EXCHANGE The Adsorption of Sulfur Dioxide by the Gel of Silicic Acid A DISSERTATION SUBMITTED TO THE BOARD OF UNIVERSITY STUDIES OF THE JOHNS HOPKINS UNIVERSITY IN PARTIAL 'FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY BY JOHN McGAVACK, JR. BALTIMORE, MD. February, 1920 EASTON, PA.:. ESCHENBACH PRINTING COMPANY 1920 The Adsorption of Sulfur Dioxide by the Gel of Silicic Acid A DISSERTATION SUBMITTED TO THE BOARD OF UNIVERSITY STUDIES OF THE JOHNS HOPKINS UNIVERSITY IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY BY JOHN McGAVACK, JR. BALTIMORE, MD. February, 1920 EASTON, PA.: ESCHENBACH PRINTING COMPANY 1920 CONTENTS. Pa & e. Introduction 5 Apparatus 7 Fig. 1 7 Materials 9 Procedure , 12 Fig. 2 12 Fig. 3 : 13 Experimental 13 Water Content and Adsorption 17 Fig. 4 18 Adsorption Reversible 20 Fig. 5 22 Fig. 6 ; 24 Fig. 7 25 Discussion 26 Fig. 8 32 Fig. 9 33 Fig. 10 , 36 Summary 37 46200i: ACKNOWLEDGMENT. This investigation was carried out under the advice and with the as- sistance of Professor Patrick. I wish to take this opportunity to express to him my sincere appreciation of the help which he gave. I also feel under obligation to Professors Frazer, Lovelace, Reid and Gilpin and to Dr. Thornton for instruction and encouragement received from them. I also wish to take this opportunity to thank Mr. W. T. Levitt for his aid in the construction of the apparatus used. The Adsorption of Sulfur Dioxide by the Gel of Silicic Acid. Introduction. Many investigations of the adsorption of vapors by porous bodies have been made without a satisfactory explanation of the phenomenon being found. The fact that the adsorbing material is not chemically definite but has adsorbent properties dependent upon its method of prepara- tion is not the least of the reasons for apparent lack of agreement both in experimental results and theoretical conclusions. Again, the possibility, and in many cases, the great probability of chemical reaction occurring during the process bring in another factor which is hard to control. In the investigations carried on in this laboratory during the war it was found necessary to test many types of adsorbents, both as to their specific action against poisonous war gases as well as to their suscepti- bility towards other vapors and gases. It was realized in the beginning that porous bodies mere mechanical condensers so to speak were going to play an important part. Charcoal was brought into use and its protective ability greatly increased by improved methods of prepara- tion. This laboratory focused a good part of its attention upon colloidal substances and gels. The gel of silicic acid, having been previously shown to possess adsorptive properties, received first attention. The main difficulty was its large scale preparation. Up to this time the method of dialysis, a long and tedious process had been used. This difficulty was overcome and a quick and simple method, of which more will be said later, was developed. A product of high adsorptive power resulted. This gel is a hard, translucent, porous solid, chemically inert and with proper precautions can be reproduced with definite exactness. Hence it is an ideal substance by which the 2 objectionable features mentioned above might be eliminated. It is true that it always contains a certain amount of water, either combined or adsorbed, but this factor may be kept constant and thus will not interfere with the more important in- vestigation. Thomas Graham 1 gives the first account of the preparation of silicic acid gel and the fact that it possesses a power of adsorption has been known since that time. Nevertheless, it was not until 25 years later, when van Bemmelen 2 commenced his lengthy and important experiments, that this property was investigated more thoroughly. This author made an exhaustive study of the hydration and dehydration of the gel in all cases, showing that these two curves did not follow the same path. This hysteresis will be taken up further on in the paper. Zsigmondy 3 became interested in this substance and has published several articles on its structure, data for which were obtained chiefly from ultramicroscopic investigations. Anderson, 4 working in Zsigmondy's laboratory, studied the systems, gel-water, gel-alcohol, gel-benzene. That is, he determined the equi- librium weight of each substance adsorbed per gram of gel at points corre- sponding to different pressures of the material adsorbed. Like that of van Bemmelen, the curve obtained by emptying the pores did not coin- cide with that observed when they were being filled, although the differ- ence between the 2 paths was by no means as great as in the earlier work. It may also be mentioned that while van Bemmelen worked entirely under normal atmospheric pressure Anderson, on the other hand, did his work under a vacuum produced by the means of a high grade oil pump. Patrick 5 was the first investigator of gas adsorption by this substance. He measured the amount of carbon dioxide, sulfur dioxide and ammonia adsorbed by this gel at different pressures for a number of different tem- peratures. He did not attempt to study the reverse adsorption path, nor did he use samples of the material containing different water content. 