-M 
 soia 
 
The Hydration of Normal Sodium Pyrophosphate 
 
 to Orthophosphate in Varying Concentrations 
 
 of Hydrogen Ion at Forty-five Degrees 
 
 Centigrade. 
 
 DISSERTATION 
 
 Submitted in Partial Fulfillment of the requirements 
 
 for the Degree of Doctor of Philosophy in 
 
 the Faculty of Pure Science of 
 
 Columbia University. 
 
 BY 
 
 WALDEMAR C. HANSEN, B. S. 
 
 NEW YORK CITY 
 1922 
 
The Hydration of Normal Sodium Pyrophosphate 
 
 to Orthophosphate in Varying Concentrations 
 
 of Hydrogen Ion at Forty-five Degrees 
 
 Centigrade. 
 
 DISSERTATION 
 
 Submitted in Partial Fulfillment of the requirements 
 
 for the Degree of Doctor of Philosophy in 
 
 the Faculty of Pure Science of 
 
 Columbia University. 
 
 BY 
 
 WALDEMAR C. HANSEN, B. S. 
 
 NEW YORK CITY 
 1922 
 
TO MY MOTHER 
 

 ACKNOWLEDGMENT 
 
 The following investigation was undertaken at 
 the suggestion of Professor Samuel J. Kiehl and car- 
 ried out under his direction. It gives me pleasure to 
 express my thanks and appreciation for his constant 
 advice and assistance received throughout the inves- 
 tigation. 
 
 A87139 
 
The Hydration of Normal Sodium Pyrophosphate to Ortho- 
 phosphate in Varying Concentrations of Hydrogen 
 Ion at 45 Centigrade. 
 
 Since the work of Graham 1 on the phosphoric acids the 
 problem of the hydration of pyrophosphoric acid has been of 
 interest. A part of the interest was due to the difference of 
 opinion among chemists as to whether the hydration of meta- 
 phosphoric acid was direct to orthophosphoric acid or 
 whether pyrophosphoric acid was formed as an intermediate 
 product 1 ' 2 > 3> 4> 5 6> 7 . Beans and Kiehl 8 showed that pyro- 
 phosphate is formed as an intermediate product in the hydra- 
 tion of sodium monometaphosphate to orthophosphate. There- 
 fore to understand more fully the hydration of sodium mono- 
 metaphosphate to orthophosphate it seems advisable to study 
 the hydration of a pyrophosphate to orthophosphate under 
 the same conditions. 
 
 One difficulty encountered by previous workers on this 
 problem was due to the lack of a suitable method for the de- 
 termination of the amounts of the different phosphates pres- 
 ent when present together. In order to study the reaction it 
 is necessary to have a method of determining the amounts of 
 each of the phosphates present at any given time. 
 
 The first to study this problem were Andre and Berthelot 5 . 
 They used a method of acidimetry to determine the amounts of 
 each of the acids present at any definite time. They discarded 
 this method and attempted 5 to develop a gravimetric separa- 
 tion. In this separation they precipitated a magnesium ammon- 
 ium pyrophosphate of indefinite composition by heating the 
 solution to be analyzed, acidified with acetic acid, for three or 
 four hours on a boiling water bath. Since temperature 9 and 
 hydrogen ion 5 > 9 both have a marked effect on the rate of 
 hydration this method could not be applicable for a quantita- 
 tive study of this hydration. 
 
 No one attempted a further study of -this problem until 
 1909 when Abbott 9 studied it by conductivity measurements. 
 In his method he measured the conductivity of aqueous solu- 
 
tions of pyrophosphoric acid of varying concentrations and 
 at different temperatures. The time at which the conduc- 
 tivity of a given solution became constant he considered as 
 the time required for the complete hydration. He determined 
 the amounts hydrated at different intervals during the reaction 
 by measuring the conductivity of mixtures of pyrophosphoric 
 acid and orthophosphoric acid corresponding in composition 
 to certain percentages of hydration of an original pyrophos- 
 phoric acid solution. He plotted these conductivity values 
 against composition and got straight line curves. So by meas- 
 uring the conductivity of his hydration solution and referring 
 to the curves he could determine the percentage hydrated at 
 that time. 
 
 These three studies are the only ones which have been 
 made heretofore in which the reaction has been followed 
 throughout its entire course. Since the method 5 of Andre and 
 Berthelot was not applicable to the problem in question, and 
 since Abbott's investigations were at temperatures w r here the 
 reaction was complete in a few hours and on a few concen- 
 trations of pyrophosphoric acid only, thus limiting the con- 
 centration of hydrogen ion to that furnished by the acid, 
 neither investigation has furnished sufficient information re- 
 garding the hydration of a pyrophosphate as compared with 
 the hydration of a metaphosphate as previously pointed out 8 . 
 Therefore this problem was undertaken to study the hydration 
 of a pyrophosphate to the orthophosphate in varying concen- 
 trations of hydrogen ion and at constant temperature. With 
 this in view, materials have been prepared and methods devel- 
 oped whereby the factors and conditions influencing the reac- 
 tion could be controlled and studied to completion. An ac- 
 count of this investigation will be presented under the follow- 
 ing headings Apparatus, Preparation of Materials, Method of 
 Procedure, Experimental Data, Discussion, and Summary. 
 
 APPARTUS 
 
 Thermostat: A Freas sensitive thermostat was used to 
 maintain a constant temperature for the entire work of hydra- 
 tion and hydrogen ion concentration measurement. By it a 
 constant temperature of 45 C. .01 was secured. 
 
 8 
 
Potentiometer : Measurements for the determination of 
 the concentration of hydrogen ion were made with a Leeds 
 and Northrup direct-reading potentiometer of low resistance. 
 
 Galvanometer: In connection with the potentiometer a 
 Leeds and Northrup, type R, D'Arsonval galvanometer equip- 
 ped with a telescope and scale was employed. Its resistance 
 was 510 ohms, its sensibility 309 megohms. The period was 
 2.7 seconds, and the critical damping resistance was 1800 
 ohms. 
 
 Standard Cell: A model 4, No. 4208 Weston standard cell 
 served as a basis for all electrical measurements. Its value 
 was 1.01872 volts at 22 C. This voltage was checked against 
 a cell whose value was checked against a Bureau of Standards 
 standard. 
 
 Calomel and Hydrogen Cells and Electrodes : The calomel 
 and hydrogen cells and electrodes employed in the measure- 
 ment of hydrogen ion concentration w|ere of the type described 
 in the article of Fales and Vosburgh 10 excepting a modifica- 
 tion of the hydrogen cell by a stop cock on the arm leading to 
 the salt bridge. 
 
 Crucible Furnace : The amount of water of hydration and 
 of constitution of the di-sodium orthophosphate and the 
 amount of water of hydration of the normal sodium pyro- 
 phosphate was determined by heating the salts in an electric 
 resistance furnace. It was calibrated for temperature by a 
 thermocouple in such a way that its temperature could be con- 
 trolled by measurement of the current with an accuracy of 
 10 C. 
 
 PREPARATION OF MATERIALS 
 
 Normal Sodium Pyrophosphate (Na 4 P 2 O 7 -10H 2 O) : The 
 purest Normal Sodium Pyrophosphate obtainable was re- 
 crystallized three times from distilled water. The solution of 
 the pyrophosphate was cooled in ice water and stirred con- 
 tinuously until the crystallization was complete; this gave a 
 very uniform crystalline product. The crystals were washed 
 three times with distilled water on a Buchner funnel with sue- 
 
tion. They were then spread out on a glass surface and al- 
 lowed to dry for about twelve hours at room temperature. 
 They were then finely pulverized in an agate mortar and 
 stored in a glass-stoppered bottle. 
 
 This normal sodium pyrophosphate was analyzed for water 
 of hydration by weighing a sample into a platinum crucible 
 and heating in the electric crucible furnace previously de- 
 scribed. The temperature was gradually raised to 450 C. 
 during the first hour by increasing the current. It was kept 
 at that temperature for two hours and then weighed ; reheat- 
 ing for an hour caused no change in weight. The following 
 table gives the analysis of the normal sodium pyrophosphate 
 used in this research : 
 
 Lot I, 
 
 Sample 1 
 Sample 2 
 Sample 3 
 Lot II, 
 
 Sample 1 
 Sampel 2 
 
 Water of Hydration Average 
 
 40.45% 
 
 40.44% 40.45% 
 
 40.46% 
 
 40.45% 
 
 40.45% 
 40.45% 
 
 The theoretical value for water of hydration of Na 4 P 2 O 7 - 
 10H 2 O is 40.36%. 
 
