrate is added in small quantities, and after each addition the bottle is closed and the contents are well shaken. This treatment is continued until 222 QUANTITATIVE EXERCISES the silver iodide separates and leaves the supernatant liquid quite clear. A little more silver nitrate, also the indicator, and the nitric acid necessary to bleach it are then added, and the excess of the silver is determined with the sulphocyanate. But since silver iodide carries down with it a quantity of silver nitrate, and the color indicating the end of the reaction is not permanent until the nitrate thus precipitated has all been converted into sulphocyanate the standard solution of sulpho- cyanate must be added in small quantities and the contents of the bottle must be vigorously agitated after each addition. The method of Volhard is usually preferred to that of Mohr for the reason that by it silver and the halogens may be deter- mined in the presence of nitric acid and therefore in solutions containing substances which, in the absence of nitric acid, reduce the salts of silver.* EXERCISE XVII IODOMETRIC DETERMINATIONS These are all based on the reaction which takes place between free iodine and sodium thiosulphate : 2 Na 2 S 2 O 3 + 2 I - 2 Nal + Na 2 S 4 O 6 . It will be seen that by the aid of this reaction it is practicable to determine all of those substances which liberate from iodides a definite quantity of iodine, and all of those also which convert into iodides, or absorb, a definite amount of free iodine. The following equations represent the reactions with iodine or the * The student should also familiarize himself with the volumetric methods of Gay-Lussac, of Pisani, and of Bohlig. See Fresenius, Quant. Analyse, 1, 302, 309, 472. SILVER AND THE HALOGENS 223 compounds of iodine, of some of the substances which are deter- mined by the iodometric method : C1 2 + 2 KI = 2 KC1 + I 2 , Br 2 + 2 KI = 2 KBr + I 2 , HC10 + 2 HI = H 2 + HC1 + I a , HBrO + 2 HI = H 2 O + HBr + I 2 , HC1O 3 + 6 HI = 3 H 2 O -f HC1 + 3 I 2 , HBr0 3 + 6 HI = 3 H 2 O + HBr + 3 I 2 , HIO 3 + 5 HI - 3 H 2 O + 3 I 2 , H a S0 8 -f H 2 + I a = H 2 S0 4 + 2 HI, As 2 O 3 + 2 H 2 O + 2 I 2 = As 2 O 5 -f 4 HI, Sb 2 3 + 2 H 2 + 2 I 2 = Sb 2 5 + 4 HI, 2 CrO 3 + 6 HI = Cr 2 O 3 -f 3 H 2 O + 3 I a , Mn0 2 + 2 HI = MnO + H 2 O + I a . I. PREPARATION OF STANDARD SOLUTIONS a. Resublimed Iodine Select two crystallizing dishes of the same diameter whose edges fit together quite closely. Place in one of them a mix- ture of 10 or 15 grams of commercial iodine and 2 or 3 grams of pulverized potassium iodide. Press the dish halfway through a hole which has been made for it in a piece of asbestus board 150 or 200 mm. square, and bring under it a sand or asbestus bath which is narrower than the board. Heat the iodine slowly, allowing the vapors to escape until it is believed that all the water has been expelled, and then invert over it the other crys- tallizing dish. Distill the iodine very slowly, and keep the upper dish cool by placing upon it a flat-bottomed metallic dish containing cold water. When the sublimation is finished, transfer the iodine to a glass-stoppered weighing flask and place the latter in a desiccator. The purified iodine is used in stand- ardizing thiosulphate solutions. 224 QUANTITATIVE EXERCISES 5. Potassium Iodide Aqueous solutions of potassium iodide are employed as a sol- vent for free iodine and also as the source of the iodine which is liberated in various reactions utilized in iodometric processes. The salt must be tested for the presence of iodate. For this purpose a small quantity of the iodide is dissolved in recently boiled water and treated with a little well-boiled dilute hydro- chloric acid. If the solution remains colorless for a few min- utes, it is free from iodates. Starch paste may be added to facilitate the detection of free iodine. Within a short time the solution will become colored in consequence of the action of the free oxygen in it on the hydriodic acid which is liberated by the hydrochloric acid. If the iodide is found to contain iodate, the latter may be removed by boiling the water solution of the salt with zinc amalgam ,until it no longer gives the reac- tion for iodic acid when treated with hydrochloric acid and starch paste. Neither zinc nor mercury is dissolved when a solution of an iodide is treated in this manner. The former is converted into hydroxide, which may be removed by filtering through a paper which has been thoroughly wet with boiling water. c. Starch Grind about one gram of arrowroot starch with a little water and pour the mixture into 150 or 200 cc. of boiling water. Continue to boil the liquid for about one minute, and then allow it to cool and settle. The clear portion only is to be used for the detection of free iodine. A new preparation of starch is to be made for each day's work. d. The Solution of Iodine To prepare this, measure into a liter flask a volume of potas- sium iodide solution which contains 18 grams of the salt. Weigh in a little over 13 grams of commercial iodine. Close SILVER AND THE HALOGENS 225 the flask and shake it until the iodine is dissolved. If the solu- tion progresses too slowly, it may be hastened by adding more of the potassium iodide. Introduce 200 or 300 cc. of water and agitate again. Continue to add water and to agitate .after each addition until the flask is filled to the mark, making sure that all of the iodine is dissolved. e. The Solution of Sodium Thio sulphate Weigh about 27.5 grams of the salt into a liter flask. Dis- solve it in water and dilute to the mark. /. Standardization of Solutions d and e Fill one burette with the solution of thiosulphate and another with that of iodine. Measure 10 cc. of the former into a beaker. Dilute with water and add 1 or 2 cc. of tho starch preparation. Titrate with the iodine solution, stirring constantly, until a faint blue color is developed which disappears on the addition of a very minute quantity of thiosulphate. Repeat the experiment until constant results are obtained. Having found the relation of the iodine and thiosulphate solutions, it remains to determine the exact strength of the latter. To do this, measure about 10 cc. of a potassium iodide solution (10 : 1) into a glass-stoppered flask, and weigh in from 0.1 to 0.2 gram of the resublimed iodine. Close the flask and shake it until the iodine is dissolved. Add a little water, then close the flask and shake it again. Proceed in this way until a solution is obtained which is so dilute that no vapors of iodine can be seen above it. Add now the thiosulphate until the color of the solution has nearly disappeared, and then 1 or 2 cc. of the starch. Add thiosulphate again until the solution becomes quite colorless, noting carefully, however, the quantity required just to destroy the blue color. From another burette add the iodine solution d until a faint blue color appears. 226 QUANTITATIVE EXERCISES Subtract from the total volume of the thiosulphate used the quantity equivalent to the iodine solution d which was used to restore the blue color. The difference is the volume of the thiosulphate which is equivalent to the known weight of pure iodine. Repeat the experiment with another weighed portion of iodine. Having found the strength of the thiosulphate solu- tion, and indirectly that of the iodine, the two solutions may be diluted to any desired standard. One-tenth normal solutions are usually employed, though it is often advantageous to dilute to one-half and even to one-tenth of that strength. Neither solution is stable, and both require frequent restand- ardization. They lose strength less rapidly when kept in a cool, dark place. It has been proposed to employ for the restandardization of the thiosulphate standard solutions or weighed quantities of stable compounds which, when acidified, in the presence of potas- sium iodide, liberate a definite quantity of iodine. The follow- ing equations represent some of the reactions which have been utilized in this way: K 2 Cr 2 O 7 + 14 HC1 + 6 KI = 8 KC1 + 2 CrCl 3 + 7 H 2 O + 3 1 2 , 2 KMnO 4 +16 HC1 + 10 KI =12 KC1+ 2 MnCl 2 + 8 H 2 O + 5I 2 , KI0 3 + 6 HC1 + 5 KI = 6 KC1 + 3 H 2 O + 3 I 2 , HIO 3 .KIO 3 + 11 HC1 + 10 KI = 11 KC1 + 6 H 2 O + 6 I 2 , NaBrO 3 + 6 HC1 + 6 KI = 6 KC1 + NaBr + 3 H 2 O + 3 1 2 . II. IODOMETRIC DETERMINATION OF SULPHUROUS ACID Weigh about 5 grams of sodium sulphite into a half-liter measuring flask. Dissolve the salt in water and dilute to the mark. Measure 10 cc. of the standard solution of iodine into a beaker and dilute with water. Add 1 or 2 cc. of dilute hydro- chloric acid, and then titrate with the sulphite solution until the solution of iodine has become nearly colorless. Add starch and then more of the sulphite until the blue color has wholly disappeared. Titrate back to color with the standard solution SILVER AND THE HALOGENS 227 of iodine. The volume of the iodine solution employed to restore color must, of course, be added to the 10 cc. which were measured out in the first place. Calculate from the results the percentage of Na 2 SO 3 in the sulphite. Repeat the experiment, omitting the hydrochloric acid. The order of the titration, i.e. the addition of the sulphite to the iodine, cannot be reversed except in the case of exceedingly dilute solutions, because in even moderately dilute solutions of sulphu- rous acid the hydriodic acid which is formed when iodine is intro- duced reacts upon a portion of the remaining sulphurous acid with formation of water and liberation of sulphur and iodine : H 2 S0 3 + 4 HI = 3 H 2 + S + 2 I 2 . The iodine thus liberated reacts at once upon another portion of the sulphurous acid and water with formation of sulphuric acid and more hydriodic acid. Hence the reaction between sulphu- rous acid and iodine is regular, i.e. in accordance with the equa- tion H 2 SO 3 + H 2 O + I 2 = H 2 SO 4 + 2 HI, only when the iodine is in excess. The reaction Na 2 SO 3 + H 2 O + I 2 = Na 2 SO 4 + 2 HI is some- times employed in standardizing acids. If the strength of the iodine solution is known, and the sulphite is neutral, the quan- tity of hydriodic acid which will be formed can be calculated. It may be employed to standardize a solution of iodine. For this purpose a solution of neutral sulphite of unknown strength, but dilute, is added to a measured portion of the iodine solution to be standardized until the color disappears. The hydriodic acid is then determined by means of some standard alkali. Methyl orange should be used as the indicator. It will be seen from the following equations that it is practicable, with a standard solution of iodine, to determine a neutral sulphite and a thiosulphate when the two occur in the same solution : 2 Na 2 S 2 3 + 1 2 = 2 Nal + Na 2 S 4 O 6 , Na 2 S0 3 + H 2 + I a = Na 2 S0 4 + 2 HI. 228 QUANTITATIVE EXERCISES The sum of the sulphite and thiosulphate is found from the iodine consumed in both reactions, while the sulphite is esti- mated separately by neutralizing the hydriodic acid with a standard alkali. III. IODOMETRIC DETERMINATION OF CHROMIC ACID Weigh from 0.1 to 0.2 gram of pure potassium bichromate into a chlorine apparatus of the form represented in Fig. 45. Drop in a small piece of compact magnesite which is free from ferrous iron, and fill the flask half full of concentrated hydrochloric acid which contains no free chlorine. Pour about 50 cc. of potassium iodide solution of FlG - 45 the usual concentration (1:10) into the receiver and connect the two parts of the apparatus as shown in the figure. Cautiously heat the flask until the reduction of the chromate is complete and all of the chlorine has been driven over into the receiver. With the lamp in one hand continue to heat the flask, and with the other hand withdraw the receiver until the curved end of the delivery tube is above the solution of potassium iodide. Immerse the closed end of the receiver in cold water and shake up the liquid from time to time to hasten the absorption of iodine vapors. Empty the receiver, introduce a fresh portion of iodide solution, connect up the apparatus, and heat again in order to ascertain whether all of the chlorine was distilled over in the first operation. Determine the iodine with the standard solution of thiosulphate. The following equations represent the reactions which are involved in the determination: K 2 Cr 2 7 + 14 HC1 = 2 KC1 + 2 CrCl 3 + 7 H 2 O + 3 Cl, 3 CL + 6 KI = 6 KC1 + 3 I 9 . Any other oxygen compound which liberates from hydro- chloric acid a definite quantity of chlorine can be determined in SILVER AND THE HALOGENS 229 the same manner provided it is free from substances which, like iron in ferrous salts, absorb chlorine or convert it into chlorides. IV. IODOMETRIC DETERMINATION OF ARSENIOUS ACID Weigh from 0.1 to 0.2 gram of pure resublimed arsenious oxide, and from 0.2 to 0.4 gram of pure potassium bichromate, into the chlorine evolution flask. Add concentrated hydro- chloric acid and a piece of magnesite. Put the same quantity of potassium iodide solution into the receiver as before. Con- nect the two parts of the apparatus, and allow the mixture to stand for an hour or more before heating and then proceed as directed under III. The difference between the quantity of iodine found and the quantity which the known weight of bichromate would have yielded in the absence of any reducing substance is due to the fol- lowing reaction, by which the arsenious oxide has been converted into arsenic acid at the expense of a part of the chlorine : As 2 O 3 + 2 H 2 O + 2 C1 2 = As 2 O 5 + 4 HC1. There is therefore a deficit of four atoms, or 503.56 parts, of iodine for each molecule, or 196.54 parts, of the arsenious oxide. EXERCISE XVIII DETERMINATION OF HYPOCHLOROUS ACID I. BY WAGNER'S METHOD Weigh about 5 grams of bleaching powder taking care to have the weighing glass tightly closed while in the balance case into a porcelain mortar and grind the material fine with a little water. Add more water and transfer the liquid through a funnel to a half-liter measuring flask. Grind what remains in the mortar again with water, etc., until all the material has been brought into the flask. Fill to the mark with water. Shake up the contents of the flask, and, without giving the 230 QUANTITATIVE EXERCISES suspended matter time to subside, measure 10 cc. of the liquid into a beaker with a pipette. Add about 100 cc. of water and 6 cc. of the usual solution of potassium iodide. Acidify with dilute hydrochloric acid, and determine the iodine with the standard solution of sodium thiosulphate. The iodine liberated is equivalent to the active chlorine in the bleaching powder, i.e. the chlorine which would be liberated if the material were treated with any acid : CaCl 2 + 2 HI = CaCl 2 + H 2 O + 1 2 , CaCl 2 O + 2 HC1 = CaCl 2 + H 2 O + C1 2 , or CaCl 2 + H 2 S0 4 - CaS0 4 + H 2 O + C1 2 . There are two ways of stating the quantity of active chlorine in bleaching powder. One gives the volume of the chlorine, under standard conditions of temperature and pressure, which a unit weight of the powder will yield, and the other the per- centage of the same by weight. A specimen which yields 100 cc. of chlorine per gram, or 100 liters per kilogram, of the material would be said to have 100 chlorometric degrees, or 100 degrees Gay-Lussac. A cubic centimeter -of chlorine weighs 3.16742 milligrams at latitude 45 and sea level. A 100-degree bleaching powder must there- fore contain 31.67 per cent of active chlorine. The results of the determination should be stated in both ways. II. BY PENOT'S METHOD There are required for this experiment : 1. Starch-iodide papers for the detection of hypochlorous acid. Grind together in a porcelain mortar 1.5 grams of starch and 125 cc. of water. Boil the mixture for a few minutes. Add 0.5 gram of potassium iodide and an equal weight of crys- tallized sodium carbonate. Dilute with water to 250 cc. Satu- rate strips of white filter paper with the solution and dry them. Keep the papers in a closed vessel. SILVER AND THE HALOGENS 231 2. A standard solution of sodium arsenite. To prepare this, dissolve 2.211 grams of pure arsenious oxide in 300 to 350 cc. of hot water to which 6.5 grams of pure crystallized sodium car- bonate have been added. Dilute the solution, when cold, to one half-liter. Each cubic centimeter of the solution is equiva- lent to one cubic centimeter of chlorine gas when measured under standard conditions of temperature and pressure, or to 3.16742 milligrams of the same. 3. A solution of the bleaching powder which is to be tested. This is prepared in the same manner as that which was used with Wagner's method. It is convenient, however, to employ a solution one cubic centimeter of which contains 0.010 gram of the original material. In all cases the solution should be well shaken just before measuring out the portion which is to be tested. Measure into a beaker the quantity of the solution which contains 0.5 gram of bleaching powder. Titrate into it, slowly and with constant stirring, the standard solution of sodium arsenite until a. drop of the liquid taken out with a glass rod and applied to the starch-iodide paper no longer gives a blue color. If exactly one half-gram of the material was employed for the determination, the number of cubic centimeters of the sodium arsenite used, multiplied by 2, is equal to the number of the degrees Gay-Lussac of the sample ; and the number of cubic centimeters used, multiplied by 3.16742, gives the number of milligrams of active chlorine found. Another method of determining the active chlorine in bleach- ing powder, which is rapid and fairly accurate, is that proposed by Lunge. It depends upon the fact that when a hypochlorite and hydrogen peroxide are brought together, a volume of oxy- gen is evolved which is exactly equal to that of the available chlorine in the hypochlorite : CaCl 2 + H 2 2 = CaCl 2 + O 2 , CaCl 2 + H 2 S0 4 = CaS0 4 + H 2 O + C1 2 . 