1 T. Graham, Phil. Trans., 151, 183-224 (1861); also Ann., 121, 1-77 (1862); Proc. Roy. Soc., 1864. 2 J. M. van Bemmelen, Z. anorg. Chem., 13, 233-356 (1896); "Die Adsorption,' 1 p. 196 (1910). 3 Zsigmondy, Z. anorg. Chem., 71, 356 (1911). 4 Anderson, "Inaugural Dissertation," Gottingen, 1914. B W. A. Patrick, "Inaugural Dissertation," Goettingen, 1914. See also Koll. Z., 13-14. The purpose of the present work may now be stated more clearly: to investigate the effect of different water content of the gel upon its ad- sorptive powers; to obtain measurements where temperature control and complete exhaustion could be more rigidly maintained than hereto- fore; and by using an inert body to interpret, if possible, the mechanism by which this phenomenon adsorption occurs. Apparatus. The apparatus used in these measurements is shown in Fig. i. In general outline it is similar to that used by Homfray 1 in her work on char- coal and later by Patrick, in the original investigation of gas adsorption by silica gel. The essential parts are the gas container A, the gas buret B, the adsorption bulb C and the manometer D. These parts were all sealed together and mounted inside of a constant temperature bath about which more will be said later. The gas container was a steel cylinder filled with liquid sulfur dioxide, the outlet of which was controlled by a sensitive valve. This was connected to the gas buret by means of drying tubes a and a', containing calcium chloride and phosphorus pentoxide, respec- tively, and the 3 -way mercury stopcock b. In order to fill the buret the stopcock b was opened to the adsorption apparatus and the mercury bulb c raised until all the air was forced out of the buret. The cock was then opened to the gas container and the mercury well c was lowered. 1 Z. pJiys. Chem., 74, 129 (1910). 8 Opening the cock b to the adsorption part of the mercury was again raised. This operation, repeated several times, removed a larger part of the air. To remove the last traces of air the bulb was lowered just so the mercury stood at the level d in the buret. The cock b was then opened to the gas container A and sulfur dioxide was allowed to sweep out the whole system for a considerable period of time. The exit tube from b was also swept out in a similar manner. The gas buret B consisted of a graduated pipet connected by a U- joint to another tube, e, of the same bore, which served as an open manometer. This buret was recalibrated, mercury being used and the operation being carried out in a 30 constant temperature bath. As with most gases, all gas volumes were measured at this temperature, and if the temperature difference was less than 10, no correction for glass expansion was deemed necessary. To determine the amount of gas introduced, the mercury in the two arms of the buret was leveled, this balance being adjusted by means of a very sensitive gear arrangement which enabled the reservoir C to be raised or lowered a small fraction of a millimeter, the correct posi- tion being ascertained by means of the cathetometer telescope. The reading of the cathetometer vernier, calibrated directly into o.oi mm. divisions, was then taken. In like manner another reading was made after the gas introduction. By reference to the calibration curve these readings were transferred into cc. and were then corrected to standard conditions, 760 mm. and o. As the height of one mm. was equivalent to 0.19 cc. and as duplicate settings of the cathetometer could be made within 0.03 mm. the maximum error in reading gas volumes was 0.005 cc. As the adsorption proved to be considerable the cc. readings are given only to the second decimal place. The gas buret was connected by a glass tube of small bore to the 3-way stopcock g, which in turn led to the expansion bulb h. This part of the apparatus had a capacity of approximately 100 cc. and served as a pre- caution against too hasty introduction of the gas. The adsorption container C was connected to the expansion bulb by glass tubing and a ground glass joint protected by a mercury seal. The volume of this bulb together with that part of the connecting tube above the mark was obtained by introducing a known volume of dry air and measuring the pressure developed. Measurements with different volumes showed close agreement and a mean of these values was used for calcu- lation purposes. The manometer needs no special mention except that it was found de- sirable to have its bore identical with the bore at I. In the apparatus first used this was not the case and a constant correction for capillary depression