 It was then analyzed for phosphorus content. The phos- 
 phorus content was calculated on the basis that the material 
 was Na 4 P 2 O 7 -XH 2 O where XH 2 O = 40.45%. The percentage 
 of phosphorus as calculated should be 13.89%. This was 
 checked by converting weighed samples to orthophosphate by 
 boiling with six molar hydrochloric acid for from four to five 
 hours. The orthophosphate was then determined by the 
 standard magnesium mixture method. The following table 
 gives the results of these analyses : 
 
 Lot I. 
 
 Na 
 
 Sample 
 1.... 
 2.... 
 3.... 
 4.. 
 
 L 4 P 2 O 7 -XH 2 O 
 
 P calc. on 
 
 P determined 
 
 Taken 
 
 basis of 13.89% 
 
 as ortho. 
 
 .3269 gms. 
 
 .0454 gms. 
 
 .0458 
 
 .4084 
 
 .0568 
 
 .0568 
 
 .3971 
 
 .0552 
 
 .0556 
 
 .4448 
 
 .0618 
 
 .0622 
 
 10 
 
The calculated and determined values for percentage of phos- 
 phorus in the material check within experimental error and 
 therefore the value of 13.89 per cent, phosphorus was used in 
 making up all solutions for hydrations. 
 
 Di-Sodium Orthophosphate (Na 2 HPO 4 T2H 2 O) : Di-Sod- 
 ium orthophosphate was prepared by crystallizing three times 
 from distilled water by the addition of an equal volume of re- 
 distilled 9S r /< alcohol and cooling in ice water. The solution 
 was stirred constantly until the crystallization was complete. 
 In this way a very uniform crystalline product was secured. 
 Di-sodium orthophosphate is similar to mono-sodium ortho- 
 phosphate 8 forming two liquid phases upon the addition of 
 the alcohol, and crystallization taking place first at the junc- 
 ture of the two liquid phases. As crystallization proceeds the 
 upper phase disappears, leaving but one phase at complete 
 precipitation. The crystals were filtered on a Buchner funnel 
 with suction and washed three times with alcohol. They were 
 dried by spreading out on a glass surface for about an hour at 
 room temperature ; at the end of that time they were finely 
 pulverized in an agate mortar and put in a glass-stoppered 
 bottle. Di-sodium orthophosphate crystallizes as Na 2 HPO 4 - 
 12H 2 O which gradually decomposes forming lower hydrates 
 when exposed to the air. It was, therefore, decided not to 
 attempt to prepare a constant hydrate, but to dry sufficiently 
 to remove all possibility of free moisture and then analyze 
 that material for water of constitution and water of hydration. 
 The analyses for water content were made by weighing a sam- 
 ple of the material into a platinum crucible and heating in the 
 electric furnace previously described until constant weight 
 was obtained. The material was heated gradually for one 
 hour at first, then the rheostat was set for a temperature of 
 450 C. and held there for two hours. In this way constant 
 results were obtained by Na 2 HPO 4 -XH 2 O being converted to 
 Na 4 P 2 O 7 and the loss of weight was the total water content of 
 the salt, that of hydration and constitution. 
 
 11 
 
Lot I. 
 
 % water of constitu- Calculated % of phos- 
 
 Sample tion and hydration Mean phorus in the material 
 
 ' SIAS iu2 
 
 Lot II. 
 
 Sample 
 
 1 ...... 51 os 11 19 
 
 2 ...... 52.06 
 
 Lot III. 
 
 Sample 
 
 1 ...... 56.51 r , ri _ 1 
 
 2 ..... . 56.52 5dSl 10 ' 14 
 
 Hydrochloric Acid : The hydrochloric acid used was pre- 
 pared by distilling a constant boiling solution through a 
 quartz condenser. The first and last portions were rejected. . 
 
 Potassium Chloride: The calomel cells and salt bridges 
 were prepared from potassium chloride which was purified by 
 re-crystallization three times from distilled water and then 
 fused in platinum. 
 
 Mercurous Chloride: The mercurous chloride employed to 
 make calomel cells for hydrogen ion concentration measure- 
 ments was prepared by the electrolytic method of Ellis 11 , from 
 mercury re-distilled according to Hulett 12 and hydrochloric 
 acid prepared as described above. 
 
 Magnesium Mixture: The magnesium mixture was pre- 
 pared by dissolving 320 grams of magnesium chloride hexa 
 hydrate, 225 grams of ammonium chloride, and 250 c.c. of 
 15 M. ammonium hydroxide (specific gravity .9) in 2250 c.c. 
 of water. 
 
 Magnesium Chloride Solution: The magnesium chloride 
 solution used was made by dissolving 110 grams magnesium 
 chloride hexa hydrate in 50 c.c. of water, which gave ap- 
 proximately a volume of 130 c.c. of solution. 
 
 12 
 
METHOD OF PROCEDURE 
 
 In planning a method of procedure -the first considerations 
 were the factors influencing the reaction and they have as far 
 as possible been either measured or controlled as in the work 
 of Beans and Kiehl in the hydration of sodium monometa- 
 phosphate. The temperature, the concentration of hydrogen 
 ion, the concentration of orthophosphate and the concentra- 
 tion of pyrophosphate are the variable factors which influence 
 the hydration of normal sodium pyrophosphate. 
 
 The temperature was regulated and controlled at 45 C. 
 ~ .01. The concentration of hydrogen ion was measured at 
 intervals during the hydration. The amount of pyrophos- 
 phate changed to orthophosphate was determined at intervals 
 by hydrogen ion concentration measurements ; this was also 
 checked over the last fifty per cent, of the hydration by gravi- 
 metric analysis. 
 
 Preparation of Solutions: 
 
 All solutions made up for hydration were prepared at 20 
 C. The finely pulverized normal sodium pyrophosphate was 
 weighed and transferred to a 1,000 c.c. volumetric flask. Dis- 
 tilled water was added leaving sufficient room for the hydro- 
 . chloric acid required to furnish the hydrogen ion concentra- 
 tion wanted in that solution. The acid used was the constant 
 boiling mixture previously described. The value of the acid 
 was determined by measuring out 30 c.c. portions by means of 
 a burette and building them up to 1,000 c.c. at 20 C. These 
 acid solutions were titrated with standard sodium hydroxide 
 solution. The value of the sodium hydroxide solution was 
 determined by titration against Bureau of Standards benzoic 
 acid. Phenolphthalein was used as indicator in all the titra- 
 tion.s. As the acid was added the flask was rotated so as to 
 avoid acquiring a greater hydrogen ion concentration in any 
 portion of the solution than that ultimately desired. The solu- 
 tion was then brought quickly to 20 C., and the flask filled to 
 the graduation, then mixed thoroughly and put in a "non sol" 
 bottle and placed in the thermostat. The whole operation be- 
 ginning with the addition of the acid required not more than 
 ten minutes. The specific gravity of the solution was taken 
 
 13 
 
at 20 C. by means of the Westphal balance calibrated at 
 20 C., at the beginning of the hydration, again at about 
 fifty per cent., and finally at complete hydration. These spe- 
 cific gravity values are given in the tables for each solution. 
 There Was no change in volume in any of the solutions during 
 hydration (except D and D 2 see Table 2) greater than one 
 part in a thousand, the precision of the balance. This was 
 further checked by measuring the specific gravity of three of 
 the solutions at the beginning and at the end of the reaction, 
 by means of a pycnometer. The change was not greater than 
 one part in a thousand so that the Westphal balance was suffi- 
 ciently accurate. The concentrations of all of the solutions 
 were calculated in moles per liter at 20 C. so by knowing the 
 specific gravity at 20 C. the concentration of the phosphates 
 in any weighed quantity of the solution could be calculated. 
 