232 QUANTITATIVE EXERCISES The measurement of the liberated oxygen is therefore equiva- lent to a measurement of the chlorine which would be evolved if the material were treated with an acid as represented in the second equation. The determination is made by placing a known weight of the bleaching powder prepared with water, as previously directed in a small flask and then lowering into the flask a flat- bottomed tube containing an excess of hydrogen peroxide. The flask is attached to a Hempel burette, or to some other suitable gas-measuring tube, which is partly filled with water. The height of the water in the burette is read, the tube con- taining the peroxide overturned, and the increase in the volume of the gas determined. It will be seen that by reversing the process i.e. by adding an excess of hypochlorite to a known volume of hydrogen per- oxide the strength of any solution of the peroxide may be determined by means of the same reaction. As a matter of fact, the method is rather more satisfactory for the determination of hydrogen peroxide than for the determination of a hypochlo- rite, because the evolution of oxygen in the latter case does not wholly cease with the destruction of the hypochlorite. The continued liberation of oxygen is due to a so-called catalytic decomposition of the excess of peroxide. It is, however, so slow that fair determinations of the hypochlorite may be made in spite of it. EXERCISE XIX DETERMINATION OF HALOGENS IN ORGANIC COMPOUNDS I. BY THE LIME METHOD In a narrow combustion tube, about 400 mm. in length and closed at one end, place a layer 60 mm. in length of pulverized lime which has been prepared from marble and is free from chlo- rine. Upon this place about 0.2 gram of pure chloral hydrate. Add another layer of lime of about the same length as the first. SILVER AND THE HALOGENS 233 Mix the materials with a wire, and then fill the tube nearly full of the lime. Hold the tube in a horizontal position and tap it upon the table until there is formed at the top a channel of suffi- cient size for the escape of gases. Place the tube in a combustion furnace and heat the lime near the open end to redness. Then, beginning at the heated end, light the other burners under the tube, one after another, and at considerable intervals of time. Having kept the whole tube at a red heat for twenty minutes or half an hour, cool it slowly and uniformly. Wipe the outside and transfer the contents to a beaker containing considerable water. Rinse the tube with water to which a little nitric acid has been added. Treat the contents of the beaker with dilute nitric acid (free from chlorine) until the liquid becomes perma- nently acid. It is not necessary to dissolve the whole of the solid material. The lime usually contains some silicate which is not readily decomposed by the acid. Filter through a small paper, and determine the chlorine in the filtrate, either gravi- metrically or by the method of Volhard. Instead of emptying and cleansing the tube in the manner prescribed, it may be closed with a stopper and placed, still hot, in a high beaker which is two-thirds full of cold water. In this way, it will be broken into small pieces, which, together with the carbon and other insoluble material, are filtered out after the treatment with dilute nitric acid. If, as often happens, the lime, notwithstanding its preparation from marble, contains chlorine, the percentage of the latter must be determined and the lime employed in the experiment must be weighed. The chlorine belonging to the lime may then be deducted from the total found. If compounds containing considerable nitrogen are decomposed by lime, there is a formation of cyanogen, and the precipitate obtained with silver nitrate is then a mixture of chloride and cyanide. The formation of cyanogen may be avoided by decom- posing nitrogenous halogen compounds with soda-lime instead of lime. 234 QUANTITATIVE EXERCISES Bromine and iodine are determined by the lime method in the same manner as chlorine. It is necessary, however, especially in the determination of iodine, to add a little sulphurous acid to the solution before precipitating with silver nitrate. Liquid substances are weighed and introduced into the com- bustion tube in small bulbs blown on the ends of capillary tubes. The bulbs should be capable of holding about twice the quantity of liquid which is required for the analysis, and the tubes to which they are attached should be from 75 to 100 mm. in length. After weighing the bulb, the outlet is immersed in the liquid, which may then be made to rise into the bulb by alter- nately heating and cooling the bulb or by placing the vessel con- taining the liquid under the bell of an air pump and exhausting. The bulb is wiped dry, closed by holding the open end in the flame of a Bunsen burner, and weighed. Before introducing it into the combustion tube, the capillary tube is scratched with a file at a little distance from the base, and broken off. Both parts are then dropped into the lime or soda-lime in the bottom of the combustion tube. II. BY CARIUS' METHOD In a thick combustion tube having a length of 400 or 500 mm. and an internal diameter of 13 to 15 mm., and closed at one end place from 2.5 to 3 cc. of nitric acid of 1.5 specific gravity. In a narrow tube, 75 or 100 mm. long, weigh about 0.2 gram of chloral hydrate, and add to it about four times its weight of crystallized silver nitrate. Place the smaller tube in the larger one and draw out the open end of the latter to a capil- lary with thick walls, taking care not to let the nitric acid and the substance come together until the tube is sealed. The explo- sions which so often occur when substances are heated in closed tubes are usually due to a faulty sealing of the tubes. It is well, therefore, for one not experienced in this kind of manipu- lation to practice for a time under supervision if possible SILVER AND THE HALOGENS 235 with odd pieces of glass tubing before attempting to seal the tube which is to be used in this exercise. It is important that the wall of the drawn-out portion of the tube should be made quite thick at every point, and the glass should be well annealed by turning it in the smoky flame until it is densely and uniformly covered with carbon. Put the closed tube in an iron one, letting the capillary end project a little beyond the mouth of the latter. Place the two tubes in the u bomb" furnace and put an empty wooden box before it to receive the material which will be ejected if an explosion occurs. Gradually raise the temperature of the fur- nace to 250, and keep it there for two hours. When the glass tube has cooled to the temperature of the room, take the capil- lary end between the thumb and forefinger and draw the tube forward under a folded towel ; and as soon as it is out of the iron tube roll it up in the towel. The opening of the tube, which requires great caution, is best accomplished in the follow- ing manner: A 300- or 400-cc. beaker, partly rilled with water, is tilted forward and secured in this position by a block ; a burner is placed directly in front of the beaker; finally, the capillary end of the tube is uncovered and cautiously heated until the glass softens, swells out, and opens for the escape of the com- pressed gases within. The issuing material should, of course, be directed into the beaker. Cut the tube near the middle, taking care that no fragments of glass fall into either part, wash the contents into a beaker, nearly neutralize the excess of nitric acid with sodium carbonate which is free from chlorine, and determine the silver chloride in the usual manner. Bromine and iodine in organic compounds may also be deter- mined by the method of Carius. The author of the method recommends in the case of iodine compounds that the mixture of silver iodide and nitrate be heated until it fuses to a yellow liquid which solidifies on cooling to an, opaque yellow mass. 236 'QUANTITATIVE EXERCISES This must afterwards be heated in the diluted liquid from one to two hours in order to effect a separation of the iodide and nitrate. The halogens may be removed from many organic compounds by treating their aqueous or alcoholic solutions with sodium amalgam. The Separation of the Halogens Any two of the halogens, when the third is absent, may be determined by an indirect method. Suppose, for example, that chlorine and bromine, in the form of a chloride and a bromide, are in solution and are to be determined indirectly. The best pro- cedure is as follows : The amount of silver required for the precipitation of both is ascertained by the volumetric method of Mohr; the precipitate of AgCl and AgBr is then collected, washed, dried, and weighed. If, for any reason, the method of Volhard is to be preferred to that of Mohr, the solution is diluted to a known volume and divided, one measured portion being used for the volumetric, and the remainder for the gravi- metric, determination. The calculation is as follows : Atomic and Molecular Weights Ag = 1 07.11, AgCl = 142.29, Cl = 35.18, AgBr = 186.46. Br = 79.35, Let x = weight of chlorine, y = " " bromine, a = " " silver required to precipitate Cl and Br, b= " AgCl + AgBr. Then x + y = b a, and r *-* 4-04462,+ 2.34984, = i; x = 1.38651 a - 0.79646 b, and y = 1.79646 b -2.38651 a. SILVER AND THE HALOGENS 237 Several methods have been proposed for the separation of bromine from chlorine, all of which depend upon the fact that certain oxidizing agents under certain conditions are capable of liberating bromine from bromides but not chlorine from chlorides. The bromine, when liberated, is expelled from the solution, with the aid usually of a current of steam or air, and is collected either in a solution of some alkali to which has been added a quantity of hydrogen peroxide in order to prevent the formation of a hypobromite, or in a solution of potassium iodide. In the latter case the equivalent quantity of liberated iodine is determined volumetrically by means of sodium thiosulphate. Some of the oxidizing agents which have been employed for the liberation of bromine in a mixture of bromides and chlorides are : 1. Lead peroxide and acetic acid (Vortmann*). 2. Potassium permanganate and acid potassium sulphate (Berglund f). 3. Potassium permanganate and aluminium sulphate (White ). 4. Potassium permanganate and acetic acid (Jannasch and Aschon). 5. Potassium bichromate and sulphuric acid (Dechan, || Fried- heim and Meyer **). 6. Ammonium persulphate (Engel ff ). 7. Potassium permanganate and ferrous sulphate (Weiss ). 8. lodic acid (Bugarszky ). 9. Potassium permanganate in the presence of copper salts (Baubingy and Rivals || ||). * Zeitsch. anal. Chem., 19, 352 ; 22, 565, 566 ; 24, 196; 25, 172. t Ibid., 24, 184. J Chem. News, 57, 283 ; 58, 229. See references cited under Exercise XX. || Jour. Chem. Soc., 49, 682. ** Zeitsch. anorg. Chem., 1, 407. ft Zeitsch. anal. Chem., 34, 616. U Ibid., 34, 615. Zeitsch. anorg. Chem., 10, 387. (Ill Comptes Rendus, 124, 859; 125, 527, 607. 238 QUANTITATIVE EXERCISES Iodine may be separated from chlorine and bromine in a mix- ture of halogen salts in various ways : 1. It may be liberated by nitrous acid,* which does not decom- pose hydrochloric or hydrobromic acid, and then removed from the solution, either by extraction with carbon bisulphide, or by passing a current of steam through the liquid. If extracted by carbon bisulphide, it is best determined by a standard solution of sodium thiosulphate. If, on the other hand, the liberated iodine is removed by steam, it is best to conduct the vapors into an alkaline solution of hydrogen peroxide, and to determine it, either volumetrically or gravimetrically, as silver iodide. 2. The iodine may be liberated by arsenic acid (Gooch and Browningf) and removed by evaporation and the resulting equiv- alent quantity of arsenious acid determined volumetrically as recommended by the authors of the method ; or it may be removed with the aid of steam, collected in a solution of potassium iodide, and determined by sodium thiosulphate as recommended by Friedheim and Meyer. J 3. The iodine maybe precipitated by thallium nitrate (Hiibner, Spezia, and Frerichs ) ; or, if the quantity of bromine is small, by palladium nitrate. In the absence of bromine, iodine may be separated from chlorine by precipitating with thallium sulphate in the presence of ammonium sulphate and alcohol (Jannasch and Aschoff ||). * See Fresenius, Quant. Analyse, 1, 659; also Gooch and others, Zeitsch. anal Chem., 30, 58; 34, 603. t Zeitsch. anal. Chem., 30, 60; Zeitsch. anorg. Cftem.,4, 178. | Zeitsch. anorg. Chem., 1, 407. Fresenius, Quant. Analyse, 1, 661. || Zeitsch. anorg. Chem., \ , 248, SILVER AND THE HALOGENS 239 EXERCISE XX THE SEPARATION OF CHLORINE, BROMINE, AND IODINE BY THE METHOD OF JANNASCH AND ASCHOFF * The apparatus which is recommended by the authors of the method is shown in Fig. 46. It consists of : 1. A metallic vessel , in which steam is produced for the expulsion of iodine and bromine. 2. The flask 6, with a capacity of about one liter, in which the iodine and bromine are successively liberated the former by nitrous acid and the latter by potas- sium permanganate and acetic acid. 3. The thin flask c, with a capacity of about 500 cc., which contains a solution of sodium hydroxide and hydrogen peroxide, and is cooled by running water. 4. The Peligot tube d, which also contains a small quantity of the alkaline solution of hydrogen peroxide. 5. The Erlenmeyer flask e, containing a dilute solution of caustic soda to which a little ammonia has been added. The required reagents are : 1. A 10 per cent solution of sodium nitrite. 2. A 5 per cent solution of sodium hydroxide. 3. A 3 per cent solution of hydrogen peroxide. 4. A 30 per cent solution of pure acetic acid. 5. A nearly saturated solution of potassium permanganate (approximately 5 per cent). FIG. 46 * Zeitsch. anorg. Chem., 1, 144; 5, 8. 240 QUANTITATIVE EXERCISES All of the reagents must be free from halogens, and the acetic acid must be free from substances with which the halogens form substitution products. Weigh out about one quarter gram each of pure chloride, bromide, and iodide of potassium. Introduce the salts into the flask 6, dissolve in water, and dilute to about 750 cc. Measure 100 cc. of a mixture of equal volumes of the sodium hydroxide and hydrogen peroxide solutions into the flask c?, and a few cubic centimeters of the same mixture into the Peligot tube d. In the Erlenmeyer flask e place a small quantity of the caustic soda solution and add to it a little ammonia. Having brought the water in a to the boiling point, add to the solution of the salts first 5 cc. of dilute sulphuric acid, and then 10 cc. of the solution of sodium nitrite. Close the flask quickly and conduct steam through it until all of the iodine has been removed, heating the contents of the flask in the mean- time with a small flame. Disconnect the absorption apparatus while the steam is still passing through, and transfer the contents of c and d quantita- tively to a porcelain dish, keeping the liquid in e separate. Make the solution of chloride and bromide in b distinctly alka- line with caustic soda and concentrate it in a porcelain dish to a volume of 50 cc. Return the solution to b and allow it to cool. Arrange and refill the absorption apparatus as for the collection of iodine, and introduce into b 60 cc. of the 30 per cent acetic acid and the volume of the permanganate solution which con- tains 1 gram of the salt. Heat the flask with a small flame and pass steam through it for not less than an hour after the con- tents have reached the boiling point. Determination of the Iodine Heat the liquid derived from c and d which probably con- tains all of the iodine for a long time in a covered porcelain SILVER AND THE HALOGENS 241 dish, add 50 cc. of the hydrogen peroxide solution to complete the oxidation of any sodium nitrite which may be present. Afterwards add the contents of the Erlenmeyer flask e, and concentrate to a suitable volume. To the alkaline solution add silver nitrate, little by little, and stir until the brown oxide of silver which is first formed is no longer converted into the yellow iodide. Acidify with nitric acid and heat for some hours upon the water bath, or until the precipitate has properly sub- sided. Filter hot, wash with boiling water, etc. Determination of the Bromine Heat the contents of c and d in a covered porcelain dish with an additional quantity of hydrogen peroxide in order to destroy any sodium hypobromite which may be present. Add the liquid in the Erlenmeyer flask and concentrate. Precipitate the bro- mine with a mixture of equal parts of 10 per cent silver nitrate solution and concentrated nitric acid. Heat from one to two hours on the water bath, filter hot, wash with boiling water, etc. Determination of the Chlorine Reduce the excess of permanganate with an ammoniacal solu- tion of hydrogen peroxide. Collect the oxide of manganese upon a roomy filter and wash with a one per cent solution of sodium nitrate. Determine the chlorine in the filtrate as silver chloride. If the liquid in which the three halogens are to be determined contains calcium, the use of sulphuric acid to decompose the nitrite for the purpose of liberating iodine is inadmissible. In such a case the authors of the method acidify the solution with a few drops of acetic acid and then conduct into the flask from the outside the vapors of nitrous acid until the space above the liquid begins to fill with the yellowish-red gas. 242 QUANTITATIVE EXERCISES Jannasch and Koelitz* have found that when the halogens are to be determined in an alkaline liquid, either sulphuric or nitric acid and not acetic acid should be employed to neu- tralize the solution, since the presence of acetates but not of sulphates or nitrates retards the quantitative liberation of bromine. To determine the halogens in organic compounds the authors f proceed as follows : If the substance is to be decomposed by the " lime method," a hard glass tube about 50 centimeters long and having an internal diameter of 4 mm. is filled to a depth of 3 or 4 centimeters with quicklime. The material previously mixed with lime in a deep porcelain mortar is then introduced. Afterwards the mortar, funnel, etc., are rinsed a number of times with small portions of finely ground lime, which are like- wise filled into the tube until there remains room only for a plug of asbestus. After heating in the usual manner, the cooled contents of the tube are transferred to a glass-stoppered liter flask containing about 300 cc. of water. The tube is rinsed first with water and then with dilute nitric acid. Strong nitric acid, in small quantities, is then added until only a small portion of the lime remains undissolved, care being taken constantly to agitate the contents of the flask and to keep them cool. If, accidentally, the whole of the lime is dissolved, more must be added in order to produce an alkaline condition. After filtering and washing the solid residue with hot water, the halogens are precipitated with a mixture consisting of equal parts of concen- trated nitric acid and a 10 per cent silver nitrate solution. The silver salts- are heated upon a water bath, with frequent agita- tion, for an hour or more, or until the precipitate has fully sub- sided, and then collected upon a small paper filter. The washed contents of the filter together with the still moist paper are transferred to a silver crucible and fused with 5 or 6 grams of pure sodium hydroxide until the paper is fully burned and a * Zeitsch, anorg. Chem., 15, 66. t Ibid., 15, 68. SILVER AND THE HALOGENS 243 tranquil liquid is obtained. Finally, the residue is treated with water, warmed upon a water bath, filtered, the excess of alkali neutralized with sulphuric or nitric acid, and the halogens sepa- rated in the manner prescribed in Exercise XX. The procedure with the silver salts is identical with that described above when the organic compound is decomposed by the method of Carius. They are collected upon a paper, washed, transferred still wet to a silver crucible, fused with sodium hydroxide, etc. CHAPTER X SULPHUR EXERCISE XXI THE DETERMINATION OF SULPHURIC ACID IN BARIUM SULPHATE Weigh in a platinum crucible from 0.3 to 0.4 gram of pure, finely pulverized and dried heavy spar. Add about five times as much sodium-potassium carbonate which is free from sulphates, and fuse over the blast lamp until the decomposition is believed to be complete. Place the crucible on its side in a porcelain dish, cover it with distilled water, and heat until the excess of the carbonate and the alkali sulphates are dissolved. Filter, and wash the barium carbonate with water to which a little ammonia and ammonium carbonate have been added. Slightly acidify the filtrate with hydrochloric acid. Dilute, if necessary, to a volume of 100 or 150 cc. ; heat nearly to the boiling point, and precipi- tate the sulphuric acid (slowly and with constant stirring) with a dilute hot solution of barium chloride, taking care to add a slight excess of the latter. Continue to heat the liquid for an hour, ^at least, and then put aside to settle. When the liquid above the precipitate has become perfectly clear, pour it through a small filter. Treat the precipitate remaining in the beaker with boiling water containing a little hydrochloric acid, and pour this also through the paper when the barium sulphate has subsided. Wash the precipitate several times in this manner, and then bring it upon the filter. Wash again with hot water until the filtrate gives no reaction for chlorine. 