was necessitated. Pressure readings were also made with the cathetom- eter and hence all such readings are accurate to within 0.03 mm. The mercury well controlling the manometer was worked by a sensitive ratchet. In order to study the curve formed while the pores were being emptied the bulb m was added by means of the ground glass joint o. This served as a holder for granulated soda lime which was introduced through the mercury-sealed ground glass joint p. The stopcock q maintained a vacuum in this vessel when removed from the apparatus for the purpose of weigh- ing. The electric furnace r, previously calibrated, was used to heat the gel to the required temperature during evacuation. The whole apparatus was enclosed in a completely water-jacketed air bath. Three gas burners under the bottom furnished rough heating ad- justment, while a system of 8 carbon lamps, inserted in different sections of the water compartments and controlled by relays and a sensitive toluene-mercury regulator, procured very close temperature control. This bath was used by Morse and his co-workers in their measurement of osmotic pressure at high temperatures and hence is described elsewhere 1 in the literature. Suffice it to say that by means of this bath the tempera- ture was maintained constant for any length of time with a maximum fluctuation of less than 0.05. In all of the work a vacuum was maintained by using in series a rotary oil pump and a Gaede high-vacuum mercury pump, both manufactured by E. Leybold. A MacLeod gage, K, served to determine when evacua- tion was complete, such being considered the case when the mercury threads in the gage became level. Materials. All the mercury used in this investigation, that for traps, buret, manom- eter and gage, was thoroughly cleaned and purified. This was accom- plished by first allowing it, in a state of very fine subdivision, to fall through 2.4 meters of dil. nitric acid for 5 or 6 times, washing with distilled water, then caustic soda, and finally with distilled water. After drying it was redistilled in vacua. The rubber tubing used to connect the mercury wells to the remaining part of the apparatus was soaked for 24 hours in dil. sodium hydroxide solution in order to remove sulfur present. This precaution prevented premature fouling of the mercury. The sulfur dioxide used was that found in the trade and was taken di- rectly from its metal cylinder a method recommended by Travers in his careful work on purification of gases. Of course its purity was first tested. This was done by immersing a 100 cc. inverted buret filled with sodium hydroxide in a sodium hydroxide solution. The buret was now filled with sulfur dioxide from the cylinder, and after a short time was completely absorbed without the appearance of any gas bubble at the top 1 Am. Chem. J., 48, 29 (1912). IO of the buret. Several experiments were also made from a sample obtained from the same cylinder which had been redistilled. No different results were observed. A further check on the purity of this substance was ob- tained from vapor-pressure measurements. No change in pressure being noticed, no matter how large a voume of gas was introduced. Hence the possibility of presence of oxygen, nitrogen and carbon dioxide, the most likely impurities, was eliminated. All of the gel used in this investigation was made by the Davis, Patrick and McGavack 1 process. In general this consists in allowing an acid solu- tion and a solution of sodium silicate, both solutions being kept at the proper concentration, to mix under violent agitation. The hydrosol "sets" in i to 1 8 hours, depending upon the temperature and concentra- tion of the solution. When the desired state of firmness is reached the material was washed with city water, the washing being continued until no trace of electrolyte could be detected in the wash water. The material was then dried at 110 in vacuo until the water content was reduced to 7 or 8%. By this method a large amount of material was prepared. The best grade of sodium silicate solution (water glass) furnished by the Philadelphia Quartz Company was used. c. p. hydrochloric was the acid used. In order to remove dust particles and possible metal impurities the gel was subjected to still more drastic treatment. This was accomplished by saturating it with nitric acid fumes and refluxing with c. P. cone, nitric acid for 12 hours. The material was then washed thoroughly by de- cantation from distilled water over a period of 4 days. This part of the operation cannot be hurried or accelerated by increasing the amount of water as the rate of diffusion from the pores of the gel is very slow. The material was then dried in an air bath at 110. As even at 110 a large amount of water (16-24%) still remained in the gel, and as uniform samples of different water content were desired, some arbitrary process had to be employed to standardize the water