 The change of specific gravity of D l and D., was two parts 
 in a thousand. Since they are the only ones that show this 
 change it is believed to be due to some other cause than the 
 change in volume due to hydration. The final hydrogen ion 
 concentrations of these solutions were also higher than expect- 
 ed from the final value obtained for the analytical curve ; all 
 the other solutions approached quite closely in final hydrogen 
 ion concentrations that determined for the analytical curves. 
 So it seems quite possible that some evaporation must have 
 taken place in solutions Dj and D 2 , thus making them more 
 concentrated. This would explain both the specific gravity 
 change and the higher hydrogen ion concentration. All solu- 
 tions were handled so as to minimize evaporation as much as 
 possible because at 45 C. and for the long times that the 
 solutions were being run evaporation would become quite 
 appreciable unless every precaution was taken to guard 
 against it. 
 
 Measurement of Concentration of Hydrogen Ion. 
 
 All hydrogen ion measurements were made at 45 C. by 
 The Saturated Potassium Chloride Calomel Cell method de- 
 veloped in this department 13 . Samples of the solution in 
 process of hydration were taken by means of a pipette and in- 
 troduced into the hydrogen cell previously rinsed three times 
 
 14 
 
with the solution being measured. The voltage was meas- 
 ured after ten minutes and again after twenty minutes which 
 was the time required for equilibrium. The hydrogen was 
 purified by passing it successively through alkaline perman- 
 ganate, mercuric chloride, alkaline pyrogallol, cotton, and a 
 portion of the same solution to be measured placed in the 
 thermostat. 
 
 The calculation of the molar concentration of hydrogen 
 ion was made by means of the formula 
 
 DT 
 
 In this formula C H+ is the concentration of hydrogen ion, 
 E the observed voltage, T the absolute temperature, D a con- 
 stant whose value is .000198, and A a constant whose value 
 is .2342 for 'forty-five degrees centigrade. 
 
 Determination of the Percentage of Hydration by Hydrogen 
 
 Ion Concentration Measurements. 
 
 It is well known that the hydration of normal sodium pyro- 
 phosphate is represented by the following equation : 
 
 Na 4 P 2 O 7 + H 2 O -+ 2Na 2 HPO 4 . 
 
 The method used in making the initial solutions for the hydra- 
 tions studied was to make up a solution of normal sodium 
 pyrophosphate of a certain concentration containing hydro- 
 chloric acid of a certain concentration. It was therefore pos- 
 sible to make up solutions containing pyrophosphate, ortho- 
 phosphate and hydrochloric acid identical in composition with 
 any sample of the particular solution in the process of hydra- 
 tion, provided the specific gravity change during hydration 
 was within the precision of experimental measurements. It 
 has been pointed out previously that the specific gravity 
 change was not greater than one part in a thousand which is 
 within the required accuracy. Therefore, it was possible to 
 make up analytical curves by which the hydration could be 
 followed by hydrogen ion concentration measurements. These 
 curves were made up by preparing six solutions which corre- 
 sponded in composition to the initial solution being studied 
 and to each twenty per cent, hydration, the final solution 
 
 15 
 
corresponding to complete hydration. The molar hydrogen 
 ion concentration measured on each of these six solutions was 
 plotted against. molar concentration of orthophosphate. This 
 gave a curve from which, by knowing the concentration of 
 hydrogen ion in any particular solution being hydrated, the 
 composition of that solution could be determined from the 
 curve. The data for these curves are given in Tables 3, 4, 5, 
 6, 7, 8, 9, 10, and 11. The curves are given in plates I, II, 
 and III. 
 
 Concentration of Na 4 P 2 7 in Moles per Liter. I Division -.025 Mole 
 J 2 $ -100 .075 .050 .025 .000 
 
 3* 
 
 \ 
 
 
 \ 
 
 
 PLATE I 
 
 ANALYTICAL CURVES 
 OF H, A AND I 
 
 ft -.OS M. Na 4 P 2 7 AND .425 M. HCI 
 A - .725" M. Ma* PZ Oj AND .350 M. HCI 
 AND .500 M. HCI 
 
 .050 .100 .150 .200 
 
 Concentration of Na 2 HP04 in Moles per Liter. I Div.-. 050 M. 
 
 16 
 
 .250 
 
Concentration ofNa'4 PZ 7 in Moles per L iter. I Div. = . 035 Mo/e 
 .175 .140 JOS .070 .035 .000 
 
 .000 .070 . .140 .210 .260 .350 
 
 Concentration of /vs 2 HP0 4 /n/wo/es per Liter. I Div. ^.070 Mole 
 
 The materials used in preparing these solutions were the 
 same as used in preparing the hydration solutions with the 
 addition of the di-sodium orthophosphate which is described 
 under preparation of materials. The method of preparing 
 these solutions was to make up 100 c.c. in exactly the same 
 way as described under preparation of solutions. The hydro- 
 gen ion concentration was measured immediately in the same 
 way as described under measurement of hydrogen ion concen- 
 tration. The entire time from the addition of the acid until 
 the final hydrogen ion concentration was mesaured was never 
 over thirty minutes, which introduced very little error into 
 these measurements due to hydration during the time of meas- 
 uring corroborated by actual work of hydration. 
 
 These analytical curves were plotted on a scale such that 
 the concentration of orthophosphate could be read to two- 
 
 17 
 
Concentration of Na 4 P 2 7 in Moles per Liter. 
 
 .180 .135 .090 
 
 . 045 Mole 
 
 045 .000 
 
 PL AT EM 
 
 ANALYTICAL CURVES E,D&B 
 
 E= .225 M. Na+ P 2 Of & .500M.HCI 
 
 D = .225 M. Na 4 P 2 7 & 425M.HCI 
 
 8 f .225 M. Na 4 P 2 7 Qc.350M.HCI 
 
 .000 .090 .180 .270 .360 .450 
 
 Concentration of Na 2 HP0 4 in Moles per Liter. I Div. - .090 Mole 
 
 tenths of one per cent. In every analytical curve the slope 
 was steep enough over the larger part that a change of two- 
 tenths of a millivolt (the precision of potentiometer readings) 
 in hydrogen ion concentration measurements gave an error in 
 composition of less than one per cent., and at the extreme end 
 where the slope became less steep the error was less than two 
 per cent., so that the composition could be determined by hy- 
 drogen ion concentration measurements with an accuracy of 
 less than two per cent, over the entire curve. 
 
 Separation of Ortho and Pyrophosphate. 
 
 The values for percentages of hydration as determined by 
 hydrogen ion concentration measurements were checked over 
 the last fifty per cent, by gravimetric separation. As pointed 
 out in the introduction, no satisfactory gravimetric separation 
 for ortho and pyrophosphate was known. It was known 14 
 
 18 
 
however, that pyrophosphate of magnesium was soluble in 
 magnesium salts. A decision was therefore made to attempt a 
 separation by use of magnesium chloride and magnesium mix- 
 ture. A number of qualitative determinations were made to 
 determine the amounts of magnesium chloride and magnesium 
 mixture necessary to keep certain amounts of pyrophosphate 
 in solution. Then determinations were made to see if ortho- 
 phosphate could be precipitated quantitatively from the mag- 
 nesium chloride mixture solutions containing certain amounts 
 of dissolved pyrophosphate. 
 
 TABLE I. 
 Separation of Orthophosphate from Pyrophosphate 
 
 Mgs. P 
 
 Mgs. P 
 
 Mgs.P 
 
 Mgs. P 
 
 Mgs.P 
 
 Mgs.P 
 
 used in 
 
 found in 
 
 used in 
 
 used in 
 
 found in 
 
 used in 
 
 form of 
 
 form of 
 
 form of 
 
 form of 
 
 form of 
 
 form of 
 
 ortho. 
 
 ortho. 
 
 pyro. 
 
 ortho. 
 
 ortho. 
 
 pyro. 
 
 30.60 
 
 30.38 
 
 40. 
 
 45.00 
 
 45.74 
 
 20. 
 
 30.53 
 
 30.38 
 
 40. 
 
 45.00 
 
 45.91 
 
 20. 
 
 30.53 
 
 30.16 
 
 40. 
 