244 SULPHUR 245 Detach the edge of the filter from the glass with the aid of a stout platinum wire flattened at one end, or a thin spatula, and lift it out of the funnel. Examine the glass carefully for pre- cipitate which may have crept over the edge of the paper, and, if any is found, wipe it up with a fragment of ashless paper which is afterwards to be placed in the filter. Fold the filter, without drying, into a compact wad, and place it in a weighed platinum crucible. The subsequent incineration requires some caution. The crucible, tilted to one side, is placed in a triangle which rests upon the ring of an iron stand. At first the ring is raised considerably above the flame, where it is kept until the paper is dry. Afterwards it is lowered from time to time until the charring process is finished, but never so far that the volatile products burst into flames. Finally, when nothing remains of the paper except carbon, the crucible is lowered into the flame and the incineration completed. The residue of carbon should burn quite readily, leaving a perfectly white ash. If it does not, measures should be taken to promote the circulation of air over the heated material. To this end the lamp is so placed that only the bottom of the tilted crucible is in contact with the flame ; and the lid, with its edge resting on the triangle, is allowed to lean against the mouth of the crucible. It is quite practicable, of course, in cases of difficult incineration to intro- duce into the crucible a current of air or of oxygen through a small glass tube. It is recommended by Richards, in precipitating sulphuric acid by barium chloride, to allow the solution of the latter to flow in a thin stream down the side of the beaker containing the former. The liquid spreads out in its passage over the glass wall, thus giving a great surface of first contact between the two solutions. The following manipulation of this method of precipitation has been found very satisfactory : By rotating the beaker in the hand, the hot solution of sulphate is given a somewhat rapid circular motion. The beaker is then placed on the sand bath or wire gauze, and the hot solution of chloride is 246 QUANTITATIVE EXERCISES slowly poured down the side. When the movement of the liquid becomes too sluggish, the beaker is taken from the bath and again rotated. With proper management a precipitate is obtained which subsides completely within a few minutes. When sulphuric acid is precipitated by barium chloride, some of the latter is always occluded by the barium sulphate, and no amount of washing suffices for its complete removal. The sulphate, however, is somewhat soluble, and under favorable conditions of precipitation the two sources of error nearly com- pensate each other. The occlusion is greater in concentrated than in dilute solutions. It is greater also in cold than in hot solutions. According to Richards the occlusion is increased by the presence of hydrochloric acid, but not by the addi- tion of barium chloride after the precipitation of the sulphuric acid has been completed. The quantity of chloride which is carried down by the sulphate is greater when the latter is formed in the presence of an excess of the former, i.e. when the sulphuric acid or soluble sulphate is added to the solution of the barium salt ; hence in precipitating, whether for the deter- mination of sulphuric acid or of barium, the solution of the barium salt is poured into that of the sulphate. This order should never be reversed. The amount of the occluded chloride can be ascertained by fusing the precipitated sulphate with an alkaline carbonate and determining the chlorine as silver chloride. The solubility of barium sulphate varies somewhat with the circumstances under which it is precipitated ; it is given as one part in 400,000 parts of water under the usual conditions of precipitation. The precipitation is retarded even by very dilute hydrochloric acid, while in the presence of the moderately con- centrated acid it is quite incomplete. The presence either of a soluble barium salt or of a sulphate (anything furnishing an ion in common with it) diminishes its solubility; hence the practice SULPHUR 247 in this case, as in quantitative work in general, of adding an excess of the precipitating agent. It is dissolved by concen- trated sulphuric acid and reprecipitated on dilution with water. For further information regarding the solubility of barium sulphate see Fresenius and Hintz, Zeitschrift fur analytische Chemie, 35, 170. There is some danger when the filter is burned too rapidly, i.e. at too high a temperature, that a little of the sulphate will be reduced to sulphide, which may be converted by the water vapor and carbon dioxide surrounding it first into hydroxide and afterwards into carbonate. It is therefore well to moisten the material, after the first ignition and weighing, with a drop of sulphuric acid, and then to evaporate, ignite, and weigh again. EXERCISE XXII DETERMINATION OF SULPHUR IN SULPHIDES The nitric acid which is to be used in this and in a subsequent experiment is to be prepared in the following manner: Pour into a tubulated liter-and-a-half retort, first 200 cc. of concen- trated nitric acid, and then 600 cc. of concentrated sulphuric acid. Fasten the retort in a clamp, and without boiling the mixture slowly distill about 100 cc. of the nitric acid into a receiver which fits the retort closely. The distillate will probably con- tain sulphuric acid, which must be removed. Place one or two grains of pulverized and thoroughly dried barium nitrate in a glass-stoppered bottle and add the nitric acid to it. Shake the bottle from time to time for several hours. Pour the acid into a small retort and distill it slowly into a receiver. The distil- late must now be tested for sulphuric acid. Place about 5 cc. of it in a clean dry retort, add about half a gram of pure potas- sium nitrate, and distill to dryness. Dissolve the residue in the retort in water, add a drop or two of hydrochloric acid, and test for sulphuric acid with barium chloride. 248 QUANTITATIVE EXERCISES Solutions which are to be tested for sulphuric acid, or in which the presence of small quantities of that acid would be harmful, must not be evaporated in open vessels over the ordi- nar}^ water bath. Owing to the presence of sulphur in the gas, solutions so treated almost invariably become contaminated with sulphuric acid. Weigh into narrow, flat-bottomed tubes two portions (0.2 to 0.3 gram each) of finely ground pyrites. This mineral is selected because it contains iron, which introduces a certain difficulty into the determination of sulphuric acid as sulphate of barium. Pour into pressure bottles so-called " Lintner bottles" from 5 to 10 cc. of the nitric acid which has been prepared as directed. Set the tubes containing the weighed material in the bottles in an upright position. Fasten the latter in their frames, and then tilt them so that the tubes fall on their sides. Shake the bottles gently until the acid and the mineral are well mixed. When the reaction ceases, or becomes very slow, place the bottles in a bath containing cold water. Heat the water and keep it near the boiling point for two hours or more. Examine the contents of the bottles for undecomposed mineral and unoxi- dized sulphur. The presence of solid matter, when sulphides are treated in this manner, is not a certain evidence that the reaction is unfinished, since it may consist of sulphates which, though soluble in water, are insoluble or only slightly soluble in nitric acid. If the reaction is incomplete, heat again in the water bath as before. If, on the other hand, it appears to be complete, transfer the contents of the bottles to porcelain dishes. If the mineral contained no insoluble foreign matter, and the oxidation is finished, the diluted solutions will be clear. If they are free from suspended matter, add to each about 0.3 gram of pure potassium chloride to insure the presence of enough base to convert all of the sulphuric acid into sulphates, and evaporate to dryness at a low temperature on a broad sand bath. Treat the residues with strong hydrochloric acid and again evaporate to dryness. Repeat the addition of hydrochloric acid SULPHUR 249 and the subsequent evaporation until all the nitric acid has been removed. Treat the residues with a few drops of hydrochloric acid and dissolve them in water. If the solutions contain sus- pended matter, they are to be filtered. Some sulphides, when decomposed with nitric acid in the manner just described, yield a deposit of free sulphur which is only very slowly converted into sulphuric acid. In such cases the bottles should be opened when cold and the contents treated with a little potassium chlorate or strong hydrochloric acid; after which they are to be closed and again gently heated. If this procedure fails to complete the oxidation of the sulphur, the diluted liquid must be filtered through a weighed paper, and the filter and its contents thoroughly washed, dried at con- stant temperature, and weighed. The residue on the paper, whose weight is determined in this manner, will consist of the unoxidized sulphur and any impurity in the mineral which has not been attacked by the nitric acid. The paper and its con- tents are therefore incinerated and the ash weighed. The loss during incineration is trie weight of the unoxidized sulphur. When sulphuric acid is precipitated by barium chloride in the presence of ferric salts, the barium sulphate carries down with it a quantity of iron, either as ferric sulphate or as a double sulphate of barium and iron, and the iron cannot be wholly removed even by washing the precipitate with dilute acids ; neither can the precipitation of the iron be prevented by the presence of any quantity of acid which would not interfere with the completeness of the precipitation of the sulphuric acid. \ Again, when barium sulphate which is contaminated with ferric sulphate is ignited, the sulphuric acid in combination with the iron is volatilized, and the barium salt becomes colored from pink to brown by ferric oxide. ; But the weight of the oxide is not equal to that of the barium sulphate which the lost acid should have formed. It is therefore found that the results are 250 QUANTITATIVE EXERCISES usually too low when sulphuric acid is determined in the ordi- nary manner in the presence of ferric salts. Various methods of obviating this difficulty have been proposed : (a) Lunge * precipitates the iron as ferric hydroxide by adding a not too large excess of ammonia to the moderately warm solu- tion, filters after 10 minutes, washes the precipitate with boiling water, and determines the sulphuric acid in the filtrate in the usual manner, i.e. by precipitating as barium sulphate in the presence of hydrochloric acid. If the ferric hydroxide is sus- pected of retaining sulphuric acid, it may be fused with sodium carbonate in a platinum crucible, the sodium salts dissolved in water, filtered, the filtrate acidified with hydrochloric acid, and tested with barium chloride. (b) Fresenius f fuses the pulverized mineral in which sulphur is to be determined in a platinum crucible with ten parts of a mix- ture consisting of two parts of dry sodium carbonate and one part of potassium nitrate, extracts the soluble matter with warm water, conducts carbon dioxide into the filtrate to precipitate any lead which may be present, filters, boils the insoluble residue in a solution of sodium carbonate, filters again, and boils the residual solid matter with water to which a little sodium car- bonate has been added. The filtrates and wash water are mixed, acidified with hydrochloric acid, warmed to expel carbon dioxide, and repeatedly evaporated in a porcelain dish with hydrochloric acid in order to expel the nitric acid and to render insoluble any silica which may be present. The residue is moistened with 2 cc. of hydrochloric acid, dissolved in water, filtered if necessary, and the sulphuric acid precipitated by barium chloride. The barium sulphate obtained in this way is frequently not quite pure ; it is therefore heated repeatedly in the platinum crucible in which it was weighed with small portions of weak hydrochloric acid, which are poured, after dilution, through a small filter. The filtrate is treated with a little barium chloride and evaporated nearly to dryness on the water bath. The residue is treated * Zeitsch. anal Chem., 19, 419. t Ibid., 16, 335. SULPHUR 251 with water and filtered through the small paper, which is after- wards burned, the ash being added to the main body of the barium sulphate. The purified material is usually found to weigh a little less than the original precipitate. \- (c) C. Meineke * and O. N. Heidenreich f reduce the ferric salt to the ferrous condition with metallic zinc, filter, wash the undissolved metal, and precipitate the sulphuric acid in the filtrate with barium chloride. (d) F. W. Kiister and A. Thiel $ treat the cold solution with an excess of dilute ammonia, heat nearly to the boiling point, add barium chloride, and then dissolve the precipitated ferric hydroxide with hydrochloric acid. The solutions of the sulphide are to be treated by methods c and d. 1. Method c Dilute one of the solutions in an Erlenmeyer flask to a vol- ume of 200 or 250 cc., add granulated zinc or filings of the metal and hydrochloric acid ; place a funnel in the mouth of the flask and warm upon a sand or asbestus bath until the reduction is complete. Filter hot through a paper wet with boiling water into a beaker, wash the undissolved metal and the filter, and precipitate the sulphuric acid with the usual pre- cautions. 2. Method d Dilute the remaining solution of the mineral to 70 or 80 cc. and precipitate the iron with a moderate excess of dilute ammo- nia. Heat nearly to the boiling point, stirring meantime, and then without separation of the ferric hydroxide by filtration * Zeitsch. anal Chem., 38, 209, 351. t Zeitsch. anorg. Chem., 20, 233. t Ibid., 19, 97. 252 QUANTITATIVE EXERCISES precipitate the sulphuric acid with barium chloride. Dissolve the ferric hydroxide with dilute hydrochloric aci'd, and keep the liquid hot for two hours. After cooling to the temperature of the room, pour the liquid through a filter and digest the remain- ing barium sulphate for half an hour with water containing a little hydrochloric acid. Decant through the filter ; repeat the digestion; wash several times with boiling water, by decanta- tion ; and then bring the precipitate upon the filter. EXERCISE XXIII THE DETERMINATION OF SULPHUR IN IRON BY FRESENIUS' METHOD There are required for this experiment : 1. A Kipp's apparatus for the generation of hydrogen. 2. Three cylinders, or wash bottles, for the liquids employed to purify the hydrogen. The first, i.e. that next to the genera- tor, is to contain a solution of caustic soda ; the second, a neu- tral or slightly alkaline solution (under no circumstances an acid one) of potassium permanganate ; and the third, a solution of lead hydroxide in caustic soda. The last is made by adding an excess of sodium hydroxide to a solution of lead nitrate. 3. A quarter-liter flask to contain the hydrochloric acid which is used to dissolve the iron. This is supplied with a doubly perforated rubber stopper, through which pass two glass tubes, both bent to a right angle. One of the tubes reaches to the bottom of the flask, and is covered with vaseline where it passes through the stopper in order that it may be easily raised and lowered. The other the one which is connected with the washing apparatus reaches only about halfway to the bottom of the flask. The flask is to be filled about half full of pure concentrated hydrochloric acid. w 4. A 300- or 400-cc. flask in which to dissolve the iron. This, like the flask 3, is supplied with a doubly perforated SULPHUR 253 stopper and two glass tubes. One of the latter is long reach- ing to the bottom of the flask and is bent to a right angle. This is connected with the long tube in 3 by a piece of rubber tubing 100 or 150 mm. in length. This rubber tube, also that by which 3 is connected with 2, is provided with a Mohr pinch- cock. The second glass tube, which should be as wide as prac- ticable, is bent to less than a right angle and is cut off even with the lower end of the stopper. The flask is to be placed on a tripod. 5. A short condenser with a comparatively wide inner tube. The condenser is fixed in an inclined position with its lower end attached to the tube in 4, which is bent to less than a right angle. 6. Two Peligot tubes, which are to be connected with each other and with the condenser. In these, corks, and not rubber stoppers, must be used. Both tubes are to be partly filled with strong hydrochloric acid in which from 3 to 5 cc. of bromine have been dissolved. At the exit end they are to be connected with a flask containing sodium hydroxide to which hydrogen peroxide has been added. Weigh about 10 grams of cast-iron borings into the flask 4, and add a few cubic centimeters of water. Conduct hydrogen through the apparatus with the Peligot tubes detached until the air in it has been displaced. Attach the Peligot tubes, press down the long tube in 3, and let the hydrogen force a little hydrochloric acid into 4. Clamp the rubber tube between 3 and 4, and gently heat the flask 4. When the reaction becomes too moderate, introduce more acid in the same manner as before. When the solution of the iron has been completed, raise the long tube in 3, and again pass hydrogen through the apparatus. Transfer the contents of the Peligot tubes to a porcelain dish, add about a gram of pure potassium chloride, and evaporate to dryness at a moderate temperature. Dissolve the residue in water, add a little hydrochloric acid, and precipitate the sul- phuric acid in the usual manner. 254 QUANTITATIVE EXERCISES The insoluble matter in the flask largely carbon will probably contain a small amount of sulphur, and this must also be converted into sulphuric acid and determined with that already precipitated. Filter the contents of the flask and wash thoroughly, first with a little dilute hydrochloric acid and then with hot water. Dry the filter and brush the material in it into a mortar. The small quantity of material which cannot be separated from the paper may safely be neglected. Add 10 grams of dry sodium carbonate and 5 grams of . potassium nitrate, and grind to a uniform mixture. Transfer the contents of the mortar to a large platinum crucible and heat raising the temperature quite grad- ually and only to the fusing point of the salts. Dissolve the cooled mass in water, filter if necessary, and evaporate the solu- tion in porcelain to dryness with hydro- chloric acid. Moisten the residue with strong hydrochloric acid and again evap- orate to dryness, repeating the treatment until all the nitric acid has been expelled. Dissolve the residue in water, adding a few drops of hydrochloric acid, filter, and precipitate the sulphuric acid with barium chloride. Collect both portions of barium sulphate on the same filter. All the materials used in the experi- ment must be examined for sulphur ; and, if reagents free from it are not obtainable, the sulphur in them must be determined. It will then be practicable by .working with weighed or meas- ured quantities of the impure reagents to correct properly the final results. This method for the determination of sulphur in iron can be applied with advantage to all those sulphides which are FIG. 47 SULPHUR 255 decomposed by hydrochloric acid with a quantitative conversion of the sulphur into hydrogen sulphide. A more convenient form of apparatus is shown in Fig. 47. The tube A is filled with beads or broken glass, and the bulb c, with the solution of bromine in hydrochloric acid. The iron, or the sulphide in which the sulphur is to be determined, is placed in B. The air in B is expelled by hydrogen which is purified in the manner already described, the gas being allowed to escape first at a and afterwards through b. The bulb d is then filled with hydrochloric acid which is admitted to the material below as occasion may require. Previous to the introduction of the acid, however, the broken glass in A is thoroughly moist- ened with the bromine solution in c. Afterwards the solution is allowed to flow from c as rapidly as may be necessary in order to keep the glass well colored by the bro- mine. The solution con- taining the sulphuric acid, which collects at the bot- x IG. 4o torn of the apparatus, is drawn off from time to time into a beaker or flask ; and when the operation is complete, the broken glass and the connecting tube b are rinsed with water into the same receptacle. Still another very effective form of apparatus for the ab- sorption of hydrogen sulphide and other gases is shown in Fig. 48. Various other substances besides a solution of bromine in hydrochloric acid are employed to absorb or to oxidize hydrogen sulphide ; for example, solutions of lead oxide in caustic alkali ; of cadmium oxide in ammonia ; of silver oxide in ammonia ; of ammoniacal hydrogen peroxide; and of potassium permanga- nate. It may also be determined iodometrically : L + H 9 S = S + 2 HI. 256 QUANTITATIVE EXERCISES EXERCISE XXIV THE DETERMINATION OF SULPHUR IN ORGANIC COMPOUNDS I. BY LIEBIG'S METHOD Place in a silver crucible about 10 grams of potassium hydrox- ide which is free from sulphur. Fuse (over an alcohol lamp if practicable), and continue to heat until the liquid becomes tran- quil. Add from 1 to 1.5 grams of potassium nitrate and stir it into the molten hydroxide with a silver spatula. Allow the crucible to cool, and place on the top of the solidified mixture a weighed quantity of any non-volatile organic sulphur com- pound which contains about 20 milligrams of sulphur. Fuse the contents of the crucible, and continue to heat until the carbon which separates is all oxidized and the liquid becomes transparent. Dissolve in water, and evaporate the solution in a porcelain dish repeatedly with an excess of hydrochloric acid until all the nitric acid has been expelled. Dissolve the residue in water containing a little hydrochloric acid. Dilute to about a liter and allow the solution to stand for several hours, observ- ing whether any silver chloride separates. If it becomes cloudy, filter. Evaporate in a porcelain or platinum dish to 150 or 200 cc. and precipitate the sulphuric acid in the usual manner with barium chloride. If gas must be used, since it always contains sulphur, care must be taken to protect the contents of the crucible from the products of combustion, and the fusion should not be unneces- sarily prolonged. It is to be remembered in this connection that much of the sulphur ordinarily in illuminating gas may be removed by passing the gas over a solution of lead oxide in sodium hydroxide. SULPHUR 257 II. BY CARIUS' METHOD In a thick-walled tube of moderately soft glass closed at one end and having a length of 450 or 500 mm. and an internal diameter of 15 to 18 mm. place a weighed quantity of any pure organic sulphur compound which contains from 15 to 20 milligrams of sulphur. Calculate how much of the nitric acid which was prepared for use in Exercise XXII will be required for the complete oxidation of the compound, and measure about three times that amount into a narrow glass tube. Place the tube containing the acid in the larger one, taking care not to allow the acid and the substance to be oxidized to come in contact. Close the outer tube with great care as directed in Exercise XIX, II. Heat the tube also as there directed. The temperature to which the bath must be raised and the length of time which it will be necessary to heat the contents of the tube will depend on the nature of the substance. If it is easily oxidized, two hours' heating at 200 will suffice. If it is attacked with difficulty by oxidizing agents like some of the sulphur derivatives of the aromatic hydrocarbons, especially the sulphonic acids it will be necessary to heat four or six hours at 250 or 260. Remove the tube from the bath and open it with all the pre- cautions mentioned in Exercise XIX, II. Transfer the liquid containing the sulphuric acid to a porcelain dish, and add about a gram of pure potassium chloride. Evaporate with hydrochloric acid repeatedly to remove nitric acid, and determine the sulphuric acid as barium sulphate. The ratio of the weight of the nitric acid, in grams, to the capacity of the tube in cubic centimeters should not exceed that of 1 to 12. In the case of substances requiring a high tempera- ture for their decomposition, e.g. 300, the tube may be heated for a time at a lower temperature, e.g. 250, then cooled and opened to relieve the pressure. It may then be resealed and heated with safety to the required temperature. 