con- tent. This was accomplished by heating a mass of gel for different periods of time under a vacuum at different temperatures For instance, Sample c was prepared by heating for one hour at 100-120 and for 3 hours at 300. Sample d was heated for one hour at 100-120, one hour at 300, and finally 2 hours at 500 a vacuum of i to 5 mm. being maintained in each case during the whole time. This treatment was rigidly held to in the preparation of all samples. The samples were then put in glass- stoppered bottles and these in a sulfuric acid desiccator. All water determinations were made by heating the gel in a platinum crucible with a blast lamp. This method was applicable, as water was 1 Reports submitted to the Chemical Warfare Service, a resume of which will be published in the near future. II the only volatile component. The usual method for obtaining the den- sity of an insoluble (in water) solid was employed, especial care being used to see that all adsorbed air bubbles were removed. Table I gives the ex- perimental results. TABLE I. WATER CONTENT AND DENSITY OF DIFFERENT SAMPLES. Sample c. d. g. f. Water, %. Density. Water, %. Density. Water, % . Density. Water, %. Density. 4-79 2 . 1693 3-53 2.244 2.36 2.2 5 " 7.92 2.123" 4.82 2.1604 3-49 2.236 2.26 > . . 8.03 4.90 .... .... . . . .... .... 8.07 Mean : 4.87 2.1648 3 51 2.240 2.31 . , . . 8.OI . . . Calculated from values obtained from c and d. Isotherms were made at 80, 54, 34-4, 33 4, o, 30, 40, 57, 80 and 100. For +30 and +40 the constant temperature both surrounding the apparatus was used. Solid carbon dioxide contained in a Dewar bulb served for 80. Liquid ammonia also contained in a Dewar bulb and with an arrangement for variable pressure served for the other low temperatures. The freezing and boiling points of water were used for o and 100, respectively. The vapor of boiling acetone and ben- zene gave the points 57 and 80. In no case was the adsorption bulb allowed to dip in the boiling liquid itself but was completely bathed with its vapor. The flask containing this liquid fitted tightly at the top around the adsorption bulb and had openings for a thermometer and also a long glass condenser which avoided the necessity of continually adding liquid. In all cases the remaining part of the apparatus was kept at a constant temperature by means of the constant temperature bath. The actual temperature points of the 2 low degree experiments were fixed by the aid of the vapor-pressure measurements made on sulfur di- oxide by Steele and Bagster. 1 These investigators furnish the only meas- urements of this constant at low temperatures ( 73 to 36) and when the logarithms of these pressures are plotted against the absolute tem- perature a fairly straight line results. In the other low temperature runs (Expts. XXVIII and XXIX) a xylene thermometer, cali- brated recently (1919) by the U. S. Bureau of Standards, was used. The corrected readings on this thermometer were 33-4 for Expt. XXVIII and 34.4 for Expt. XXIX. The vapor pressures ob- served in these runs correspond to temperatures 37.8 and 38.8 with reference to the Steele and Bagster results. Regnault, 2 Pictet 2 and Sajot, 2 however, have measured the vapor pressure of sulfur dioxide from 30 to -j-ioo. Their results are in good agreement with each other and it is interesting to note that the logarithmic curve plotted 1 Steele and Bagster, J. Chem. Soc., [2] 97, 2613 (1910). 2 Results tabulated in Landolt-BSrastein "Tabellen." 12 from them when extended fixes the temperatures in question at 34 and 35, respectively, values which seem to be the true ones. Procedure. The gel was weighed directly into the adsorption bulb which was then attached to the apparatus. The furnace was put in position and heating and evacuation were commenced at the same time. The temperature and length of heating were governed primarily by a consideration of the water content of the gel. A temperature higher than that used in the preparation of the gel was never employed this was done so as not to change the amount of water present. The evacuation was continued until the Mac- Leod gage indicated no pressure. The adsorption bulb was then allowed to come to the tempera- ture desired and the first intro- duction of gas was made. Amounts of gas such that points might be obtained at 2, 5, 10, 20, 30, 50, 60 and 70 cm. were introduced. After introduction, the mercury level was brought to point / (see Fig. i), and by reading this height and also that on the manometer itself, the point where equilibrium was reached could be ascertained easily. The difference between these 2 readings gave the pressure of the system. In the same manner another quantity of gas was introduced and its equilibrium pressure measured. This was continued until atmos- pheric pressure was reached. For points on the reverse curves the following method was used. The bulb m was partially filled with soda