 45.00 
 
 45.55 
 
 30. 
 
 30.53 
 
 30.75 
 
 40. 
 
 45.00 
 
 45.52 
 
 30. 
 
 30.53 
 
 30.58 
 
 30. 
 
 45.00 
 
 45.29 
 
 30. 
 
 30.53 
 
 30.30 
 
 30. 
 
 45.00 
 
 46.13 
 
 30. 
 
 30.53 
 
 30.61 
 
 30. 
 
 45.00 
 
 45.77 
 
 20. 
 
 30.53 
 
 30.53 
 
 20. 
 
 45.00 
 
 45.91 
 
 20. 
 
 30.53 
 
 30.38 
 
 20. 
 
 45.00 
 
 44.83 
 
 none 
 
 45.00 
 
 45.20 
 
 30. 
 
 45.00 
 
 44.74 
 
 none 
 
 45.00 
 
 44.83 
 
 none 
 
 45.00 
 
 46.41 
 
 30. 
 
 45.00 
 
 44.52 
 
 none 
 
 45.00 
 
 45.88 
 
 30. 
 
 44.90 
 
 45.69 
 
 30. 
 
 21.60 
 
 21.74 
 
 30. 
 
 45.00 
 
 46.41 
 
 30 
 
 21.60 
 
 21.49 
 
 30. 
 
 45.00 
 
 45.88 
 
 30. 
 
 
 
 
 In Table 1 it is shown that from 30 to 45 milligrams of phos- 
 phorus as orthophosphate can be determined within two per 
 cent, in the presence of 40 milligrams or less of phosphorus as 
 pyrophosphate. Attempts to determine orthophosphate in 
 greater concentrations of pyrophosphate were not successful 
 because of the large amounts of the magnesium chloride mix- 
 ture necessary to keep the pyrophosphate in solution which 
 made the method cumbersome and inaccurate. 
 
 19 
 
The following method for separation was developed: 170 
 c.c. of magnesium mixture and 85 c.c. of magnesium chloride 
 solution (described under preparation of materials) were 
 mixed just before using. This mixture of the two solutions 
 has been called throughout this article "the magnesium chlor- 
 ide mixture." The pyrophosphate was dissolved in a few c.c. 
 of water and added slowly with continuous stirring to the 
 magnesium chloride mixture and stirred until any precipitate 
 which formed was re-dissolved. The orthophosphate solution 
 was added slowly with continuous stirring from a burette. 
 The solution was then stirred until the precipitate became 
 crystalline. It was then allowed to stand from twelve to four- 
 teen hours, then filtered and washed with an ammonium ni- 
 trate and ammonium hydroxide solution. This precipitate 
 was then dissolved in cold six molar hydrochloric acid and re- 
 precipitated by adding twenty c.c. of 15 M. ammonium hy- 
 droxide and a few c.c. of magnesium mixture, stirring well 
 during precipitation. It was allowed to stand from six to 
 twelve hours, then filtered into a Gooch crucible and ignited 
 and weighed as magnesium pyrophosphate. 
 
 By this method it was possible to precipitate the ortho- 
 phosphate in a crystalline form. In most cases however, the 
 first precipitate showed traces of pyrophosphate which forms 
 a gelatinous precipitate with magnesium mixture. To mini- 
 mize as much as possible hydrating this pyrophsophate to the 
 orthophosphate during the dissolving of the precipitate with 
 acid, cold acid was used and the solution run directly into the 
 ammonium hydroxide used for re-precipitation. In spite of 
 these precautions a small amount of pyrophosphate was hy- 
 drated during the operation as may be seen in Table 1, where 
 a majority of the values show a slight increase in orthophos- 
 phate over that taken in the sample. 
 
 This method of separation can be used where the concen- 
 tration of phosphorus as pyrophsophate does not exceed about 
 45 milligrams and the concentration of phosphorus as ortho- 
 phosphate is about 30 to 45 milligrams in the total volume of 
 160 c.c. used. The limits of this method allow its use then 
 only after the pyrophosphate solutions are over fifty per cent, 
 hydrated and it was therefore used to check the values ob- 
 
 20 
 
tained b'y hydrogen ion measurements over the last fifty per 
 cent. 
 
 The method of sampling and analyzing the solutions being 
 rn-drated was as follows : 
 
 The concentration of the hydrogen ion was measured as de- 
 scribed under measurement of hydrogen ion concentration at 
 intervals of about every eight to ten per cent hydration. 
 After the solutions were over fifty per cent hydrated gravi- 
 metric samples were taken at the same time as the hydrogen 
 iov> concentration samples. These samples were taken by 
 means of a Bailey weighing burette. An effort was made to 
 get samples in which the phosphorus as orthophosphate was 
 within 30 to 45 milligrams. The sample was added drop by 
 drop with constant stirring to the magnesium chloride mix- 
 ture. When these samples containing both ortho and pyro- 
 phosphate were added a curdy precipitate of ortho with some 
 pyrophosphate was formed. In order to re-dissolve the pyro- 
 phosphate it was necessary to stir for some time until the pre- 
 cipitate became distinctly crystalline and no curdy precipitate 
 could be observed. The lengths of time to accomplish this 
 varied, but thirty minutes was usually sufficient. 
 
 In this way two values were obtained for the percentage of 
 hydration over the last fifty per cent. By referring to the 
 tables under experimental data it may be seen that the first 
 gravimetric samples gave values which were usually three to 
 five per cent, higher than those obtained by hydrogen ion con- 
 centration measurements, and as the hydration neared com- 
 pletion and the concentration of pyrophosphate became less 
 the agreement between the two values became better and near 
 completion checked within the experimental limits. The rea- 
 son for the greater deviation at first is due to the pyrophos- 
 phate carried down in the first precipitation which was partly 
 hydrated on dissolving in acid for the second precipitation. 
 It was found more difficult to re-dissolve the pyrophosphate 
 in these samples than it was when it was added alone as was 
 done in the development of the separation, and with the 
 utmost precaution the first precipitates when filtered always 
 showed the presence of a little pyrophosphate. Then as the 
 pyrophosphate concentration in the samples decreased the 
 
 21 
 
amount carried down was much less and agreement 'was ob- 
 tained in the values by both methods. So by use of this gravi- 
 metric method it was possible to have a check over 'the last 
 fifty per cent, on the values obtained by the hydrogen ion 
 concentration measurements. 
 
 It can be seen by a comparison of the tables that the hy- 
 drogen ion concentration in each solution approached a final 
 value very nearly the same as the value obtained for the 
 analytical curves where the final solution was made up of di- 
 sodium, orthophosphate and hydrochloric acid. Every solu- 
 tion was left in the thermostat from two weeks to a month 
 and the hydrogen ion concentration measured two or three 
 times after the final value which is given in the tables was 
 obtained, and in every case the hydrogen ion concentration 
 remained constant which shows that equilibrium had been 
 reached. 
 
 In determining orthophosphate by magnesium mixture it 
 is usually difficult to get perfectly white ignited precipitates. 
 Nearly all show black spots after they have been ignited to 
 the magnesium pyrophosphate. It was thought this might be 
 due partly to suspended organic matter in the reagents or 
 from such material in the air getting into the precipitate be- 
 fore it was ignited. To see if extra precautions to avoid con- 
 tamination of the precipitates in this way would decrease the 
 black spots after ignition, all reagents used in .the final pre- 
 cipitation and washing were filtered and the precipitate pro- 
 tected from dust and dirt from the air as much as possible. 
 These precautions were taken throughout this work and the 
 majority of the precipitates were white, showing no black 
 spots. 
 
 EXPERIMENTAL DATA 
 
 In the following table are outlined the solutions of normal 
 sodium pyrophosphate and hydrochloric acid studied in se- 
 curing the data for the hydration and for the effect of hydro- 
 gen ion concentration upon the rate of the hydration. 
 
 22 
 
Solution 
 
 TABLE 2. 
 Solutions Studied 
 
 Concentration of Concentration of 
 
 Na 4 P 9 O 7 in moles HC1 in moles 
 
 per Liter at 20 C. per Liter at 20 C. 
 