258 QUANTITATIVE EXERCISES Liquid substances which are too volatile for manipulation in open tubes are weighed in bulbs blown on the end of thin, nearly capillary tubes. A file mark made near the bulb will enable one to break off the stem after sealing the outer tube. III. BY SAUER'S METHOD For Liquids The apparatus required for the experiment is shown in Fig. 49. A combustion tube 850 mm. long is narrowed down at the point a to a diameter of about 5 mm. The rear end is closed with a stopper through which passes one limb of the branching tube b, c. The front end is closed with a stopper through which FIG. 49 pass two tubes. One of these is cut off even with the smaller end of the stopper and serves to con- nect the combustion tube with the Peligot tube e. The other, t?, extends into the larger tube to the constriction a. The bend at / is made large so that the portion from d to / may lie outside of the furnace. If desired, the tube may be cut near/ and the two parts joined by a piece of rubber tubing. The absorption apparatus e contains a solution of bromine in hydro- chloric acid, and is connected in turn with another apparatus of the same kind which is partly filled with caustic soda to which hydrogen peroxide has been added. The tubes c and d are con- nected with a gasometer containing oxygen. The branch b is connected with a Kipp's carbon dioxide generator. Both gases are dried by calcium chloride before entering the combustion tube. The rubber connections of the tubes 5, c, and d are pro- vided with screw pinchcocks in order that the flow of the gases may be regulated. SULPHUR In a bulb blown on the end of a narrow, thin tube, weigh a quantity of any pure liquid organic sulphur compound which contains from 15 to 20 milligrams of sulphur. Make a file mark near the bulb, and lay the bulb in a porcelain boat with the scratch underneath and the stem extending over the end of the boat. Place the boat in the combustion tube in the position indicated in the figure. Pass carbon dioxide through the appa- ratus and heat the combustion tube at a to redness. Remove the rear stopper, and break the tube containing the liquid by pressing upon it with a glass or iron rod just over the file mark. Replace the stopper quickly, slow down the current of car- bon dioxide, admit oxygen through d, and cautiously warm the material. The flow of carbon dioxide through 6, and of oxygen through c?, also the heating of the substance, must all be so regulated that the combustion which will consist of a series of flashes will take place in the immediate vicinity of the con- striction a. If the flame recedes towards the boat, the flow of carbon dioxide must be increased or the temperature must be increased. If it moves too far in the other direction, the flow of oxygen through d must be increased or the temperature of the substance lowered. When there is no more volatile matter to burn, cut off the carbon dioxide, admit oxygen through , THE DETERMINATION OF CARBONIC ACID 327 and c have a height of 170 mm. and an internal diameter of 16 mm. The tubes d, e,f, g, and h are smaller, having a height of 110mm. and a diameter of 12mm. a, 5, c, c?, g, and h are closed with rubber stoppers ; while e and /, in which the carbonic acid is absorbed and weighed, are closed with corks covered with sealing wax. It is better, however, to use for e and / glass-stoppered U -tubes with small side tubes, which are opened and closed by turning the stoppers. The whole system of tubes is suspended at a convenient height above the working table from hooks driven into a horizontal strip of wood. The tube a, which is nearest the flask, contains just enough calcium chloride to fill its horizontal portion; b is filled with calcium chloride ; and rf CO CO O CO t~ I-H ^ odd o" d d d d o d !-' d d d d do o" d r-i r-J rn d o" d d d d d d d -H d i-i d TH CO CO ^ M grains of /.ine sulphate which does not reduce permanganate in solutions acidified with sulphuric acid. If a suitable specimen of the sulphate is not obtainable, heat to redness in a platinum dish, in a inutile, somewhat more than the requisite amount of com- mercial /inc oxide, and add it to a quantity of hot dilute sul- phuric acid which is insufficient to diss61ve the whole of the oxide. Filter, and dilute the filtrate so that each cubic centi- meter of the solution shall contain about one-tenth of a gram of zinc sulphate. Measure 10 cc. of the manganese sulphate solution into a three-quarter liter flask. Add 10 cc. of the zinc sulphate solu- tion and 2 or 3 drops of dilute nitric acid. Dilute with water, which does not reduce permanganate, to about 250 or 800 cc. Heat to the boiling point and then add rapidly nearly as much standard potassium permanganate as it is thought will be required to precipitate the manganese according to the equation : Mn 2 O 7 + 3 MnO = 5 MnO 2 . Shake the flask vigorously and then add more cautiously the remainder of the permanganate required to produce a perma- nent color, shaking the flask from time to time. If the solu- tion is turbid and slow to clear in consequence of the fineness of the precipitate, it may be heated again, but not to the boil- ing point. Having found by the first experiment very nearly the amount of permanganate required, repeat the determination with another equal portion of the sulphate, adding at once, to within one- or two-tenths of a cubic centimeter, all of the per- manganate which the previous experiment has shown to be necessary, and finishing the determination with greater caution than before. Test the constancy of the results by several repetitions of the experiment, using varying quantities of the manganese sulphate. 170 QUANTITATIVE KM-HICISES Proceed also in tho following manner: Measure out, a quan- tity of tlio sulphate solution and prepare it for the precipitation of (lie manganese as previously directed. Measure into another Ilask of sullie.iont si/e (lie quantity of permanganate which the previous work has shown to be required by the given volume of sulphate, and warm it upon the water bath. When the solu- tion of the sulphate is boiling hot and that of the permanganate is warm, pour the former into the latter, rinsing the emptied Ilask with boiling water. During the transfer, the mixing of the liquids should he facilitated as much as possible by shaking and rotating the Ilask, and whenever the pouring is interrupted for this purpose, the flask containing the remainder of the sul- phate should l)e again placed over the flame. It will be found that, a further addition of permanganate is required in order to produce a permanent color. III'.mV.TION OF PERMANGANIC ACID BY THE OXIDES OF M AN<; AN USE Measure 50 cc. of tho standard permanganate solution into a Ilask and add to it tho quantity of manganous sulphate which is required to reduce one-half of the permanganate to MnO.,. Immerse the body of the ilask in boiling water and heat until the color of the permanganate disappears, which may require from "2 to 3 hours. Now determine the remaining "active" o\ \ gen by adding a measured but excessive quantity of a stand- ard solution of oxalic acid or of tetroxalate, also a little sul- phuric acid and titrating to color when the manganese oxides have disappeared with potassium permanganate. It will be found that, about throe-tenths of the oxygon has dis- appeared, in other words, that the excess of the permanganate has been reduced with the evolution of free oxygen by the oxide precipitated by the action of a portion of the permanganate on the manganous sulphate : 2 IIMn0 4 = 1 1/) + 2 Mn0 2 + 3 O. POTASSIUM PERMANGANATE 171 If (ho determination is made immediately after the disappear- ance of the color of the permanganate, the quantity of oxygen found will be very nearly that which would be obtained if all the manganese in the solution were in the dioxide condition. If the determination is postponed for any length of time, the quantity of oxygen found will bo somewhat less. EXERCISE LV DKTKKMINATION OF MANC ANKSK AS PYROPIH >SIII AIT, BY GIBBS' METHOD Acidify 20-cc. portions of the manganese sulphate solution used in the previous exercise with 8 or 4 cc. of dilute hydro- chloric acid. Heat to the boiling point, and add a moderate excess of ammonium phosphate (H(NH 4 ), 2 PO 4 ) in solution. Add ammonia, drop by drop, with constant stirring until a per- manent precipitate forms. Stop adding the ammonia, but con- tinue the stirring at the boiling temperature until the precipitate assumes a silky crystalline appearance. Add more ammonia, stirring vigorously after the addition of each drop, until all the manganese has been precipitated and the whole of the precipi- tate has become crystalline in appearance. Add a few more drops of ammonia. Place the beaker in ice water and let it remain there until the solution is perfectly cold. Filter through paper and wash the precipitate with a cold, faintly ammoniaeal, 10 per cent solution of ammonium nitrate. The subsequent treatment of the precipitate is the same as in the determination of magnesium or phosphoric acid as magnesium pyrophosphale. Test the filtrate for manganese. The precipitate has the com- position NII 4 MnPO 4 , and like the corresponding magnesium salt, it is eonyerted by heat into the pyrophosphate MiiyP./ > 7 . 472 QUANTITATIVE EXERCISES EXERCISE LVI DETERMINATION OF HYDROGEN PEROXIDE If the solution of peroxide is concentrated, dilute 10 cc. of it to 100 cc. Measure off 10-cc. .portions of the diluted solu- tion, add water and dilute sulphuric acid, and titrate with per- manganate. There are in use two ways of expressing the value of hydrogen peroxide solutions. One gives the percentage by weight, and the other the volume of free oxygen which a cubic centimeter of the solution would yield if the peroxide were decomposed into water and oxygen. Another method (Lunge's) for the determination of hydrogen peroxide is based on the following reaction : CaCl 2 + H 2 2 = CaCl 2 + H 2 O + O 2 . The free oxygen is determined by direct measurement or by absorption. EXERCISE LVII DETERMINATION OF NITROUS ACID Weigh off about 5 grams of the commercial potassium nitrite, taking care to secure an average sample of the whole lot from which the material is taken. Dissolve in water and dilute to a liter. Measure 10-cc. portions into beakers. Add to each a measured but excessive quantity of permanganate, remember- ing that in the alkaline solutions only 1^ atoms of oxygen per molecule of permanganate will be available for the oxi- dation of the nitrite. Warm for half an hour upon the water bath. In the meantime prepare a solution of oxalic acid whose strength is nearly equal to that of the permanganate. Add to the contents of each beaker the volume of oxalic acid which is equivalent to the volume of permanganate which was added to the nitrite. Acidify with sulphuric acid. When the solu- tion lias become clear and colorless, titrate to color with the POTASSir.M PERMANGANATE 473 permanganate. The quantity of permanganate used in the last case is equivalent to the nitrite. Measure off 10 cc. of the nitrite solution. Dilute with 300 cc. of water. Make the solution very slightly acid with sulphuric acid. Add permanganate until the nitrous acid is nearly all oxidized, then make the solution more strongly acid, and com- plete the titration. Owing to the limited solubility of nitric oxide in water, the solution of the nitrite must be very dilute, containing not more than 1 part of nitrous acid anhydride to 5000 parts of water. The end reaction is somewhat indefinite in consequence of the slowness with which nitric oxide is oxidized by permanganic acid. Nitrogen dioxide may also be determined by permanganate. For this purpose a measured portion of the solution containing it, e.g. fuming nitric acid, is slowly stirred into a large quan- tity of cold water and the dilute solution titrated. Each molecule of the nitrous anhydride found is equivalent to four molecules of NO 2 , since 2 NO 2 + H 2 O = HNO 3 + HNO a . CHAPTER XXI THE ELECTROLYTIC DETERMINATION OF METALS ELECTRICAL UNITS AND THEIE KELATIONS 1. THE AMPERE AND THE COULOMB The ampere is the unit of the quantity of electricity flowing through a circuit. It is denned as the strength of the current which a unit of electromotive force (one volt) will cause to flow through a conductor whose resistance is unity (one ohm). It is also the quantity of current which, under certain conditions, will precipitate per second 0.3292 milligram of copper or 1.1172 milligrams of silver. The coulomb is the quantity of electricity which flows through a circuit during one second when the strength of the current is one ampere. The ampere-hour is the quantity of electricity which flows through a circuit during one hour when the strength of the current is one ampere. It is therefore equal to 3600 coulombs. The current strength is the same in all parts of an undivided circuit. 2. THE OHM The ohm is the unit of the resistance to the flow of a current in a conductor. It is equal to the resistance offered at by a column of mercury whose length is 106.3 centimeters and whose cross section is equal to one square millimeter. The resistance of a conductor of any given material is directly proportional to its length and inversely proportional to the area of its cross section. 474 ELECTROLYTIC DETERMINATION OF METALS 475 The specific resistance of a substance is the resistance found in a conductor made from that material whose length is one centimeter and whose cross section has an area of one square centimeter. The resistance of any conductor is equal to the specific resist- ance of the material of which it is made multiplied by its length and divided by the area of its cross section : _ specific resistance X length area of cross section With rising temperature the specific resistance of metals in- creases, while that of carbon, liquids, and generally of solutions, diminishes. The specific resistance of solutions also varies with concentration. The conductivity of a material is the reciprocal of its resist- ance. If a current is given two or more paths between two points in a circuit, it will distribute itself among them in quantities which are inversely proportional to the resistance or directly proportional to the conductivity of the several conductors, and the total conductivity of the divided line will be the sum of the conductivities of the individual lines. If, for example, the resistances of three parallel lines are 10, 20, and 30 ohms respec- tively, their separate conductivities will be -j 1 ^, ^, and ^, and the total conductivity will be J^, or 0.18333; while the resist- ance of the lines, taken together, will be , or 5.45 ohms. O.loooo 3. THE VOLT The volt is the unit of electromotive force. It is the electrical pressure which will send one ampere of current through a con- ductor whose resistance is one ohm. 476 QUANTITATIVE EXERCISES 4. OHM'S LAW Ohm's law of the current is expressed by the following equation : r E - = R> in which C represents the current in amperes, E, the electromotive force in volts, and R, the resistance of the circuit in ohms. It will be seen that if any two of these values are known, the third can be calculated, for 2F= CR and R = -. Determination of the Strength of the Current The strength of the current is ascertained by measuring either its chemical or its electro-magnetic effects. Instruments for the former purpose are known as voltameters, and these are classified as gas (oxy-hydrogen or hydrogen), or as weight voltameters, according as the gas resulting from an electrolysis of definite duration is measured, or the metal depos- ited on an electrode is weighed. The quantity of gas which is liberated per second in the oxy-hydrogen voltameter and the weight of metal which is precipitated in the silver or copper voltameter in the same unit of time have, for fixed conditions, perfectly definite equivalents in coulombs of current; hence, by noting the time of an electrolysis and measuring or weighing the products, the strength of the current can be ascertained. But voltameters are little used in the laboratory, owing princi- pally to the long time required for a determination. Instruments depending on the electro-magnetic effects of the current are likewise of two kinds. In one of these a magnet is displaced by the current flowing in its vicinity, while in the other a bar or needle of soft iron is employed which becomes a ELECTROLYTIC DETERMINATION OF METALS 477 magnet under the influence of the current and is then displaced. Instruments of the first kind are known as galvanometers, and of the second as amperemeters or ammeters. Only amperemeters are used in ordinary electrolytic work. These are provided with a scale for the direct reading of the amperage and often with two scales, one for small and the other for large currents. Amperemeters have a small resistance and are inserted in the circuit. Determination of Voltage The measurement of the fall or difference of potential between any two points in a circuit is usually made for practical purposes by means of a so-called voltmeter. This instrument resembles the amperemeter, but differs from the latter in that its resistance is so high that when it is inserted in a shunt between the two points, only a minute fraction of the current passes through the voltmeter ; its employment does not, therefore, materially affect the conductivity of the line as a whole. An instrument meas- uring from to 150 volts has a resistance of about 12,500 ohms. The range of the voltmeter is greatly enlarged by using " mul- tipliers," i.e. standard resistances which are placed in series with it in the shunt circuit and thus increase the value of the scale divisions by definite multiples. . . Having ascertained the quantity of the current flowing through the circuit, and the fall of potential between any two points on the same, the resistance in the line between them is found by the equation 5. THE JOULE The joule is the electrical unit of energy. It is equivalent to the quantity of heat developed in a circuit by one coulomb of a current whose electromotive force is one volt : 1 joule = 1 coulomb x 1 volt. 478 QUANTITATIVE EXERCISES According to Joule's law, the heat in calories which is devel- oped in a circuit with a resistance It, by a current C\ in the time , is expressed by the equation: calories = C*Rt x 0.2381 = CR x Ct x 0.2381. But according to Ohm's law CR = E, the electromotive force of the current ; hence calories = E x Ct x 0.2381. If C is one ampere and t is one second, Ct is the coulomb; therefore calories = E x coulombs (joules) x 0.2381. calories 05881- 1 joule = 0.2381 calorie. 