lime granules, Stopcock q opened and the whole system thoroughly evacuated. After removing and weigh- ing, the bulb was again attached and the system thoroughly evacuated. The mercury controlling the MacLeod gage was now raised to a point sufficient to cut off its large bulb. Then lowering the mercury in the ex- pansion chamber, h, the stopcocks g and q were opened and gas was given off from the gel. When sufficient had escaped the cock g was closed and the mercury in h raised to /. The pressure gage showed almost instant adsorption by the soda lime, but to avoid any error q was left open for an hour in order not to miss the last traces of the gas. It was then closed and 760 and the bulb removed and weighed. The same process was repeated for every point desired. Of course pressure readings were made for every point determined. All pressure readings were corrected to o all gas volumes to mm. and o. The vol- ume of the gas above the gel was calculated each time and subtracted from the amount intro- duced. Knowing the volume of the bulb C to the mark /, also the tem- perature and pressure, this value was easily cal- culated from the gas laws. When the bulb and the remaining part of the apparatus were at different temperatures the volume and tern- . -O --O J^ X* ^ ^ x> " ^>- D Jf ^^ I ^ f /cr x c ^ * ^ *3> ^fl X r^*^ ^ ^ x^ X ,O J x ^ x^ J$ ^ ^ ^cr x^ >0 "0- -,** X \ ^x x^ X k ^x ? ^ ^ ^ X * I X X X /J y , ^ X x ^ , X , X X X ^ X ^x" ? X X ' X X \ x X ^ X X X X s # X x x " ^y X X t X x ^ X. X ,x "Q 3. -S p perature of each part were considered in the calculation. Experimental. The results for Sample c of the gel are given below. show these facts graphically. Figs. 2 and 3 Expt. XII. 2.4256 p. 105.88 229.93 397.00 544.20 671.50 V . 18.24 33.94 51.32 64.57 73.65 Vi. 2.18 4-74 8.19 11.23 13-85 X. 16.06 29.20 43-13 53-34 59-80 100 . a 1.125. i / = 0.745. X/M. log P. log X/M. X/M calc. 6.62 .02478 0.82086 6.50 12.04 36159 I . 08063 11.62 17.78 59879 1.24993 17-43 21.99 73576 1.34223 22.08 24.65 .82705 I.39I82 25.83 2.6000 g. (c). 47.00 192.19 224.73 407 . 88 575-32 671.95 12.66 47.60 53-30 80.73 101 .09 111.56 Fi. i .00 4.09 4.78 8.70 12 .24 14.29 Expt. XIX. 80. X/M. 4.48 16.73 18.66 27.70 34-17 37-41 X. 11.66 43-57 48.52 72.03 88.85 97-27 a 2.239. log P. 0.67210 28373 .35166 .61053 75991 .82733 1/11=0.662. log X/M. 0.65128 22350 27091 44248 53364 57299 1/n. 0.448 0.680 0.681 0.678 0.672 0.669 2.6500 g (** .S 0^ ^ V* s d t ^ / sf 3 ,/ / s ~s ^, ^ .-/ /I S *<, '/ / ^ 8 n'/ / n j / ^'V H // / / \L r ; n ion f m rpt on Wit ,J / / ' Vat: _r Li j 7 / , / a _ J 1U i n jz 2 \ . . V ? f . 0| t '/ . TV/ 185 215 40 70 77 6O . ' IOO 130 205 15 45 75 5 ^ 4.4. . . . ' JQC 135 165 195 15 30 60 82 78 ... . . < oo y\_/ 125 150 1 80 f is 1 45 114. 66 .. . S 75 250 [280 15 30 141 22 . . . < 125 155 185 215 85 172 7O 150 215 255 Total time. . 25 hours. 4.5 minutes. Pressure (mm.). 30.60 26.40 25-80 25-30 25-30 51.50 47-70 46.75 46.25 46.20 93-90 75-95 71.00 69.80 69.65 69.40 69.45 195-99 170.50 153-10 149.35 148.70 148.85 148.85 343-65 308 . 20 291.05 285.75 285 . 80 500.10 461.40 428.40 425.00 426.05 425.95 656 . 6O 640.17 638.50 638.45 Discussion. Certainly there must be a mathematical interpretation possible and from the well defined regularity and similarity of the curves this appears to be far from complicated. A brief review of those equations in general use is certainly appropriate. 27 Many adsorption formulas have been proposed. That of Arrhenius, 1 later amplified by Schmidt, 2 is certainly logical and has been used over a wide range of cases. It has the following form when applied to gases: where p is the pressure of the gas, 5 the amount adsorbed at saturation per gram of substance, x the amount adsorbed at the different pressure intervals, K and A are constants and e has its usual value. Changing this somewhat, we may write PS which states that the amount adsorbed is equal to the product of the pressure, the saturation value and a constant, itself a function of the tem- perature, which fact is expressed by the power -^ - - to which e is raised. Written in the logarithmic form, ^4 (5 _ %\ log p log 5 = log K log x -^ g - log e, since log e, A and 5 are constants, and, as Schmidt has shown, log K = k log S, the expression is simplified, giving log p log x B(S x)=k. This gives an equation well suited for calculation purposes. The re- sults of adsorption of sulfur dioxide by silica gel fits excellently this equa- tion when the isotherms at the higher temperatures are used, those above o. Even those at the lower temperatures give fairly satisfactory results if proper manipulation of the constant B is made. The value of k in- creases with the temperature while there is a tendency for B to remain constant, although this also seems to increase with temperature. Theo- retically B should remain unchanged throughout the temperature range. A great drawback to this equation, as has been pointed out before by Marc, 3 is that it is too pliable. For instance, fixing arbitrarily the value of 5 the constant B may vary through wide limits and still fit the observa- tions. Also, the value 5 can be changed at will and by slight changes in B and k the observations are again correlated. Another objection is the fact that 5 is not a constant through a wide temperature range. It is logical to believe that it must vary with the density of the condensed gas. This correction would be considerable and would give another variable to contend with in the Schmidt* equation. The adsorption ideas of Langmuir 4 in their present form are not applica- 1 S. Arrhenius, Medd. K, Vetenskapsakad. Nobelinst., 2, 7 (1911). 