 .125 
 .125 
 .125 
 .125 
 .125 
 .125 
 .175 
 .175 
 .175 
 .175 
 .175 
 .175 
 .225 
 .225 
 .225 
 .225 
 .225 
 .225 
 
 .350 
 .350 
 .425 
 .425 
 .500 
 .500 
 .350 
 .350 
 .425 
 .425 
 .500 
 .500 
 .350 
 .350 
 .425 
 .425 
 .500 
 .500 
 
 Specific 
 Gravity 
 at 20 C. 
 1.029 
 1.029 
 1.030 
 1.030 
 1.031 
 1.031 
 1.041 
 1.040 
 1.041 
 1.041 
 1.043 
 1.043 
 1.052 
 1.052 
 1.054 
 1.054 
 1.056 
 1.056 
 
 It may be observed in the above outline that all hydra- 
 tions were run in duplicate. In every case the two checked 
 within experimental error and therefore the data for only one 
 is given. 
 
 All synthetic solutions for analytical curves are lettered 
 the same as the respective solutions to be hydrated. 
 
 TABLE 3. 
 
 Data for Analytical Curve I in Plate I. 
 Concentration of HC1 = .500 M. at 20 C. 
 
 Temperature = 45 C. 
 Barometric Pressure = 766.0 mm. at 19 C. 
 
 Molar 
 Concentration 
 
 Solution 
 1 
 2 
 3 
 4 
 5 
 6 
 
 of Na 4 P 2 O_ 
 at20C. 
 .125 
 .100 
 .075 
 .050 
 .025 
 .000 
 
 Molar 
 
 
 Molar 
 
 Concentration 
 
 
 Concentration 
 
 of Na 2 HPO 4 
 
 Voltage 
 
 of Hydrogen 
 
 at 20 C. 
 
 E 
 
 Ion X 10 2 
 
 .000 
 
 .2892 
 
 13.39 
 
 .050 
 
 .2919 
 
 12.14 
 
 .100 
 
 .2958 
 
 10.52 
 
 .150 
 
 .2999 
 
 9.06 
 
 .200 
 
 .3056 
 
 7.36 
 
 .250 
 
 .3112 
 
 5.99 
 
 23 
 
Solution 
 1 
 2 
 3 
 4 
 5 
 6 
 
 Solution 
 1 
 2 
 3 
 4 
 5 
 6 
 
 Solution 
 1 
 2 
 3 
 4 
 5 
 6 
 
 TABLE 4. 
 
 Data for Analytical Curve H in Plate I. 
 Concentration of HC1 = .425 M. at 20 C. 
 
 Temperature = 45 C. 
 Barometric Pressure = 758.0 mm. at 21.5 C. 
 
 Molar 
 
 Molar 
 
 
 Molar 
 
 oncentration 
 
 Concentration 
 
 
 Concentration 
 
 of Na 4 P 2 O 7 
 
 at20C. ' 
 
 of Na 2 HPO 4 
 at20'C. 
 
 Voltage 
 E 
 
 of Hydrogen 
 Ion X 10 3 
 
 .125 
 
 .000 
 
 .3080 
 
 67.4 
 
 .100 
 
 .050 
 
 .3137 
 
 54.7 
 
 .075 
 
 .100 
 
 .3211 
 
 41.8 
 
 .050 
 
 .150 
 
 .3278 
 
 32.6 
 
 .025 
 
 .200 
 
 .3322 
 
 27.7 
 
 .000 
 
 .250 
 
 .3379 
 
 22.6 
 
 TABLE 5. 
 
 Data for Analytical Curve A in Plate I. 
 Concentration of HC1 = .350 M. at 20 C. 
 
 Temperature = 45 C. 
 Barometric Pressure 744.0 mm. at 21 C. 
 
 Molar 
 
 Molar 
 
 
 Molar 
 
 oncentration 
 
 Concentration 
 
 
 Concentration 
 
 of Na 4 P 2 O 7 
 
 at20C. 
 
 of Na 2 HPO 4 
 at 20 C. 
 
 Voltage 
 E 
 
 of Hydrogen 
 Ion X 10 3 
 
 .125 
 
 .000 
 
 .3313 
 
 28.7 
 
 .100 
 
 .050 
 
 .3392 
 
 21.6 
 
 .075 
 
 .100 
 
 .3470 
 
 16.4 
 
 .050 
 
 .150 
 
 .3535 
 
 12.8 
 
 .025 
 
 .200 
 
 .3597 
 
 10.0 
 
 .000 
 
 .250 
 
 .3646 
 
 8.5 
 
 TABLE 6. 
 
 Data for Analytical Curve G in Plate II. 
 Concentration of HC1 = .500 M. at 20 C. 
 
 Temperature = 45 C. 
 Barometric Pressure = 764.0. mm. at 20.5 
 
 Molar Molar 
 
 Concentration Concentration 
 of Na 2 HPO 
 at 20 C. 
 
 of Na 4 P 2 7 
 at20C. 
 
 .175 
 .140 
 .105 
 .070 
 .035 
 .000 
 
 .000 
 .070 
 .140 
 .210 
 .280 
 .350 
 
 C. 
 
 Molar 
 
 Concentration 
 Voltage* of Hydrogen 
 Ion X 10 3 
 43.3 
 31.8 
 23.6 
 17.7 
 
 E 
 
 .3201 
 .3285 
 .3367 
 .3445 
 .3509 
 .3565 
 
 14.0 
 11.4 
 
 24 
 
Solution 
 1 
 2 
 3 
 4 
 5 
 6 
 
 Solution 
 1 
 2 
 3 
 4 
 5 
 6 
 
 TABLE 7. 
 
 Data for Analytical Curve F in Plate II. 
 Concentration of HC1 = .425 M. at 20 C. 
 
 Temperature = 45 C. 
 Barometric Pressure = 766.0 mm. at 19.5 C. 
 
 Molar 
 
 Molar 
 
 
 Molar 
 
 Concentration 
 
 Concentration 
 
 
 Concentration 
 
 of Na 4 P 7 
 at20C. 
 
 of Na 2 HP0 4 
 at 20 C. 
 
 Voltage 
 E 
 
 of Hydrogen 
 Ion X 10 3 
 
 .175 
 
 .000 
 
 .3557 
 
 11.80 
 
 .140 
 
 .070 
 
 .3661 
 
 8.06 
 
 .105 
 
 .140 
 
 .3738 
 
 6.08 
 
 .070 
 
 .210 
 
 .3809 
 
 4.58 
 
 .035 
 
 .280 
 
 .3865 
 
 3.82 
 
 .000 
 
 .350 
 
 .3910 
 
 3.24 
 
 TABLE 8. 
 
 Data for Analytical Curve C in Plate II. 
 Concentration of HC1 = .350 M. at 20 C. 
 
 Temperature = 45 C. 
 Barometric Pressure = 759.0 mm. at 19.5 C. 
 
 
 Molar 
 
 Molar 
 
 
 Molar 
 
 
 Concentration 
 
 Concentration 
 
 
 Concentration 
 
 
 of Na 4 P 2 7 
 
 of Na 2 HPO 4 
 
 Voltage 
 
 of Hydrogen 
 
 Solution 
 
 at20C. 
 
 at20C. 
 
 E 
 
 Ion X 10 6 
 
 1 
 
 .175 
 
 .000 
 
 .4961 
 
 69.6 
 
 2 
 
 .140 
 
 .070 
 
 .4966 
 
 61.3 
 
 3 
 
 .105 
 
 .140 
 
 .5038 
 
 52.5 
 
 4 
 
 .070 
 
 .210 
 
 .5086 
 
 44.1 
 
 5 
 
 .035 
 
 .280 
 
 .5149 
 
 35.0 
 
 6 
 
 .000 
 
 .350 
 
 .5235 
 
 25.5 
 
 TABLE 9. 
 
 Data for Analytical Curve E in Plate III. 
 Concentration of HC1 = .500 M. at 20 C. 
 
 Temperature = 45 C. 
 Barometric Pressure = 770.0 mm. at 18 C. 
 