1 calorie = 4.2 joules. 6. THE WATT The watt is the electrical unit of work. It is the mechanical equivalent of the joule. Since the mechanical equivalent of the calorie is 3.0968 foot pounds per second, that of the joule ( = 0.2381 calorie) is 0.73732 foot pound. The watt, therefore, is 0.73732 foot pound per second, and 745.94 watts equal 550 foot pounds per second, or one horse power. The work, in watts, which can be accomplished by any cur- rent is the product of its quantity in amperes by its pressure in volts. Expressed in horse power, it is ^77^77 ' ^ n ^ e case ^ powerful currents, e.g. those of large dynamos, it is customary to employ the kilowatt (= 1000 watts = 1.3406 horse power) as the unit of work. ELECTROLYTIC DETERMINATION OF METALS 479 SOURCES OF CURRENT The general employment of electricity for lighting, mechani- cal, and other purposes has brought the current in great abun- dance within the reach of nearly all laboratories. The current as it is obtained from the town supplies has, however, a far too high electromotive force for the ordinary electrolytic processes, and it must be transformed to a lower voltage. This is accom- plished by means of dynamos, or by means of storage batteries (accumulators) which are charged either directly from the street current or by the current of a small dynamo located in the building and driven by the street current. The highest electromotive force required for the quantitative precipitation and separation of the metals and for most other electrolytic work does not exceed 10 volts, while the pressures of the currents received from the street are ordinarily 110, 115, 220, 230, and even 500 volts. The economical transformation of these to currents of the low voltages which are adapted to laboratory purposes is a matter of much importance. The too common practice of charging small storage batteries by inserting resistance in the line from the street until the cur- rent normal for the particular type of cell is obtained is attended by an enormous loss of energy. The voltage of the charging current should only slightly exceed the counter electromotive force of the battery. All ex- cess of the former over the latter is wasted. Suppose, by way of illustration, that a battery consisting of four cells with a nor- mal charging rate of 12.5 amperes is to be charged. Arranged in series, the batteiy toward the close of the charging period will have an electromotive force of 10 volts, 2.5 volts per cell. The maximum work to be done is, therefore, 10 x 12.5 = 125 watts, or 0.168 horse power. Suppose, however, that the battery is charged from a line on which the pressure is 115 volts, resist- ance being inserted until a current of 12.5 amperes is obtained, the work accomplished in charging the battery or lost in heating 480 QUANTITATIVE EXERCISES the resistance will be 115 x 12.5 = 1437.5 watts, or 1.927 horse power. In other words, the waste of energy amounts to more than 91 per cent. As the number of cells in series increases, the waste diminishes. But to charge economically with a cur- rent of 115 volts, the number of cells which must be placed in series is, approximately, ^f- = 46. Similarly, if the pressure upon the charging line is 230 volts, the number of cells should be nearly 92, etc. Such large batteries are, however, not ordi- narily necessary, and even when currents equal to their capaci- ties are needed, it is more economical, and less troublesome, to employ suitable dynamos unless great steadiness of current pres- sure is required. If a dynamo is to be used and there is no opportunity to utilize power employed for other purposes in the building, a FIG. 67 motor to run it must be provided. A motordynamo, or rotary transformer like the Crocker- Wheeler machine shown in Fig. 67, is in every way satisfactory. These machines are built in a great variety of sizes from one-sixth horse power upwards. In some of them the motor and dynamo armatures are separately wound upon a single shaft, each having its own field. Either end may operate as a motor or as a dynamo, or if, as in some cases where power is available, the shaft is extended and provided with a pulley, the machines may be employed as double dynamos to furnish currents of different pressures. The armature of the ELECTROLYTIC DETERMINATION OF METALS 481 motor is wound to suit the voltage of the street current, while that of the dynamo is wound to meet the needs of the laboratory. The dynamo is provided with a field rheostat by which the volt- age of its current may be economically cut down step by step to any required extent. The size of the machine will, of course, depend upon the amount of work to be done, while the charac- ter of the dynamo winding will be determined by the nature of that work. If the motor is one horse power, the output of the dynamo will probably be somewhat over 600 watts, and the latter may be wound so as to secure any desired relation of pressure to current, provided, of course, the product of the two does not exceed the maximum rated output. For example, if the output of a dynamo is 600 watts, it may be wound so as to give a current of 60 volts and 10 amperes, 10 volts and 60 amperes, 6 volts and 100 amperes, 20 volts and 30 amperes, or 30 volts and 20 amperes, etc. The maximum current (but not more) may be generated at any of the lower voltages which are secured by throwing resistance into the field. A storage battery of moderate size is always convenient, even where dynamos are employed, and in preparing specifications for a machine, its use as a battery charger should be kept in mind and provided for. We will suppose that for the ordinary work of the laboratory a current of 25 amperes and 10 volts is required, but that a battery of eight elements with normal charging rate of 25 amperes is to be maintained, and it is desired to charge them all simultaneously, i.e. in series, which would call for a current pressure of 20 volts. In this case a dynamo with an output of 500 watts and wound to 20 volts and 25 amperes would answer both purposes. Used as a charger, the maximum voltage of the dynamo would be utilized, while at other times it would be cut down to one-half with little waste of energy by throwing resistance into the field. An automatic cut-out should be inserted in the line from the dynamo to the battery to break the circuit and thus prevent a return of the battery current through the armature whenever 482 QUANTITATIVE EXERCISES the dynamo, from any cause, fails to generate. All circuits, moreover, should be provided with safety fuses. Another form of machine which may be used with advantage wherever the work to be done is continuous and varies but little in quantity is the so-called dynamotor, Fig. 68. Dynamo tors differ from motordynamos in that the motor and dynamo arma- tures are wound together upon the same core, so that a single field suffices for both motor and dynamo. The voltage of the current generated by these machines is constant and cannot be economically regulated, as in motordynamos, by changing the resistance in the field. They are much used as battery chargers, electroplaters, tele- phone ringers, and in telegraphy. For work through considerable resist- ances, e.g. 50, 100, or 200 ohms, dynamos of relatively large elec- tromotive force and moderate current should be used. An example will illus- trate the advantage of such a machine over one with small electromotive force and large current when the resistance to be overcome is high. Suppose the resistance of a circuit is 100 ohms. A dynamo with an output of 5 00 watts, if wound for 20 volts and 25 amperes, would send a current of -f-^ = 0.2 ampere through the circuit ; while another machine with the same output and consuming the same amount of energy in its motor, if wound for 100 volts and 5 amperes, would give l-g-g- = 1.0 ampere, i.e. five times as much current. There is also a great waste of energy in using dynamos of high electromotive force when the resistance to be overcome is small, for then additional resistance must be inserted in the circuit to prevent the machine from FIG. 68 ELECTROLYTIC DETERMINATION OF METALS 483 generating more than its normal maximum of current. It is well, therefore, to have two motordynamos in a laboratory, one of low electromotive force and large current for work involv- ing small resistance, such as the precipitation and separation of metals, and another of comparatively large electromotive force for work in which higher resistance is to be dealt with. It is frequently necessary to take a current of low electro- motive force from one of high pressure. This may be accom- plished by inserting in the circuit a lamp; or two or more lamps in parallel, and a rheostat, and regulating the rheostat until the required current is obtained. Or a rheostat may be inserted in the line and a portion of its resistance short-circuited by means of a shunt. The voltage of the shunted current will equal the fall in potential between the two points where the shunt joins the main line. It should be remembered, however, that the cutting down of pressure by these methods is attended by a great waste of energy. The currents obtained from dynamos are usiially somewhat unsteady owing to fluctuations in the speed of the machines. Hence, when currents of great constancy are required, storage batteries, rather than dynamos, should be employed. STORAGE BATTERIES The storage battery (accumulator, secondary or reversible battery) is a device for the conversion of electrical into chemi- cal energy which may be reconverted into electrical energy when needed. It consists essentially of two series of parallel and rigidly connected lead plates immersed in sulphuric acid of 1.2 specific gravity. The plates of one series, taken together, constitute the positive electrode, while those of the other series constitute the negative electrode. They are so spaced and arranged in the liquid that every positive plate lies between two negative ones, there being usually one more of the latter than of the former. The alternating negative and positive 484 QUANTITATIVE EXERCISES plates are kept from accidental contact and therefore from short circuits within the cell by inserting between them at intervals narrow strips of hard rubber or of some other nonconducting material. Owing to the large surface of the plates, the internal resistance of the battery is exceedingly small. If the two series of plates are covered with lead sulphate and suspended in dilute sulphuric acid, and a current from an exter- nal source is passed through the cell, the lead of the sulphate is converted on the plates belonging to the pole by which the current enters into peroxide, while on the plate belonging to the pole by which the current leaves the cell it is deposited as a spongy metal. The two series of plates thus acquire different and characteristic colors, the first a dark brown and the second a light slate color. The brown or oxide-covered plates, together with the heavy lead bar to which they are joined, make up the positive electrode, while the negative electrode consists of the slate-colored plates. The so-called " active " material, which before charging is lead sulphate and after charging is lead per- oxide on the positive and metallic lead on the negative electrode, is originally deposited upon and within the plates by various patented processes. If the two poles of a charged cell are connected, the spongy lead on the negative plates is converted into sulphate, and simultaneously an equivalent amount of peroxide on the posi- tive plates is reduced by hydrogen to the lower oxide, which is then converted also into sulphate. Meanwhile a current passes from the negative to the positive plates within, and from the latter back to the former without the cell. The following tentative explanation has been given for the conduct of the battery during the discharging and charging periods. When charged, i.e. when . the negative plates are properly supplied with spongy lead and the positive plates with peroxide, the liquid contains sulphuric acid and lead sulphate in the electro- lytically dissociated condition. In the vicinity of the positive plates there is probably also some dissociated peroxide, that is, ELECTROLYTIC DETERMINATION OF METALS 485 quadrivalent lead ions together with an equivalent number of hydroxyl ions. Suppose now the poles are joined and that an atom of spong}*- lead at the negative pole is dissolved, i.e. passes into the liquid carrying its two charges of positive electricity. The consequences would be twofold. In the first place, the pole would be negatively charged ; secondly, two hydrogen ions belonging to the dissociated sulphuric acid would be compelled to leave the solution. This they may do by uniting at the positive pole with two hydroxyl ions belonging to the dissoci- ated peroxide. The lead ion would thus be reduced from the quadrivalent to the bivalent condition, giving up simultaneously two of its four positive charges of electricity to the adjacent pole. In this way the two poles would become oppositely charged to the same degree. The bivalent lead would, of course, react with sulphuric acid, forming sulphate and water. Suppose, when the battery is in the discharged condition, i.e. when the plates of both poles are covered with lead sulphate and the liquid is saturated with the same compound, that a current from an external source is passed into it at the posi- tive pole, and that a lead ion carrying two charges of elec- tricity receives two more and separates from the solution with four hydroxyl ions derived from dissociated water. The liquid would now contain too many hydrogen ions by two, and this would compel the deposition of a molecule of hydrogen or an equivalent amount of lead upon the negative pole. As a mat- ter of fact, the lead is deposited. The acid which is used in a storage battery should be free from metals other than lead, from arsenic, and from hydrochlo- ric and nitric acids. Its concentration should be maintained by adding distilled water from time to time to replace the water which is lost by evaporation. When set up for the first time, the cells are in the discharged condition ; that is, most of the lead which takes part in the chemical reactions is in the form of sulphate. The charging should begin immediately after placing the electrodes in the acid and should be continued at 486 QUANTITATIVE EXERCISES " normal rate " with the least possible interruption until it is fin- ished. It takes much longer to charge a battery for the first time than for any subsequent recharging. For example, a battery whose normal rate is 12.5 amperes for 8 hours will require the same current for nearly 30 hours when it is first set up. Though the first charge should be at normal rate, that is, at the maximum rate suitable for the particular type of cell, the battery may be recharged with smaller currents. The time required, however, will be proportionately increased. If a battery may be charged in 8 hours with a current of 12.5 amperes, it will require 8 x 12.5=100 hours to charge it with one ampere. When charged for the first time, it is recommended by the manufacturers to discharge the battery about one-half and then to recharge it immediately, and to repeat this treatment two or three times, or until the color of the positive plates is a deep brown and that of the negative plates a light slate. The volt- age of the charging current should only slightly exceed the counter electromotive force of the battery. There are certain facts connected with the charging of a battery which require attention in order that it may be known whether the process is advancing normally and when it is to be discontinued: 1. In discharging, the voltage of a cell is not allowed to fall below 1.8. On recharging, the electromotive force of the cell rises quickly to perhaps 2.35 volts, where it remains during the larger portion of the charging period. Later it rises quite rapidly to 2.5 volts. At this point the charging should be dis- continued. If cells which have been discharged to different degrees are in series, some of them will be filled before others. In this case the charging current should not be allowed to flow through the whole series until all the cells are full. Each cell should be cut out as soon as its electromotive force reaches 2.5 volts. This may be done, but the voltage of the charging cur- rent should be correspondingly diminished, or a resistance equal to that of the cells retired should be inserted in the circuit. ELECTROLYTIC DETERMINATION OF METALS 487 2. When the charging of a cell is nearly finished, i.e. when most of the lead of the sulphate produced in discharging has been reconverted into peroxide at the positive pole or deposited as metal at the other electrode, it begins to " gas " because of the liberation of oxygen at the positive and of hydrogen at the negative pole ; and finally the evolution of gas becomes so rapid as to give the liquid the appearance of boiling. At this stage the cell should have an electromotive force of 2.5 volts, and the negative plates should exhibit the characteristic slate color. If a cell fails to " gas " after a reasonable period, it should be examined for a short circuit, which may occur in consequence of a warping of the plates or of the presence of conducting material between them. In prying the plates apart or dislodg- ing material which has fallen between them, a rod of hard rub- ber or of wood and never a metallic one should be used. 3. During the discharge of a battery much of the sulphuric acid is converted into lead sulphate, which, owing to its sparing solubility, is mostly deposited upon the plates. The conse- quence of this disappearance of acid from the solution is a lowering of the specific gravity of the liquid, which is lightest, of course, when the battery is fully discharged. On recharging, the acid is regenerated and the specific gravity of the liquid increases, reaching its maximum when there is no more sulphate to be decomposed. Hence, if care is taken to maintain a nearly constant volume of liquid in a cell by replacing the water lost by evaporation, one can judge quite accurately of its condition by simply taking the specific gravity of the liquid. 4. As noted already, the electromotive force of a cell should not be allowed to fall below 1.8 volts. When this point is reached, it should be recharged with the least possible delay. If the discharge has been carried too far, or if a cell has been allowed to stand in the discharged condition, it should be re- charged at half rate and until the potential rises to 2.4 volts. The charged cell has an electromotive force of 2.5 volts only while the charging current is flowing. On discontinuing the 488 QUANTITATIVE EXERCISES current, the potential falls to 2.2 volts, and soon after begin- ning to discharge it sinks to about 2 volts. From this point the loss of electromotive force is gradual. If a battery is to be " put out of commission " for a time, the manufacturers recommend the following procedure : It is first fully charged. The acid is then removed by means of a siphon, and the jars are immediately filled with water. Lastly, the battery is discharged until the potential sinks below one volt per cell, when the water is withdrawn. To bring the battery into use again, it is to be treated as if it were receiving its first charge. ELECTROLYSIS 1. THE ELECTRODES A simple platinum dish with a capacity of 200 or 250 cc. serves well as a cathode for the deposition of most metals. In order that a good contact between the dish and the negative wire of the circuit may be secured, a heavy brass plate is pro- vided with a binding screw at one end and is hollowed out in the middle to fit the bottom of the dish. If the contents of the dish are to be warmed during an electrolysis, as they frequently must be, a piece of asbestus board is laid upon a tripod or upon the ring of an iron stand, and upon this are placed the brass plate and the dish. A small flame under the asbestus easily raises the temperature of the liquid in the dish to 50 or 80 without danger that the boiling point will be reached. A suitable anode, or positive electrode, is made from a disk of heavy platinum foil 50 mm. in diameter.. To the center of this is attached a stout platinum wire about 150 mm. in length. To secure a good contact between the wire and the disk the former is flattened at one end and bent to a right angle. The disk is laid on a hard, smooth, and nonconducting surface, e.g. on a porcelain block, the flattened portion of the wire is placed upon the center of the disk, and the parts in contact are heated ELECTROLYTIC DETERMINATION OF METALS 489 with the flame of the blast lamp. When quite hot the parts can be firmly welded by striking with a small hammer. The disk should be provided with a considerable number of small holes for the escape of gas, which otherwise would accumulate under it and interfere with the electrolysis. These should be made by inverting the disk on a block of wood and punching it with an awl. If the holes are made from the upper side of the disk, gas will collect and remain under the electrode, owing to the down- ward direction of the conical elevations produced by the awl. The dish is to be covered during an electrolysis with a watch glass which has been bored in the center to accommodate the standard of the anode. Such holes are easily made in glass by boring with a piece of tem- pered steel, using a solution of camphor in turpentine as a lubricant. An efficient bor- ing implement for the purpose may be made by grinding to proper shape, and then tem- pering, the soft end of a small file. The point of the drill should be quite fine and must have a number of sharp edges. A great variety of other forms have been proposed for electrodes and some of these are in general use for particular determinations, such as that of copper, but the platinum dish and disk described above are satisfactory for nearly every kind of electrolytic deposition. A convenient stand for electrodes is shown in Fig. 69. The standard on which are mounted the brass ring with its three platinum points for the support of the platinum dish and the clamp for the anode, consists of a stout glass rod. The relation of the area of an electrode used as cathode to the quantity of the current determines, to a great extent, the character of the metallic deposits. If the current is large and the electrode small, the rapid separation of metal upon the limited surface is apt to give poorly adhering and even spongy deposits ; 490 QUANTITATIVE EXERCISES while if the current is small and the electrode large, the deposits lack uniformity of thickness and present the appearance of irreg- ular patches. It is therefore necessary to select a unit of elec- trode surface and to define the density of the current with respect to it. The unit chosen is 100 square centimeters, which is des- ignated by the symbol ND 100 . If the current is 1 ampere and the area of the electrode is 100 square centimeters, the density is said to be 1 ampere with respect to the electrode ; while if the electrode were half as large, 50 square centimeters in area, the density would be 2 amperes, etc. In precipitating metals, the density of the current with respect to the cathode is of importance, but the anode may be of any convenient size. 2. RHEOSTATS The current is regulated to the requirements of the work in hand by means of rheostats. The form of the instrument shown in Fig. TO is to be recommended. These rheostats are made with any range of re- sistance and to carry with safety any quan- tity of current which the purchaser may des- ignate. Three small instruments, with ten steps each, when con- FIG. 70 L j ' ' -n nected in series, will give every degree of resistance from 0.1 ohm to 111 ohms, by tenths of a unit, if the resistances of the three are respectively 10 ohms, 1 ohm, and 0.1 ohm on each step. In other words, with such an arrangement, 1110 different combinations can be. made. It is well to construct the rheostat of highest resistance with more than 10 steps, since each additional step in this instrument makes possible a hundred new combinations. There is no subdivision or multiplication of the resistance that is likely ELECTROLYTIC DETERMINATION OF METALS 491 to be desired which cannot be effected by the system. For instance, if a fourth rheostat with 0.01 ohm resistance on each step is added to the series, the number of possible combinations rises immediately to 11,110. It should be borne in mind in pre- paring specifications for rheostats that the higher the required resistance the finer must be the wire, and that fine wires cannot carry large currents. In other words, it is impracticable, as it is also unnecessary, to combine large current-carrying capacity with high resistance. In general, only rheostats of small resist- ance are required to carry large currents. 3. FARADAY'S LAWS 1. When a current is passed through an electrolyte, the quan- tities of the ions which separate at the poles are proportional to the intensity of the current. For example, if 1 ampere in 1 second (1 coulomb) precipitates 0.0011172 gram of silver, then 2 amperes will precipitate 2 x 0.0011172 gram in the same time. 2. If a given current is passed through any number of elec- trolytes arranged in series, the weights of the ions which separate at the various poles are related to each other as their chemically equivalent weights. If, for instance, a current passes through three cells in series, the first containing a solu- tion of a silver salt, the second a salt of zinc, and the third a cupric salt, the weights of the metals precipitated upon the f\A. Q fiQ 1 three cathodes will be related as 107.11 : ^- : ^- . The weights of the ions which are chemically equivalent are found, of course, by dividing their atomic weights or the sum of the weights of the atoms contained in them if they are complex by their respective valencies. The so-called electro-chemical equivalent of an ion is the weight of it which is separated at an electrode by 1 coulomb of current, that is, by 1 ampere in 1 second. It may be readily found in any case (if the system of atomic weights based on the 492 QUANTITATIVE EXERCISES weight of hydrogen as unity is employed) by multiplying the atomic weight of the ion or the sum of the weights of the atoms in it, by 0.0000104304 (the electro-chemical equivalent of hydro- gen) and dividing by the valence of the ion. It is to be noted that metals which, like copper, mercury, iron, etc., form more than one series of salts with electro- negative elements or groups, have also more than one electro- chemical equivalent. The equivalent of copper, for example, is 0.0003292 gram in cupric salts, and 0.0006584 gram in cuprous salts. In ferric salts the equivalent of iron is 0.00019331 gram, and in ferrous salts 0.00028998 gram. To separate the number of grams of any ion which is equal to its chemically equivalent weight e.g. 1 gram of hydrogen, 35.18 grams of chlorine, 107.11 grams of silver, 47.6T5 grams SO 4 , etc. 95,874 coulombs are required. To find what weight of any ion will be separated in a given time by a given current, it is necessary only to reduce the current and time to coulombs and to multiply by the electro- chemical equivalent of the ion. To find what current will be required to separate a given weight of any ion in a fixed time, the weight is divided by the electro-chemical equivalent of the ion, and the quotient by the time in seconds. The second quotient will be the number of amperes which must be employed. A necessary conclusion from the facts embraced by Faraday's law is that ions of equal valence carry equal charges of electricity, positive or negative ; also that bivalent ions carry twice as much as univalent ions, etc., in other words, that the magnitude of the charge carried by an ion is strictly proportional to its valence. The current enters a solution at the anode or positive elec- trode, and leaves it at the cathode or negative electrode. The ions which move toward the anode are negatively charged and are called anions, while those which move toward the cathode, i.e. in the direction of the current, are positively charged and are called cations. ELECTROLYTIC DETERMINATION OF METALS 493 4. POLARIZATION CURRENTS The metal which is deposited upon the cathode during the progress of an electrolytic separation tends to return to the ionic condition owing to its so-called electrolytic solution pressure. The same phenomenon presents itself whenever any separa- tion takes place upon insoluble electrodes, whether the depos- its are solids or gases. The result is an electromotive force or " polarization current " in the cell opposed to that which is pro- ducing the deposition. In order, therefore, that a metal may be precipitated or, more generally, that any kind of electrolytic separation may be effected, a current must be employed whose electromotive force is superior to that of the polarization cur- rent. Otherwise no continuous separation will take place. These statements do not apply to cells like plating baths, in which the anodes are made of the plating metal and are therefore dissolved as fast as the metal is deposited on the cathode. In such cells there is no polarization current in the usual sense. Le Blanc has determined the magnitudes of the electromotive force which just suffices for the decomposition of a number of substances in normal solutions. The following values were found for salts from which the metal is precipitated: ZnSO 4 = 2.35 volts Cd(NO 3 ) 2 = 1.98 volts ZnBr 2 - =1.80 CdSO 4 =2.03 NiSO 4 =2.09 CdCl 2 =1.88 NiCl 2 =1.85 CoSO 4 =1.92 Pb(NO 8 ) 2 = 1.52 CoCl 2 =1.78 AgNO 8 = 0.70 volt The decomposition values of the common acids and bases were : Acids Hydrochloric = 1.31 volts Hydrobromic = 0.94 volt Nitric = 1.69 " Hydriodic = 0.52 Sulphuric = 1.67 " Oxalic = 0.95 Phosphoric =1.70 " 494 QUANTITATIVE EXERCISES Bases Sodium hydroxide = 1.69 volts Potassium hydroxide =1.67 " Ammonium hydroxide = 1.74 " The fact that each metal requires for its precipitation a certain minimum electromotive force, below which it cannot separate from solutions of its salts, and that these minima are different for different metals, is of great practical importance, since it makes possible a satisfactory electrolytic separation of several of the metals. If, for example, a solution contains copper and zinc as sulphates, the former may be completely precipitated by a current whose voltage is kept above 1.22, but is not allowed to rise above 1.4, while all of the zinc remains in solution. On raising the voltage to 2.35 or higher, the zinc also is precipi- tated. The pressure of current which is required for the electro- lytic decomposition of a substance may be calculated from the heat of its formation. For example, the heat of formation of an electro-chemical gram-equivalent weight of zinc sulphate | - - = 80.13 grams J is approximately 53,045 calories, while the equivalent of the calorie in electrical energy is 4.2 joules. The heat of formation of 80.13 grams of zinc sul- phate is, therefore, expressed in electrical units, equivalent to 53045 x 4.2, or 222789 joules ; and ^sW' or 2 - 82 volts > is the current pressure which must be maintained in order to effect the electrolysis of the salt. The value found experimentally by Le Blanc was 2.35 volts. ELECTKOLYTIC DETMKMIN ATION OF MKTALS 495 EXERCISE LVIII ELECTROLYTIC DETERMINATIONS 1. COPPER a. Classen s Method Dissolve a weighed quantity (0.2 to 0.5 gram) of pure copper sulphate in a little water and add an excess of a saturated solu- tion of ammonium oxalate. Heat to about 80 and electrolyze for a few minutes ; then add from a burette with a fine outlet, at the rate of about 10 drops per minute, a saturated solution of oxalic acid, allowing the acid to fall upon the covering glass, from which it will find its way into the dish through the hole in the center of the glass. To determine when the precipitation of the copper is finished, a drop of the liquid is taken out from time to time after about two hours, and tested on a porcelain surface with a drop of a solution of potassium ferrocyanide which has been acidified with hydrochloric acid. At the end of the electrolysis the liquid in the dish is to be removed and replaced by water without interrupting the cur- rent. For this purpose two siphons are employed, one for the removal of the liquid and the other for the introduction of water. Finally, the deposited metal is washed repeatedly with water and then with small quantities of alcohol, and dried in an air bath at 80 to 90. The conditions of the experiment as given by the author of the method are : Temperature of the liquid, 80. Density of the current, ND 100 = 0.5 to 1.0 ampere ; most favorable density, 1.0 ampere. Electrode tension, 2.5 to 3.2 volts. Time, 2 hours. 496 QUANTITATIVE EXERCISES The particular advantage claimed for the method is the short time required for the deposition of the metal. In the case of quite dilute solutions of copper salts the oxalic acid may be introduced from the beginning of the electrolysis, whereas in concentrated ones such a course would result in the precipitation of a difficultly soluble oxalate of copper. b. Deposition in the Presence of Nitric Acid Dissolve a weighed quantity of copper sulphate in water, add 2 or 3 cc. of dilute nitric acid, and electrolyze. Conditions of the experiment : Temperature, 20 to 30. Density of the current, ND 100 = 0.5 to 1 ampere, the last only when no other metal than copper is present. Electrode tension, 2.2 to 2.5 volts. Time, 5 to 6 hours. Chlorides must be absent, owing to the tendency of copper in their presence to precipitate in spongy form. Copper can be separated from iron, nickel, cobalt, manganese, zinc, and cadmium in the manner described under 6, but the quantity of the nitric acid must then be increased to 20 cc. (sp. gr. 1.21). It cannot be separated from antimony, arsenic, mercury, silver, tin, and bismuth. 2. NICKEL Classen's Method Dissolve a weighed quantity of ammonium nickel sulphate in about 25 cc. of water, warm, add from 6 to 8 grams of ammo- nium oxalate, and dilute the solution to 100 or 120 cc. During the electrolysis maintain a temperature of GO to 70. The com- pletion of the deposition is tested with ammonium sulphide. ELECTROLYTIC DETERMINATION OF METALS 497 Conditions of the experiment : Temperature, 60 to 70. Density of current, ND 100 , = 1 ampere. Electrode tension, 3.1 to 3.8 volts. Time, 3 to 5 hours. Cobalt may be satisfactorily determined under precisely the same conditions. Nickel and cobalt may also be determined under the condi- tions recommended by Fresenius and Bergmann as follows: The solution of the salt is treated with from 4.5 to 6 grams of ammonium sulphate and 40 cc. of ammonia of 0.96 specific gravity, and diluted to 150 or 170 cc. If more than 0.5 gram of the metal is to be precipitated, the quantity of the ammonia is increased to 50 or 60 cc. Conditions of the experiment : Temperature, that of the room. Density of the current, ND 100 , = 0.5 to 0.7 ampere. Electrode tension, 2.8 to 3.3 volts. Chlorides, nitrates, fixed organic acids, and magnesium com- pounds should not be present. 3. IRON Classen's Method Dissolve from 6 to 8 grams of ammonium oxalate in the least possible quantity of warm water, add slowly and with constant stirring the solution of the iron salt ((NH 4 ) 2 FeSo 4 ). Dilute to 100 or 150 cc. and electrolyze. Conditions of the experiment : Temperature, 20 to 40. Density of the current, ND 100 , = 1 to 1.5 amperes. Electrode tension, 3.6 to 4.3 volts. Time, 3 to 4 hours. 498 QUANTITATIVE EXERCISES At the close of the precipitation the dish is quickly emptied. The deposit is washed repeatedly with water and with small quantities of pure alcohol, and then dried at a temperature of TO to 90. The best compounds from which to precipitate iron in the manner described above are the double ammonium sulphates. If the solutions to be electrolyzed contain chlorides or nitrates, they should be evaporated with sulphuric acid until all hydro- chloric and nitric acids have been expelled. The excess of the sulphuric acid is afterwards neutralized with ammonia. 4. ZINC Classen's Method Owing to the difficulty of removing electrolytically deposited zinc from platinum, the dish used as cathode should first be plated on the inside with copper or silver. The former metal may be deposited in the manner described under 1, a, or 1, b. If the dish is to be plated with silver, the metal is best precipitated from a solution of its double salt with potassium cyanide by a current of 0:2 to 0.5 ampere. Having prepared the dish, dissolve the zinc salt in the smallest possible quantity of warm water, and add about 4 grams of ammonium oxalate. Heat, adding small quantities of water if necessary until all of the salt is dissolved, and transfer the solu- tion to the dish. Electrolyze at 50 to 60 from 3 to 5 min- utes, arid then introduce a saturated solution of oxalic acid or a 6 per cent solution of tartaric acid, as directed under 1, a. Potassium ferrocyanide is employed to determine when the precipitation is finished. The dish must be washed without interruption of the current. ELECTROLYTIC DETERMINATION OF METALS 499 Conditions of the experiment : Temperature, 50 to 60. Current density, ND 100 = 0.5 to 1.0 ampere. Electrode tension, 3.5 to 4.8 volts. Time, 2 hours. NOTE. The few examples given above will serve as an introduction to analysis by electrolysis. For further information regarding electrolytic determinations and separations, the student is recommended to consult Classen's Quantitative Analyse durch Electrolyse, or the English translation of the same by Herrick. CHAPTER XXII BUTTER The fats and oils, whether of animal or of vegetable origin, are principally made up of mixtures of the neutral glycerin salts of certain organic acids. Of these acids it may be said, in general, that they are all mono-basic and contain, in most in- stances, an even number of carbon atoms ; also that they belong, with few exceptions, to the series represented by the formulas C w H 2n 2 , C M H 2n _ 2 2 , C n H 2n _ 4 2 , and C tt H 2n _ 6 O 2 . The following table gives the composition of the more important acids, together with some examples of the fats in which their occurrence is characteristic. ACETIC ACID SERIES C K H 2 ,0 2 Acetic, C 2 H 4 O 2 Rare. Butyric, C 4 H 8 O 2 In butter, of which about 6 per cent consists of buty- rin, the neutral glycerin salt. Isovaleric, C 5 H 10 O 2 In porpoise and dolphin oils. Caproic, C 6 H 12 O 2 In butter and cocoanut oil. Caprylic, C 8 H 16 O 2 In butter, human fat, and cocoanut oil. Capric, C 10 H 20 O 2 In butter and cocoanut oil. Laurie, C 12 H 24 O 2 In laurel oil, cocoanut oil, spermaceti, etc. Myristic, C 14 H 28 O 2 In nutmeg butter, Dika oil, and cocoanut oil. Palmitic, C 16 H 32 O 2 In most animal and vegetable fats and oils. Stearic, C 18 H 36 O 2 In most fats. Arachidic, C 20 H 40 O 2 In arachis oil. Behenic, C 22 H 44 O 2 In oil of behen. ACRYLIC ACID SERIES Tiglic, C 5 H 8 O 2 In croton oil. Oleic, C 18 H 34 O g In most fats and oils. Erucic, C 2 ,,H 42 O 2 In rape oil. 500 BUTTER 501 LINOLIC ACID SEKIES C n II 2n _ 4 2 Linolic, C 18 H 32 2 In linseed and other drying oils. LINOLENIC ACID SERIES C n H 2n _ 6 O 2 Linolenic, C 18 H 30 O 2 In linseed and other drying oils. The chemical methods which are employed to distinguish genuine butter from the various manufactured substances resembling it (oleomargarine, butterine, etc.), and to determine whether butter has been adulterated with other fats or oils, are all based on a single characteristic difference in composition between butter, on the one hand, and all those fats, on the other, which can be successfully employed to counterfeit or adulterate it. This difference lies in the fact that butter con- tains a considerable proportion of the glycerin salts of acids of comparatively small molecular weight, butyric, caproic, caprylic, and capric, while the other fats, with possibly one exception, are nearly destitute of them. These acids of low molecular weight are soluble in water and can therefore be readily separated from those of high molecular weight, like palmitic, stearic, and oleic acids, which are insolu- ble in water. On this difference is based the process of Hehner, to whom belongs the credit of having been the first to propose a rational method for distinguishing butter from its admixtures with other fats, and from oleomargarine. They are also volatile with water vapor, while the other acids occurring in fats and oils are either nonvolatile, or only slightly volatile with steam. This is the basis of Reichert's method. Again, since butter contains a larger proportion of acids of small molecular weight, it follows that a fixed weight of it requires more alkali for its saponification than the same weight of other fats. On this fact is founded the method of Koettstorfer. 