 Molar 
 Concentration 
 
 Molar 
 Concentration 
 
 ofNa.P O ofNaHPO, 
 
 at20C. 
 .225 
 .180 
 .135 
 .090 
 .045 
 .000 
 
 at20C 
 .000 
 .090 
 .180 
 .270 
 .360 
 .450 
 
 Voltage 
 
 E 
 
 .3767 
 .3883 
 .3970 
 .4036 
 .4101 
 .4138 
 
 Molar 
 
 Concentration 
 
 of Hydrogen 
 
 Ion X 10 3 
 
 5.45 
 
 3.58 
 
 2.61 
 
 2.05 
 
 1.61 
 
 1.41 
 
 25 
 
Solution 
 1 
 2 
 3 
 4 
 5 
 6 
 
 TABLE 10. 
 
 Data for Analytical Curve D in Plate III. 
 Concentration of HC1 = .425 M. at 20 C. 
 
 Temperature^ 45 C. 
 Barometric Pressure = 752.0 mm. at 19 C. 
 
 
 Molar 
 
 Molar 
 
 
 Molar 
 
 
 Concentration 
 
 Concentration 
 
 
 Concentration 
 
 
 of Na 4 P O. 
 
 of Na 9 HPO 4 
 
 Voltage 
 
 of Hydrogen 
 
 Solution 
 
 at20C. ' 
 
 at 20 C. 
 
 E 
 
 Ion X 10 6 
 
 1 
 
 .225 
 
 .000 
 
 .5273 
 
 22.2 
 
 2 
 
 .180 
 
 .090 
 
 .5315 
 
 19.1 
 
 3 
 
 .135 
 
 .180 
 
 .5354 
 
 16.5 
 
 4 
 
 .090 
 
 .270 
 
 .5402 
 
 13.9 
 
 5 
 
 .045 
 
 .360 
 
 .5468 
 
 10.9 
 
 6 
 
 .000 
 
 .450 
 
 .5522 
 
 9.0 
 
 TABLE 11. 
 
 Data for Analytical Curve B in Plate III. 
 
 Concentration of HC1 = .350 M. at 20 C. 
 
 Temperature = 45 C. 
 
 rometric Pressure = 762.0 mm 
 
 . at 19 C. 
 
 Molar 
 
 Molar 
 
 
 Molar 
 
 Concentration 
 
 Concentration 
 
 
 Concentration 
 
 of Na 4 P 9 0_ 
 
 of Na 2 HPO 4 
 
 Voltage 
 
 of Hydrogen 
 
 at20C. 
 
 at20C. 
 
 E 
 
 Ion X 10 6 
 
 .225 
 
 .000 
 
 .5742 
 
 4.10 
 
 .180 
 
 .090 
 
 .5775 
 
 3.55 
 
 .135 
 
 .180 
 
 .5818 
 
 3.04 
 
 .090 
 
 .270 
 
 .5857 
 
 2.63 
 
 .045 
 
 .360 
 
 .5887 
 
 2.36 
 
 .000 
 
 .450 
 
 .5903 
 
 2.22 
 
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 36 
 
DISCUSSION 
 Change of Hydrogen Ion Concentration During Hydration. 
 
 By adding acid directly to the normal sodium pyrophos- 
 phate solutions it was possible to obtain any desired concen- 
 tration of hydrogen ion and determine its influence. In order 
 to show this influence the hydration curves of one concentra- 
 tion of normal sodium pyrophosphate in the three different 
 acid concentrations used have been plotted on one plate. All 
 hydration curves are plotted from the results obtained by 
 
 Concentration in Moles per Liter. IDiv.=.07Mole. Na z HP0 4 & Hydrogen Ion 
 
 .00 .07 .14 '.21 .28 35 
 
hydrogen ion concentration measurements except the last two 
 points on curve D in which the hydrogen ion concentration 
 measurements did not agree with the gravimetric determina- 
 tions used. 
 
 On plate IV are plotted the hydration curves of .125 M. 
 normal sodium pyrophosphate in .350 M., .425 M., and .500 M. 
 hydrochloric acid, and on plates V and VI are plotted the 
 hydration curves of .175 M. and .225 M. normal sodium pyro- 
 phosphate respectively in each of the three concentrations of 
 acid. On the same plates are plotted the hydrogen ion con- 
 centration curves for each of the solutions. The hydrogen 
 ion concentrations have been multiplied by values such that 
 they could be plotted on the same concentration scale as the 
 hydration curves, thus showing the relative decrease in hy- 
 drogen ion concentration as the hydration proceeded. From 
 these hydrogen ion concentration curves in the three plates it 
 is seen that in every solution there was a gradual decrease in 
 hydrogen ion concentration as the hydration proceeded, 
 
 30 60 
 
 Time in Days 
 
 90 120 
 
 /Division -30 Days 
 
 38 
 
finally reaching a constant value at completion. The gradual 
 decrease of hydrogen ion concentration as the concentration 
 of orthophosphate gradually increased is accounted for by the 
 less dissociated orthophosphoric acid. 
 
 By referring to the tables of data for the analytical curves 
 it is seen that in the same hydrochloric acid concentration an 
 increase both of pyrophosphate and of orthophosphate causes 
 a decrease in hydrogen ion concentration. So it was possible 
 by the use of three concentrations of pyrophosphate and three 
 concentrations of acid to have nine solutions of different hy- 
 drogen ion concentration and in that way to study the effect 
 of the hydrogen ion concentration on the rate of hydration. 
 
 By a comparison of the hydration curves in the three 
 plates, and of the data for these curves given in the tables for 
 the different solutions it may be seen that the times required 
 for equilibrium within experimental error for .125 M. Na 4 P 2 O 7 
 solution with .500 M., .425 M., and .350 M. HC1 were respec- 
 tively 250 hours, 702 hours, and 1,302 hours; for a .175 M. 
 Na 4 P,O 7 solution with .500 M., .425 M., and .350 M. HC1 the 
 times for equilibrium were 1,160 hours, 1,493 hours and 2,386 
 hours respectively ; and for a .225 M. Na 4 P 2 O 7 solution with 
 .500 M. and .425 M. HC1 the times for equilibrium were 1,688 
 hours and 2,719 hours respectively ; and for .225 M. Na 4 P 2 O 7 
 solution with .350 M. HC1, 2,766 hours were required for 
 81% hydration. If it continued at the rate at which it was 
 going over the last 20 per cent., it would require at a mini- 
 mum three months longer for completion. 
 
 From a comparison of the hydrogen ion concentrations 
 in these solutions it is observed that the solutions of highest 
 initial hydrogen ion concentration required the least time 
 for equilibrium, the time increasing as the initial hydrogen 
 ion concentration decreased. This was also shown in the 
 hydration of sodium monometaphosphate 8 . These times 
 show the great influence that hydrogen ion has upon this 
 hydration. 
 
 Effect of Concentration of Pyrophosphate on the Rate of 
 Hydration. 
 
 Abbott 9 from his investigation of the hydration of pyro- 
 phosphoric acid calculated the rate of hydration (1) "on the 
 
 39 
 
assumption that the rate of hydration is proportional both 
 to the hydrogen ion concentration and to that of the pyro- 
 phosphoric acid undergoing hydration," and (2) "on the 
 assumption that the rate is independent of the hydrogen ion 
 concentration and is determined only by the concentration of 
 the pyrophosphoric acid." The constants calculated on the 
 second assumption were more nearly constant and he con- 
 cludes from that, that the rate of hydration is approximately 
 proportional to the! concentration of pyrophosphoric acid 
 present and that it increases with the concentration of 
 hydrogen ion. 
 
 To see if the reaction studied in this investigation was of 
 the first order and if constants calculated for a first order 
 reaction would be of value in studying it, they have been 
 calculated from the first determination for each solution 
 
 1 C x t 
 
 hydrated according to the formula K= log where 
 
 t x - tl C-x 
 
 C is the original concentration of pyrophosphate and x the 
 amount changed to orthophosphate in time t. This assumes 
 then that the rate of hydration is a direct function of the 
 concentration of pyrophosphate. These constants are given 
 in the tables of data for each solution ; they show a pro- 
 gressive decrease as the hydrogen ion concentration shows 
 a progressive decrease from the solutions which have the low- 
 est concentration of pyrophosphate and highest concentra- 
 tion of hydrogen ion down to the solutions having the high- 
 est concentration of pyrophosphate and lowest concentration 
 of hydrogen ion, both in the individual solutions and among 
 the solutions except in solutions C and D where they ap- 
 proach more nearly a constant value. 
 