502 QUANTITATIVE EXERCISES EXERCISE LIX DETERMINATION OF THE INSOLUBLE ACIDS HEHNER'S METHOD Melt about 100 grams of butter in a beaker glass, taking care not to raise the temperature unnecessarily, and filter the upper oily portion through a dry, warm paper into a large test tube. Place the tube in water having a temperature of 50 or 60, and keep it there until the oil appears to be free from water. Filter through a dry, warm paper into large weighing glasses, taking care not to allow any water which may have separated from the butter to come upon the filter. Stir the filtrate while it is solidi- fying in order to prevent any separation of the constituents. Place a filter, of double thick paper and about 100 mm. wide, in a weighing glass and dry it to constant weight at 100. Weigh about 2 grams of the butter into a beaker glass and add to it 50 cc. of 85 per cent alcohol and a piece of pure potas- sium hydroxide weighing from 1 to 2 grams. Heat the beaker gently upon a water bath from 20 to 30 minutes. Add water, drop by drop, stirring the liquid after each addition. If it remains clear, the saponification is complete. If it becomes turbid, the addition of water must be stopped and the heating continued. Evaporate the alcohol and dissolve the residue in about 150 cc. of water. Add to the clear solution a moderate excess of dilute hydrochloric acid. Heat until the insoluble acids collect in liquid form at the top and the solution beneath becomes quite clear. Place the weighed filter in a funnel, fitting it tightly to the glass. Pour boiling water through it, and, while it is still half full of water, begin to filter the contents of the beaker. Cleanse the beaker thoroughly with the boiling water, and wash the acids on the filter with not less than 1| liters of boiling water. Place the filter, while it is still some- what damp, in the weighing glass in which it was previously dried, and heat to very nearly constant weight at 100. BUTTER 503 The insoluble acids, according to Hehner, the author of this method, constitute from 86.5 to 87.5 per cent of genuine butter, though in some cases the percentage rises to 88. In other fats and oils the percentage of insoluble acids is, as a rule, about 95.5. He would therefore regard as spurious any specimen of reputed butter which is found to contain more than 88 per cent of these acids. To calculate the extent of the adulteration, where a higher per cent has been found, he assumes that 87.5 is the normal percentage of insoluble acids in butter, and finds the proportion of the foreign fats by means of the difference between that number and the higher per cent which the sample contains. Accordingly, a specimen which yields 91 per cent of insoluble acids would be regarded as containing 43.75 per cent of foreign fats, since 95.5 - 87.5 = 8, and 91.0 - 87.5 = 3.5, and 8: 3.5:: 100: 43.75. The conclusions of Hehner regarding the quantity of insol- uble acids which is normal to butter have been repeatedly veri- fied, but not by all observers. Some have found 89 and even over 90 per cent of insoluble acids in butter whose genuineness could not be questioned. The following table gives the percentage of insoluble acids which several of the fats and oils have been found to contain. Butter 87.50 Olive oil 95.43 Lard 96.15 Palm oil 95.60 Tallow 95.50 Peanut oil .... 95.00 Oleomargarine . . . 95.56 Rape oil 95.10 'Cocoanut oil . . . 86.43 Sesame oil .... 95.48 Cotton-seed oil . . . 95.75 A portion of the soluble acids of the butter is lost during sapon- ification in consequence of the formation of volatile ethyl salts. If the liquid under the layer of insoluble acids is turbid at the time of filtration, the filtrate will also be cloudy from the presence in it of insoluble acids in a finely divided condition. It is therefore important to postpone the filtration until the liquid becomes quite clear. A slight turbidity can be removed 504 QUANTITATIVE EXERCISES by passing the filtrate repeatedly through the filter. The fil- trate should be carefully examined, not only with respect to its clearness, but also for the presence in it of minute globules of the insoluble acids. The washing of the insoluble acids is the most critical feature of the determination. In the liquid condition they dissolve con- siderable quantities of the soluble acids and retain them with great tenacity. The water should be forced into tne funnel in such a way as to break up the layer of insoluble acids to the greatest possible extent. In this manner a much larger surface is brought into contact with the water, and the removal of the soluble acids is correspondingly more rapid. The water in the funnel should be allowed to drain out quite completely before introducing a fresh portion. A very faintly alkaline solution of phenolphthalein may be used to test the reaction of the filtrate. The insoluble acids cannot be dried to a perfectly constant weight in the air. According to Hehner they lose for a time and then gain in weight in consequence of oxidation. How- ever, a fairly satisfactory approach to constancy may be obtained if the soluble acids have been completely removed by the wash- ing process. The weight of the insoluble acids may be obtained by placing the filter, after drying it in a current of air, in a Soxlet appa- ratus and extracting it with ether. The ether is then distilled off and the residue heated to constant weight at 100. EXERCISE LX DETERMINATION OF THE VOLATILE ACIDS REICHERT'S METHOD Weigh very nearly 5 grams of the butter, prepared as directed under LIX, into a quarter-liter Erlenmeyer flask. Add to it 10 cc. of 95 per cent alcohol which has been treated with a BUTTER 505 little sodium hydroxide and then redistilled, and 2 cc. of a caustic soda solution made by dissolving 100 grams of sodium hydroxide in 100 cc. of water. Attach the flask to an inverted condenser and heat for one hour in a water bath, immersing the flask nearly to the neck in the boiling water. Evaporate the alcohol and dissolve the residue in 135 cc. of recently boiled water. To the clear soap solution, when its temperature has fallen to 60 or 70, add 5 cc. of dilute sulphuric acid, prepared by diluting 200 cc. of the strongest acid to one liter. Attach the flask to the inverted condenser and heat until the insoluble acids collect in a clear oily layer at the top. Allow the con- tents of the flask to cool to the temperature of the room. Intro- duce a few pieces of pumice stone which have been thrown into water while at a white heat and kept there until needed. Attach the flask to a condenser arranged for distillation and distill off 110 cc. in 30 minutes as nearly as possible. Receive the distillate in a narrow graduated cylinder so that the rate of the distillation may be properly regulated. Filter the dis- tillate, after shaking it well, through a dry paper. Titrate 100 cc. of the filtrate with a tenth-normal solution, either of barium hydroxide in water or of potassium hydroxide in alco- hol, using an alcoholic solution of phenolphthalein as the indi- cator. Add one-tenth for the portion of acid not titrated. According to Reichert and many other chemists who have tested his method with care, the distillate from 2.5 grams of genuine butter neutralizes from 13 to 15 cc. of tenth-normal alkali ; while that from an equal weight of any other fat or oil which could be successfully employed to adulterate or imitate butter neutralizes, generally, less than 2 cc. Possibly an excep- tion should be made in the case of cocoanut oil, whose distillate has been found to neutralize from 3.5 to 3.7 cc. of tenth-normal alkali. Reichert would regard as certainly adulterated, or as consisting of other fats than butter, any sample whose volatile acids neutralize less than 12.5 cc. of alkali. The following table gives, in cubic centimeters, the quantity of tenth-normal 506 QUANTITATIVE EXERCISES alkali required to neutralize the volatile acids derived from 2.5 grams of some of the fats and oils. Butter .... 13.0 to 15.0 Cocoanut oil . . . . 3.70 Lard 0.30 Palm-nut oil . . . . 2.40 Tallow 0.25 Palm oil 0.80 Oleomargarine . . . 0.95 Rape oil 0.25 Cotton-seed oil . . . 0.30 Sesame oil .... 2.20 Only about four-fifths of the volatile acids in the butter are found in the distillate, and the quantity which a distillate of given volume will contain varies somewhat with the volume of the liquid distilled and the rapidity of the distillation. Hence the necessity of following fixed rules as to the volume of the liquid distilled, the volume of the distillate collected for exam- ination, and the time within which the distillation is made. It is preferred by some to effect the saponification in a strong flask, which is closed during the reaction by a cork securely tied to the neck. EXERCISE LXI DETERMINATION OF THE ALKALI REQUIRED FOR SAPONIFICATION KOETTSTORFER'S METHOD Dissolve about 10 grams of potassium hydroxide in 2 liters of 95 per cent alcohol and redistill. Dissolve about 15 grams of the purest potassium hydroxide in 400 or 500 cc. of the redistilled alcohol and dilute with the same to one liter. Pour the solution into a bottle and allow it to stand undisturbed until the potassium carbonate which was in the hydroxide settles out and becomes firmly attached to the glass. - Prepare a standard solution of hydrochloric acid, each cubic centimeter of which contains the quantity of acid required to neutralize 11.14 milligrams of potassium hydroxide. Weigh BUTTER 507 from 1 to 2 grains of butter into a small Erlenmeyer flask and add to it the volume of the alcoholic potash solution which has been found to be equivalent to 40 cc. of the standard acid. Attach the flask to an inverted condenser and heat it on a water bath until the saponification is complete. Allow the flask to cool to the temperature of the room before removing it from the condenser.' Add an alcoholic solution of phenolphthalein and titrate the excess of alkali with the standard acid. Koettstorfer found that one-gram quantities of genuine butter from different sources required for saponification from 221.5 to 232.4 milligrams of potassium hydroxide, while an equal weight of various other fats and oils required a much smaller amount of the alkali. The following table gives in milligrams the quan- tity of potassium hydroxide required to saponify one gram of the substances named. Butter . . . 221.5 to 232.4 Olive oil . 189.3 to 192.6 Lard . . 192.0 to 196.5 Palm oil . 196.3 to 202.5 Tallow . . . 193.2 to 198.0 Palm-nut oil . 220.0 to 247.6 Butterine . . 193.5 to 196.5 Peanut oil . . 196.6 Cocoanut oil . 246.2 to 268.4 Rape oil . 170.2 to 176.4 Cotton-seed oil 191.0 to 196.6 Sesame oil . . 190.0 to 192.4 Experiments made in this laboratory indicate that the quan- tity of alkali required to saponify one gram of butter obtained from milk by evaporating the water and extracting the residue with ether is quite exactly 230 milligrams. It was found by Moore that one gram of a mixture consisting of 49.3 per cent of cocoanut oil and 50.7 per cent of oleomar- garine required for its saponification 220 milligrams of potassium hydroxide. An equal quantity of another mixture of the same substances containing 70.2 per cent of cocoanut oil and 29.8 per cent of oleomargarine required 234.9 milligrams. 508 QUANTITATIVE EXERCISES EXERCISE LXII DETERMINATION OF THE ALKALI NEUTRALIZED BY THE SOLUBLE AND THE INSOLUBLE ACIDS METHOD OF MORSE AND BURTON There are required for this determination a solution of potas- sium hydroxide in alcohol and one of hydrochloric acid. It is not necessary to know the strength of either solution. They should, however, be quite dilute and approximately equivalent. The solutions used in the preceding exercise will answer very well for this. It is also unnecessary to weigh the butter. Place a quantity of butter, judged to weigh not more than two grams, in a small Erlenmeyer flask and add to it a meas- ured but excessive quantity of the alkali. Attach the flask to an inverted condenser and heat it on a water bath until the saponification is complete. Allow the flask to cool to the tem- perature of the room and then titrate the excess of the alkali with the solution of hydrochloric acid, using phenolphthalein as the indicator. Attach the flask to a condenser arranged for distillation. Immerse it to the neck in water and distill off all the alcohol, collecting the distillate for subsequent use. Draw off a number of cubic centimeters of the alkali equal to the number which was added to the butter in the first place and titrate with the acid. Having found how much acid is required to neutralize the whole of the alkali, and also the alkali which remained after saponification, add an amount of the acid equal to the difference between these quantities to the soap in the flask. It is also well to add from 50 to 75 cc. of water. The quantity of acid added is, of course, just sufficient to liberate all the acids of the butter. Attach the flask to the inverted condenser and heat it on a water bath until the insoluble acids have collected in an oily layer at the top and the liquid below has become quite clear. The minute globules of molten insol- uble acids sometimes remain suspended for a long time, giving BUTTER 509 the liquid a milky appearance. If filtration is attempted while the liquid is in this condition, some of the finely divided insol- uble acids will pass through the filter. The difficulty can be remedied in either of two ways : first, by introducing a small quantity of long-fiber asbestus and rotating the flask for a few minutes ; or, second, the liquid may be allowed to cool and stand for a few hours. In the latter case the suspended acid solidifies and rises to the top, and on reheating, the liquid below the oily layer is usually found to be free from suspended glob- ules. Filter through a double-thick paper which has been satu- rated with water, and wash the insoluble acids as directed under LIX. Add the alcoholic distillate to the filtrate and titrate with the alkali. Dissolve the insoluble acids in hot alcohol and titrate them with some of the same alkali. Express the relation of the quantities of the alkali neces- sary to neutralize the soluble and the insoluble acids in the form of percentages of the whole amount of the alkali which was required to saponify the butter. It is evident that the sum of the volumes of the alkali used in neutralizing the two classes of acids must equal the volume of the alkali required for the saponification. This fact fur- nishes a check of some value upon the correctness of the work. The following table gives the percentages of alkali required to neutralize the soluble and the insoluble acids in butter, cocoa- nut oil, cotton-seed oil, oleomargarine, lard, and tallow. Per cent KOH required for Insoluble Acids Per cent KOH required for , Soluble Acids Butter 86 57 13 17 Cocoanut oil (unwashed) . .... 91 95 8 17 Cocoanut oil (washed with hot water) . . Cocoanut oil (washed with dilute Na 2 C0 3 ) . Cotton-seed oil 92.43 92.33 92 05 7.42 7.45 7 76 Oleomargarine 95 40 4.57 Lard . . .... 95 96 3 82 Beef tallow 96 72 3 40 510 QUANTITATIVE EXERCISES It was found by Moore that a mixture of 50, per cent of but- ter, 27.5 per cent of oleomargarine, and 22.5 per cent of cocoanut oil could not be distinguished from genuine butter, either by the method of Hehner or by that of Koettstorfer. Such a mixture, examined by this method, gave 90.17 per cent KOH required for insoluble acids; 9.70 per cent KOH required for soluble acids. EXERCISE LXIII DETERMINATION OF THE IODINE ABSORBED HUBL'S METHOD Dissolve iodine, 12.5 grams, and mercuric chloride, 15 grams, each in 250 cc. of 95 per cent alcohol. Filter the mercuric chlo- ride solution, if necessary. Mix the two solutions and allow the mixture to stand for twelve hours. Dissolve about 24 grams of sodium thiosulphate in water and dilute to a liter. Determine the strength of the solution in the usual manner with resublimed iodine. Test the chloroform which is to be used by adding to 10 cc. of it 10 cc. of the iodine solution. After three hours determine the iodine in the chloroform and also in 10 cc. of the original iodine solution. The quantities of iodine found should be the same. Dissolve 25 grams of potassium iodide in 250 cc. of water. Prepare a one per cent starch solution in the usual manner. Weigh about 0.8 gram of butter into a 200-cc. Erlenmeyer flask. Dissolve it in chloroform. Add 20 cc. of the v iodine solu- tion. Close the flask with a rubber stopper and shake it. If the solution becomes cloudy, add a little more chloroform. Close the flask and allow it to stand 2 hours. If the color of the solution fades to any considerable extent, add more of the iodine solution. The excess of the iodine must be quite large. Add from 10 to 15 cc. of the potassium iodide solution and shake well. Dilute with 150 cc. of water. Titrate with the thiosulphate solu- tion until the color becomes quite faint, then add starch paste and BUTTER 511 titrate to the end-reaction. Draw off a quantity of the iodine solution equal to that added to the butter in the first place. Add potassium iodide and determine the iodine in it. The difference between the quantities of iodine found by the two titrations is equal to the quantity which has been absorbed by the butter. The quantity of the iodine absorbed is stated in the form of percentage, by weight, of the butter taken. The number of parts of iodine absorbed by one hundred parts of any fat or oil is known as its " iodine number." The following table gives the iodine number of several of the fats and oils. HUBL MOOEE ARCHBUTT 97.5-98.9 81.6-84.5 97.0-105.0 105.0-108.0 105.0-108.0 156.0-160.0 148.0 84.0-84.7 98.1 83.0 101.0-104.0 102.7 106.0-109.0 155.2 Olivp nil Linseed oil (raw) Linseed oil (boiled) .... Castor oil . . 84.3 147.9 84.3 71.9 Sperm oil . .... Neat's-foot oil 66.0 50.4-52.4 8.9 34.0 4.2 26.0-35.1 55.3 59.0 40.0 Palm oil 50.3 8.9 Japan wax Butter 19.5-38.0 50.0 61.9 Oleomargarine .... Lard Tallow It will be observed that the iodine number of butter, as given in the table, varies between wide limits. The lower values, however, were obtained from samples which were in an advanced stage of decomposition. It has been shown by Moore that the addition of cocoanut oil in certain proportions to lard, to oleomargarine, and to a mixture of 512 QUANTITATIVE EXERCISES butter and oleomargarine, gives products whose iodine numbers are about equal to that of genuine butter. It was also found by him, as previously stated, that certain mixtures of cocoanut oil with other fats yield the same results as butter when tested by the methods of Hehner and Koettstorfer. All such mixtures are, however, readily distinguished from butter by the method of Reichert. It is doubtful whether cocoanut oil which, if it were added in the right proportions, would render the methods of Hehner, Koettstorfer, and Hubl useless in butter analysis is, or can be, successfully employed in adulterating butter or in the manu- facture of its substitutes. Its taste and odor seem to render such a use of it impracticable. The chief value of Hubl's method lies in its efficiency as a means of detecting the adulterations of oils. EXERCISE LXIV DETERMINATION OF BUTTER IN MILK I. DETERMINATION BY THE ORDINARY GRAVIMETRIC METHOD To about one liter of commercial ether, in a strong bottle, add thin shavings of metallic sodium. Close the bottle with a cork having a groove on one side, or with one through which a glass tube with a small onitlet has been passed. When the sodium becomes so much incrusted as to prevent contact between the ether and the metal, clean it by pressing and rub- bing the pieces against the bottom of the bottle with a stout glass rod. Continue to clean the metal from time to time, add- ing more of it, if necessary, until the evolution of hydrogen ceases. Keep the ether in the bottle with an excess of sodium until it is needed for the extraction of the butter. Ignite some asbestus in a platinum dish over a blast lamp and place a portion of it in a " Hofmeister " capsule, a thin glass shell which can be readily crushed. BUTTER 513 Measure 10 cc. of well-shaken milk into a large weighing glass. Close the glass and weigh it. Pour the milk upon the asbestus in the capsule. Close the glass and weigh it again. Evaporate to dryness in a steam bath consisting of a liter- Erlenmeyer flask, and a funnel having a diameter of about 120 mm. at the top and a wide neck. Pass the neck <=* of the funnel through a cork which fits the flask, and J provide a rest for the capsule by placing a small tri- angle in the bottom of the funnel, or by hanging glass rods with curved ends over the edge of it. Prepare a filter for the Soxlet apparatus, Figs. 71 a and 71 b , which is to be used in the extraction. For this purpose a cylinder of wood or other material is required. It must be square and smooth at one end, and of some- what smaller diameter than the extraction apparatus. Wind a strip of the best and strongest filter paper twice around the cylinder, allow- ing one edge to extend considerably beyond the square end, and fasten it with pins. Fold in the free edge upon the end of the cylinder and press the folds against some hard object. If necessary, the folds may be secured in their places by wiring them together. If it is feared that the bottom of the filter will permit solid material to pass through it, a little paper pulp sus- pended in water may be poured into the filter and the water drawn off with the pump as in the prepara- tion of a Gooch filter. The filter should be long enough to extend from the bottom of the extractor to the point where the ether vapors enter it, and so wide that no place will be left between the paper and the glass. Filters especially made for the Soxlet apparatus can now be obtained and are to be preferred to the one described above. 514 QUANTITATIVE EXERCISES Distill on the water bath a quantity of the ether which will somewhat more than fill the extractor. Place the dry filter and a roll of filter paper in the extractor and extract them with the redistilled ether for 2 hours. The heat should be so regu- lated during the extraction that the apparatus will fill and siphon off in four or five minute periods. Great care must be exercised in selecting the corks by which the different parts of the apparatus the inverted condenser, the extractor, and the flask are joined together. The flask should be heated in an air bath and not in water. A thin iron crucible somewhat lar- ger than the flask answers very well as a bath. The heat rising from the bath sometimes interferes with the automatic action of the siphon. This difficulty is easily remedied by placing a shield of cardboard between the bath and the extractor. Place the capsule containing the dried milk, bottom upwards, in a porcelain mortar. Cover the mortar with a piece of card- board having a hole in the center just large enough for the pestle. Hold it in place with the fingers of one hand, and, with the pestle in the other hand, crush and grind the capsule and its contents. Transfer the ground material to the filter, and place it in the extractor. Pour a little ether into the mor- tar and rub it over the inside with the pestle. Then pour the ether down a glass rod into the filter. Continue washing the mortar in the same mariner with small quantities of ether until it is believed that all the fat has been removed from it. Cover the contents of the filter with some of the extracted paper. Attach a weighed flask containing ether to the extractor, and extract the filter for not less than 4 hours. Distill off the ether and dry the butter residue to a constant weight at a tem- perature of 60 or 70. During the latter part of this process a current of dried air should be drawn through the flask to facilitate the removal of the last traces of the ether. Having found the weight of the butter, determine, by the method of Koettstorfer, how much potassium hydroxide is required to saponify it. BUTTER 515 The ether, when not in use, should be returned to the main supply in the bottle containing metallic sodium. II. DETERMINATION BY ADAMS' METHOD Cut off strips of thick filter paper, 65 mm. wide and 600 mm. long. Roll them up loosely and extract thoroughly with anhy- drous ether. Measure 5 cc. of well-shaken milk into a weighing glass and weigh. Open one of the rolls and stretch the strip of paper horizontally and at some distance above the table be- tween two clamps. Distribute the milk as uniformly as possible over the central portion of the paper. Close the glass from which the milk was taken and weigh it. Place a heated air bath under the paper, and when it appears to be nearly dry, roll it up loosely. Place the roll on a watch glass in the air bath and heat for an hour at 100. Put the roll into the filter in the extractor and extract with anhydrous ether for not less than 3 hours. Proceed with the extract as directed under I. Instead of opening the roll of extracted paper and distribut- ing the milk in the manner described above, the roll may be tied with a thread and one end of it dipped into the milk. When the milk has all been absorbed, the roll is placed on the unsoiled end in a watch glass and dried at 100. Having found the weight of the butter, determine how much alkali is required to saponify it. III. DETERMINATION BY THE METHOD OF MORSE, PIGGOT, AND BURTON In this method the milk is dried by means of anhydrous cop- per sulphate and the fat extracted either with the low-boiling products of petroleum or with ether. In the former case the quantity of the butter is to be determined by saponification. Prepare a quantity of anhydrous copper sulphate by heating the recrystallized salt in a porcelain dish at a temperature of 516 QUANTITATIVE EXERCISES 250. It may be prepared more expeditiously by heating the salt upon a copper plate with the naked flame; but, in that case, the material must be constantly stirred and not allowed to harden upon the metal. In a porcelain mortar provided with a lip and having a diameter of 90 or 100 mm. at the top place about 20 grams of the anhydrous copper sulphate. Make a depression in the center with the pestle, and pour into this a weighed 10-cc. portion of milk. Draw the copper sulphate which was pushed aside in making the cavity into and over the milk, and, while the mass is still somewhat moist, begin to grind with the pestle. Continue the grinding until the material is reduced to a fine powder, and extract it with ether in the Soxlet apparatus. CHAPTER XXIII ELECTRIC HEATING APPLIANCES FOR LABORATORY USE The advantages of employing electricity for heating purposes in the laboratory are numerous. 1. The heat required can be generated within the space to be heated, that is, where it is needed. 2. Since the heat is generated where needed, it can be econ- omized very effectively by surrounding the heated space with nonconducting materials and confined air spaces. 3. With practically constant electromotive force, such as we have in the storage battery, the temperatures can be controlled with a high degree of exactitude. 4. Having once calibrated an electric heating device, that is, having determined for each temperature the resistance of the portion of the circuit in which the heat is generated, one can thereafter at any time ascertain the temperature without the aid of thermometer or pyrometer. 5. Where calibrated electric furnaces or baths are used, it is feasible in many cases to ascertain at what temperatures reactions take place and to determine when they begin and cease. 6. There is no contact of the substances heated, with dele- terious products of combustion, as often happens when gas is used. 7. Heating by electricity is much less destructive than heat- ing by gas to the materials used in the construction of furnaces, baths, etc. 8. Owing to the less destructive effects upon costly materials and to the practicability of preventing waste through loss of heat to the outside air, and of so adjusting the resistance of the heating device to the electromotive force of the current that 517 518 QUANTITATIVE EXERCISES little is lost in external resistance, heating by electricity is, in many operations, more economical than heating by gas. Some of the appliances in use in the author's laboratory in which the electric current is utilized for heating purposes are here described. 1. CRUCIBLE FURNACE Figure 72 represents a furnace for heating materials, fusion of silicates, etc., in platinum crucibles. The three hard-burned perforated clay rings, a, 5, and c, are held in place by three platinum rods made from No. 16 wire (B. & S. gauge). The ends of these rods are threaded and each end is pro- vided with two small plati- num nuts between which the rings a and c are firmly fas- tened. The purpose of the ring b is to keep the crucible from coming in contact with the platinum wires. It is adjustable up or down, but may be fixed in any desired position by twisting short pieces of wire about the rods. The internal diameters of b and c are equal, while that of a is smaller in order to fur- nish a rest for the crucible support. Each ring is provided with 60 perforations in two rows of 30 each, through which the platinum wire (No. 26 B. & S. gauge) is threaded up and down in the manner shown in the figure. The inner row of wires also crosses from side to side under a. The total height of the furnace, as represented in the figure, is 80 mm., and the total length of the wire is 16 feet. The platinum rods serve FIG. 72 LABORATORY ELECTRIC HEATING APPLIANCES 519 FIG. 73 two important purposes. They support the whole weight of the furnace and its contents, and thus prevent any stretching of the wires while hot ; and, having at all times about the same temperature as the wires, they keep the latter perfectly straight, and thus prevent any danger of short circuits through contact between adjacent strands. The furnace as represented in Fig. 72 is surrounded by the clay cylinder c?, as shown in Fig. 73, the ring c, Fig. 72, resting upon the upper edge of d. The cylinder d is provided with the perforated cover e and the bottom / which li rests upon the three truncated clay cones g. The hole in e serves for the introduction of a thermometer or pyrometer. Figure 74 represents a cylinder h of larger dimensions which surrounds d. It is also fur- nished with a perforated cover i, a bottom j, and the supports k. The complete furnace is shown in Fig. 75, in which I is a Le Chatelier pyrometer ; m, a galvanized iron cyl- inder with cover, both of which are lined and covered with asbestus paper ; w, a series of asbestus boards with ventilating spaces between them ; o, a block of soapstone ; and p, a wooden board on which the whole arrangement rests and can be moved without disturbing any of the parts ; q and r are firmly fixed steel rods which serve to FIG. 74 520 QUANTITATIVE EXERCISES connect the wires coming from the furnace with the external circuit and to protect the former from injury through strains of any kind ; *, * are short pieces of pipestem which keep the plat- inum wires from contact with the metallic cylinder m. The crucible support t is made as light and open as possible, coming in contact with the crucible at three points only. The method of making the clay parts and the process of wir- ing this furnace have been described in the American Chemical Journal for 1904. The first step to be taken with a furnace of this kind is to calibrate it, that is, to determine its resistance for every tem- perature up to the limit to which it is afterwards to be heated ; for it will then be feasible at all times, without the aid of a thermometer or pyrometer, to maintain in it with certainty any desired temperature, or to ascertain at any time what the tem- perature in it is. The furnace, in fact, becomes, by virtue of such a calibration, a resistance pyrometer. For the calibration of the furnace in use in the author's labo- ratory there were employed a mercury thermometer registering to 550, a Le Chatelier platinum platinum-rhodium pyrometer, and a Keiser-Schmidt decimillivoltmeter, all of which had been tested at the German Physikalisch-Technischen Reichsanstalt. We give below in tabular form the data for the furnace up to 967. The calibration was not carried higher because the tem- perature 950 is sufficient for ordinary crucible work. The temperatures given are probably correct to within 5 or less. The voltmeter which was used to measure the electromotive force which was developed at the junction of the platinum and platinum-rhodium wires is furnished with two scales, one in which each division has the value of a decimillivolt, and another in which a division corresponds to 20 of temperature. Not- withstanding the coarseness of the needle in this instrument, the errors of parallax in reading could not have amounted to more than one-fourth of a division on either scale. LABORATORY ELECTRIC HEATING APPLIANCES 521 522 QUANTITATIVE EXERCISES CURRENT VOLTAGE RESISTANCE WATTS TEMPERATURE 2.5 33.7 13.48 84.25 383 2.6 36.0 13.846 93.60 407 2.7 38.5 14.259 106.38 434 2.8 41.0 14.671 114.80 463 2.9 43.6 15.034 126.44 488 3.0 47.4 15.80 142.20 526 3.1 50.2 16.193 155.62 558 3.2 52.7 16.468 168.72 587 3.3 55.3 16.757 182.49 615 3.4 58.3 17.147 198.22 640 3.5 61.2 17.486 214.20 663 3.6 ' 64.3 17.861 231.48 690 3.7 66.9 18.081 247.53 710 3.8 70.1 18.447 266.38 741 3.9 73.3 18.795 285.87 766 4.0 76.3 19.075 305.20 793 4.1 79.5 19.390 325.55 813 4.2 82.5 19.643 338.25 840 4.3 85.3 19.837 366.79 867 4.4 88.7 20.159 390.28 888 4.5 92.0 20.444 414.00 914 4.6 95.0 20.652 437.00 940 4.7 98.0 20.851 460.60 967 Unless absolutely unavoidable, a calibrated furnace like the foregoing should not be heated above 1150. At higher tem- peratures the metal is volatilized to an extent which sensibly affects the resistance of the wires, making a recalibration necessary. It will be readily understood that an accurately calibrated resistance furnace is theoretically an admirable instrument for the study of reactions at high temperatures; for, if external conditions are constant, it will always require the same amount of electrical energy to maintain any given temperature in the empty furnace, or, what is the same thing, a given amount of electrical energy is bound to maintain in it always a certain fixed LABORATORY ELECTRIC HEATING APPLIANCES 523 temperature. If now any reaction involving the disappearance or evolution of heat takes place within the heated space, the amount of electrical energy required to maintain the tempera- ture at which it takes place will be increased or diminished according as the reaction is endothermic or exothermic. And the difference, if it can be ascertained, will serve as a measure of the heat energy of the reaction. There is little difficulty in discovering at what temperature reactions involving consider- able heat effects take place in such an electric furnace. If, for instance, a substance is losing water in the furnace, it will be noticed that the amount of current required to maintain the temperature as determined by the resistance is considerably greater than that required to maintain the same temperature in the empty furnace, showing that a reaction involving the loss of heat is going on within. Again, when a fusible substance is heated in the furnace and the temperature of fusion is reached, there is noticed an increase in the flow of the current without any corresponding increase in the resistance of the platinum wire, i.e. in the temperature within the furnace. The increased flow of current continues for a time and then diminishes to its original volume, showing that the fusion is finished. If the furnace has been calibrated, a determination of its resistance during the time of the increased flow of current will give the melting point of the substance. In this way it was found that the fusing point of sodium carbonate is between 860 and 863. The exact time of fusion may also be ascertained by arranging to have the sinking of a platinum weight into the softened material either close or break a circuit in which there is a sensitive ammeter. Notwithstanding the favorable location of the wires in this furnace with respect to the space heated, and the double- inclosed air spaces surrounding it, the temperature within does not immediately rise to its maximum when the current passing through the furnace is increased, that is, some time elapses before the temperature within adjusts itself to that of the 524 QUANTITATIVE EXERCISES external atmosphere. The tardiness of this adjustment between internal and external conditions lessens somewhat the precision of the results obtained when the furnace is employed for the investigation of reactions at high temperatures. It is, however, to be hoped that a remedy will be found for this defect of a method which is otherwise so promising. 2. AIR BATHS WITH GRAPHITE STOVES Graphite is a substance which conducts electricity, but differs from metallic conductors in that its conductivity increases with rise of temperature. If it could be evenly distributed in suffi- cient quantity over a smooth surface and made to adhere to the same with sufficient tenacity, it should afford a ready means of raising temperature by electricity up to that at which graphite is burned by the oxygen of the air. Unfortunately the rubbing of ground dry graphite upon a smooth surface does not give a sufficiently heavy coating of the material to conduct the requisite amount of current. A thicker covering can be obtained by repeated applications of it, in a wet condition, with a flat camel's-hair brush. The surface to which it is applied must, however, be hot enough to evaporate the water almost instantaneously ; otherwise the deposit will be quite uneven. The results obtained by the last method are nevertheless unsatisfactory. The material lacks adhesiveness, and when an attempt is made to harden it by polishing with a stiff brush, much of the graphite is detached, and the surface which is produced is easily injured by handling or by contact with other objects. To secure a satisfactory deposit, some other material must be mixed with the graphite, and all of the substances which lend themselves to this purpose are incapable of withstanding as high temperatures as graphite itself. There are two substances with which the graphite may be mixed with excellent results so far as the conducting surface is concerned: first, washed and bolted LABORATORY ELECTRIC HEATING APPLIANCES 525 FIG. 76 clay, and second, some kinds of soap. Of these the former is much to be preferred. The best results are secured with the paste form of a well- known stove polish which is obtainable everywhere in this coun- try, and this material is to be recommended for the preparation of graphite stoves above any mix- ture of graphite with clay or with soap which can be made in the laboratory. Soapstone is undoubtedly the best of all available materials on which to spread the graphite for heating purposes. It is easily cut to any desired form ; its surface can be made very smooth, which is essential to the best results ; and, above all, it withstands better than any other non- conducting material great and sudden changes of temperature. Figures 76 and 77 represent two forms of graphite stoves for ordinary hot-air baths, a, Fig. 76, is a soapstone block of con- venient size for the usual rec- tangular copper air bath. It is seen in place in Fig. 78. 6, 5, J, b are strips of iron which are bolted to the block at the ends, the central bolt at each end serving for the attachment of the wires of the circuit. The corner bolts, which are longer than the others, are covered with the soapstone caps 6 e_ I GO