 From this decrease in the constants it is evident that the 
 rate of hydration of normal sodium pyrophosphate in the 
 presence of hydrogen ion is not a direct function of the pyro- 
 phosphate concentration alone. It is increased by the hy- 
 drogen ion present and as the hydrogen ion concentration 
 decreases the rate decreases. 
 
 In Table 23 for solution C 2 in which the ratio of pyro- 
 phosphate to hydrochloric acid is 1 mole to 2 moles, the con- 
 
 40 
 
stants do not decrease regularly but tend to approach a con- 
 stant. The mean value of these constants has been calcu- 
 lated and is given in the table. This mean neglects point 
 four which is probably in error as shown by the hydration 
 curve, and also the first and last values which are less ac- 
 curate in most of the tables. In the last column of that table 
 are the percentages of deviation of each of the constants 
 from the mean. In this column it is shown that eight and 
 four-tenths per cent, is the greatest deviation from the mean 
 while most of. the values are within four to five per cent. 
 Constants were calculated for some of the value by using a 
 value for the percentage hydrated at time t two per cent, 
 greater than that determined and given in the table. It was 
 found that this change of two per cent, caused an increase 
 in the value of the constant from five to ten per cent., de- 
 pending on what part of the curve the value was selected. 
 
 While it may seem that values for the constants in solu- 
 tion C 2 are tending to approach a constant within experi- 
 mental error, they are, however, still tending to show a very 
 small decrease. It does not seem then that the rate of hydra- 
 tion in this solution can be said to be directly proportional 
 to the pyrophosphate concentration but to approach it very 
 closely. 
 
 In Table 26 for solution D where the ratio of pyrophos- 
 phate to acid is 1 mole to 1.888 moles, the constants are also 
 quite constant. The mean value and percentage deviations 
 from it have been calculated and are given in the table as 
 described above for solution C. The error caused by two 
 per cent, change in percentages hydrated is from five to 
 ten per cent, in this solution as in solution C. It is seen that 
 in this solution the constants are also tending to approach a 
 constant value within experimental error but as in solution 
 C the constants are tending to show a small decrease so that 
 the rate of hydration in this solution also is not quite a di- 
 rect function of the pyrophosphate concentration alone but 
 is approaching it. 
 
 Since the constants for solutions C and D where the ratio 
 of pyrophosphate to acid is about 1 mole to 2 moles are very 
 nearly constant 1 and in all other solutions the constants show 
 
 41 
 
a gradual decrease, it seems that two influences must be 
 active in this hydration. Any discussion of the mechanism 
 of the reaction is necessarily limited by the lack of the ioni- 
 zation constants of pyrophosphoric and orthophosphoric 
 acids at this temperature and by the lack of a method for 
 determining the concentration of any of the respective pyro 
 and orthophosphate ions. The results show that hydrogen 
 ion has a marked influence on the rate of hydration and as 
 the concentration of hydrogen ion decreases the rate also de- 
 creases. Therefore if the hydrogen ion was the only factor 
 in this hydration, the constants as calculated should show a 
 progressive decrease as the hydrogen ion concentration 
 shows a progressive decrease. Since the constants do not 
 show this decrease in solutions C and D, some influence must 
 be at work in the reaction to balance the decreasing influence 
 of the hydrogen ion. 
 
 In this investigation where the concentration of hydro- 
 gen ion was not sufficient in most of the solutions to form 
 very much pyrophosphoric acid it seems that the active com- 
 ponent undergoing hydration must be one of the ionic prod- 
 ucts of pyrophosphoric acid, as the pyrophosphoric acid 
 would decrease as the hydrogen ion concentration decreased. 
 If, then, the active component undergoing hydration is one 
 of the ions, the rate of hydration would therefore depend 
 in part on the concentration of that ion. It then follows that 
 hydrogen ion should show a slight negative influence on this 
 hydration due to repression of the active ion. The negative 
 influence of hydrogen ion must be very slight compared to 
 the positive influence because the results show the higher the 
 concentration of hydrogen ion the greater is the rate of hy- 
 dration. It seems not impossible, however, that an initial 
 concentration of hydrogen ion and of pyrophosphate might 
 be obtained in which the removal of a very small amount of 
 hydrogen ion would result in the* formation of a much larger 
 corcentration of this active ion undergoing the hydration and 
 therefore as the influence of the hydrogen ion on the hydra- 
 tion decreased the effect of the active ion would increase and 
 the two balance each other. This seems to be the case in solu- 
 
 42 
 
tions D and C where the constants obtained for a firaj^prder 
 reaction show a very slight decrease in their values. 
 
 The curves obtained by plotting molar concentration of 
 pyrophosphate against molar concentration of hydrogen ion 
 are straight lines or very nearly so for solutions C, D, and I. 
 Therefore the hydrogen ion concentration in these solutions 
 is apparently directly proportional to the pyrophosphate con- 
 centration as the hydration proceeds. Similar curves for the 
 other solutions are not straight lines but show decreasing 
 slopes as the pyrophosphate concentration decreases. Since 
 the orthophosphoric acid ions H 2 PO 4 ~ and HPO 4 ~ are much 
 less dissociated than the respective pyrophosphoric acid ions 
 H 2 P 2 O 7 ~ and HP 2 O 7 ~, it follows that in order for the pyro- 
 phosphate concentration to show a constant ratio to the hy- 
 drogen ion concentration that the pyro phosphoric acid ions 
 must maintain a sufficient concentration of hydrogen ion 
 through dissociation to keep the ratio constant, as the hydro- 
 gen ion concentration is being decreased in forming the less 
 dissociated orthophosphoric acid ions. Therefore the rate of 
 dissociation of the pyrophosphoric acid ions must continu- 
 ally increase as the orthophosphate is formed. 
 
 If as postulated the active principle undergoing hydration 
 is one of the ions of pyrophosphoric acid it is evident then 
 that its^ positive influence would increase as the hydration 
 proceeded and this influence might approach a value sufficient 
 to counterbalance the decreasing influence of hydrogen ion 
 upon the hydration and therefore give a constant value for the 
 constants as calculated for a first order reaction. From the 
 greater influence which hydrogen ion has upon the reaction, 
 its decrease could only be counterbalanced by the positive 
 influence of pyrophosphate concentrations in solutions in 
 which the initial hydrogen ion concentration was relatively 
 small as in solution D where it was 22.1 X 10" 6 moles per liter 
 and in solution C where it was 69.4 X 1O 6 moles per liter. 
 Whereas in solution I where the initial hydrogen ion concen- 
 tration was 13.4 X 10- 2 moles per liter and the ratio of acid 
 was four moles to one mole of pyrophosphate, the curve is a 
 straight line but the the constants show a progressive de- 
 crease. This seems to point to the conclusion that one of the 
 
 43 
 
lower acid ions of pyrophosphoric acid or the pyrophosphate 
 ion is the active component undergoing hydration and that 
 the influence of its concentration is very small compared to 
 the influence of hydrogen ion. It appears, therefore, that in 
 the higher concentrations of hydrogen ion the formation of 
 the active ion undergoing hydration is not sufficient to coun- 
 terbalance the decreasing influence of the hydrogen ion con- 
 centration and accordingly the constants calculated show a 
 progressive decrease. 
 
 In solution B, however, the ratio of acid to pyrophosphate 
 was 1.555 moles to 1 mole and the initial hydrogen ion con- 
 centration was 4.1 X 10~ 8 moles per liter. So the influence of 
 the hydrogen ion upon the repression of the active ion is less 
 at the start than in solutions C and D. Therefore as the hy- 
 drogen ion concentration decreases and its influence decreases 
 it ib not balanced by the formation of an appreciably greater 
 concentration of the active ion. Accordingly in this solution 
 the constants show a progressive decrease. 
 
 In the foregoing discussion of the hydration in solutions 
 C, D, and I, it was pointed out that the concentration of hy- 
 drogen ion was directly proportional to the pyrophosphate 
 concentration. Therefore it. is possible to express the con- 
 centration of hydrogen ion in terms of pyrophosphate concen- 
 tration. By doing this and by assuming that the rate of 
 hydration is a direct function of both the pyrophosphate con- 
 centration and the hydrogen ion concentration it is possible 
 to formulate an expression which would give the influence of 
 the changing hydrogen ion concentration at any instant in the 
 hydration. 
 
 With this assumption the following development is made : 
 
 dx 
 
 = K 1 (c-x)C H . 
 dt 
 
 c = molar concentration of pyrophosphate. 
 x = amount of pyrophosphate changed in any time t. 
 C H +=a(c x)+K 2 
 
 a = the slope of the line. 
 
 K 2 = hydrogen ion concentration at complete hydration. 
 This equation represents the concentration of hy- 
 drogen ion at any time t. 
 
 44 
 
.-.--=K 1 (c-x)(a(c-x)+K 2 ) 
 
 The integration of the above expression between the limits 
 t x and t x gives the following formula : 
 
 1 (K 4 -X)(c- Xl ) 
 
 K, = log 
 
 (ti-OK, (c-xXK.-XJ 
 
 K 
 4 ~ 
 
 a 
 
 Using this formula constants have been calculated for 
 solutions Ij, C 2 , and D x . They are given in the last column 
 of Tables 12, 23, and 26 respectively. 
 
 In Solution I the concentration of pyrophosphate was 
 .125 M. and the concentration of hydrochloric acid was .500 
 M. The change of hydrogen ion concentration was from 
 13.35 X 10- 2 to 6.10 X 10- 2 moles per liter. The constants cal- 
 culated by this formula show a slight tendency to decrease as 
 they do when calculated on the assumption that the rate of 
 hydration is directly proportional to the pyrophosphate con- 
 centration alone. 
 
 In solution C 2 the constants show a progressive increase. 
 In this solution the concentration of pyrophosphate was .175 
 M. and the hydrochloric acid was .350 M. The change of 
 hydrogen ion concentration was from 69.4 XlO~ 6 to 27.3 X 10~ 6 
 moles per liter. 
 
 In solution D x the constants decrease to a minimum and 
 then increase to their former values. In this solution the con- 
 centration of pyrophosphate was .225 M. and the concentra- 
 tion of hydrochloric acid was .425 M. The change of hydro- 
 gen ion concentration was from 22.3 X 10- to 10.0 X 1Q- 6 
 moles per liter. 
 
 In solution I x the concentration of pyrophosphate was low 
 and the hydrogen ion concentration was high. In solution 
 D! the pyrophosphate concentration was high and the hydro- 
 gen ion concentration was low. In solution C 2 the pyrophos- 
 phate concentration was between that of solutions I 2 and D lf 
 and the hydrogen ion concentration was a little greater than 
 that of D!. The constants for solution I by both formulas 
 
 45 
 
show about the same decrease. In solutions C 2 and D a by the 
 first formula the constants approach quite closely a constant 
 value. By the second formula in solution C 2 they show a pro- 
 gressive increase. In solution D l they pass through a 
 minimum. 
 
 From this study then the results seem to point to the con- 
 clusion that one of the ionic products of pyrophosphoric acid, 
 possibly the pyrophosphate ion, is the active component un- 
 dergoing hydration and that hydrogen ion shows a slight 
 negative influence due to the repression of this active compo- 
 nent but this negative influence is only very slight compared 
 to the positive influence shown by the hydrogen ion. There- 
 fore, the rate of hydration of sodium pyrophosphate is not a 
 direct function of the pyrophosphate concentration nor of the 
 hydrogen ion concentration, due to the three influences that 
 hydrogen ion must have in the hydration ; first of repres- 
 sion of the pyrophosphoric acid ionization, second of re- 
 pression of the orthophosphoric acid ionization, and third, 
 and by far the greatest, that of increasing the rate of the 
 hydration. 
 
 The curves appearing in this article were prepared from 
 tracing made by Mr. S. J. Ballard, draftsman, of the Depart- 
 ment of Chemical Engineering. 
 
 SUMMARY 
 
 I. Three concentrations of Normal Sodium Pyrophos- 
 phate each in three different concentrations of hydrochloric 
 acid, making nine solutions of different hydrogen ion concen- 
 tration were studied. 
 
 II. By use of analytical curves obtained by making up 
 synthetic solutions and plotting molar concentration of hy- 
 drogen ion against molar concentration of di-sodium ortho- 
 phosphate, each hydration was followed to completion by 
 hydrogen ion concentration measurements. 
 
 III. The last fifty per cent, of each hydration was checked 
 by the standard gravimetric method. The separation of 
 
 46 
 
ortho- and pyrophosphate was made by use of a magnesium 
 chloride mixture. 
 
 IV. The hydrogen ion concentration in each solution 
 decreased progressively with time reaching a final constant 
 value. 
 
 V. The times required for equilibrium within experi- 
 mental error for a .125 M. Na 4 P 2 O 7 solution with .500 M., 
 .425 M., and .350 M. HC1 were 250 hours, 702 hours, and 1,302 
 hours respectively; for a .175 M. Na 4 P.,O 7 solution with .500 
 M., .425 M., and .350 M. HC1 the times for equilibrium were 
 1,160 hours, 1,493 hours ,and 2,386 hours respectively; and 
 for a .225 M. Na 4 P,O 7 solution with .500 M. and .425 M. HC1 
 the times for equilibrium] were 1,688 hours and 2,719 hours 
 respectively. 2,766 hours were required for 81% hydration 
 of a .225 M Na.P.O, solution with .350 M. HC1. It would 
 require at a minimum three months longer for completion if it 
 continued at the same rate as it was going over the last twenty 
 per cent. 
 
 VI. The influence of hydrogen ion cannot be accounted 
 for by its effect upon the ionic equilibrium of the pyrophos- 
 phoric and orthophosphoric acid alone. 
 
 47 
 
REFERENCES 
 
 1 Graham, Phil, Trans., 123, 53, 1833. 
 
 2 Sabatier, Compt. Rendu., 106, 63, 1888. 
 
 8 Montemartini and Egid, Gass. Ital. Chim., 31 I, 394, 1901. 
 
 4 Balarefr, Zeit. Anorg. Chem., 67, 234, 1909; 68, 288, 1901; 
 96, 103, 1916. 
 
 5 Berthelot and Andre, Compt. Rendu., 123, 776, 1896; 124, 
 265, 1897; 124,261, 1897. 
 
 c Giran, J. Russ. Chem. Soc., 30, 99. 
 
 7 Holt and Meyers, J. C. S. Trans., 99, 385, 1911. 
 
 8 Beans and Kiehl, Unpublished work. (Submitted as Disser- 
 
 tation by Kiehl, 1921). 
 
 9 Abbott, J. A. C. S., 31, 763, 1909. 
 
 10 Fales and Vosburg, J. A. C. S., 40, 1291, 1918. 
 
 11 Ellis, J. A. C. S., 38, 737, 1916. 
 12 Hulett, Zeit, Physik. Chem., 33, 611, 1920. 
 18 Fales and Mudge, J. A. C. S., 42, 2434, 1920. 
 14 Arnold and Werner, Chem. Zeit., 29, 1905. 
 
VITA 
 
 Waldemar C. Hansen was born in Meade County, South 
 Dakota, February 9, 1896. He was graduated from Montana 
 State College in June, 1917. He served from October, 1917 
 to March, 1919, with The First Gas Regiment United States 
 Army, A. E. F. During the summer of 1919 he was Food 
 and Drug Inspector for the Montana State Board of Health, 
 Helena, Montana. He was a graduate student and an assist- 
 ant in the Department of Chemistry of the State University 
 of Iowa ,Iowa City, Iowa, during the year 1919-20 and sum- 
 mer of 1920. He was a graduate student in the Department 
 of Chemistry of Columbia University during the years 
 1920-21, 1921-22, and summer of 1921. He was a laboratory 
 assistant during the years 1920-21 and 1921-22, and an as- 
 sistant in the Department of Chemistry in Columbia Univer- 
 sity from February 1 to July 1, 1922. 
 
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