2 G. C. Schmidt, Z. Phys. Chem., 78, 667 (1912). 8 Marc, ibid., 81, 679 (1913). 4 J. Am. Chem. Soc., 39, 1848 (1917); 40, 1361 (1918). 28 ble to the measurements of adsorption by porous bodies. The stray field of force, eminating from the surface of the adsorbent, it is believed, reaches out, attracts and holds those molecules of the gas that approach its sur- face. The maximum adsorption is reached when this surface is covered by a film of the adsorbed substance which is but a molecule in thickness. Hence, from this theory, other factors being equal, adsorption is dependent primarily upon the amount of surface exposed. The fact that the pressure of the gas phase changes gradually is ascribed to the difference in the strength of the individual lines of force given off from the surface. Much evidence is brought forth to support this conception. Thus, in order to apply the formula to porous bodies a measure of the internal surface would be necessary. The difficulty of such an undertaking is easily seen. It is true that a rough approximation might be arrived at by making ultramicroscopic measurements of the size of the pores, such as Zsigmondy 1 has done in the case of silicic acid gel, and combining this value with that number representing the internal volume of a definite mass of the substance. This, at least, would give an idea of the internal surface. Yet, granting that a fairly accurate estimation were possible, it certainly must be admitted that forces other than residual valence come into play, especially so when the pores themselves approach the vicinity of molecular dimensions. This fact Langmuir recognizes and suggests that true adsorption should deal with plane or smooth surfaces only. It is thus evident that the observations made in this investigation cannot be expressed by the Langmuir equation in its present form. The simplest and most widely used adsorption equation is that pro- posed by Freundlich. This is purely an empirical relation, but one that is very elastic and easy of manipulation. If % is the amount adsorbed, m the mass of the gel, p the pressure of the gas, a and i/n constants, the equation is expressed as follows: x/m = ap i/n, or writing in the logarithmic form, log x/m = log a + i/n log p. This is an equation of a straight line and hence the constants a and i/n are easily interpreted a being the amount adsorbed when the pressure is unity, and i/n representing the slope of the line. It is readily seen that the constants change with a change from one temperature to an- other. So in order to make a perfect general equation this change must be expressed. An inspection of Figs. 2 and 3 will show that the results obtained with silica gel and sulfur dioxide are very well represented by the Freundlich equation. For this reason the constants a and i/n have been given in 1 Loc. cit. 29 the tables containing the data. The value of i/n given at the head of each experiment was obtained by the method of mean errors and from that the value of a was found by substitution in one of the equations. This value of a, you will notice, corresponds very closely to what would be read from the graph shown in Fig. 3. A very exhaustive treatment of this equation and its relation to tempera- ture is given by Freundlich 1 and for this reason it is not necessary to carry through the somewhat extended proof for the validity of the general equation, which takes into consideration all the variables pressure, temperature and amount adsorbed. It has the following form: log (x/m) t = log (*/m) (z y log p)t, d log a d i In , where z = -7^ and y = . These values y and z should be constants and although the experimental results do not strictly bear this out, yet there is sufficient constancy to make calculations that give good approximate agreement. Table III gives the observed values and those calculated from the equation above, using the observations made in Expts. XVIII and XIX. For this particular sample of gel z = 0.0146 and y = 0.0035, values obtained by taking a weighted mean of these differ- entials actually observed at the temperatures from o to 100. TABLE HI. Expt. XVIII (c) 40. Expt. XIX (c) 80. P. X/M obs. X/Mcalc. P. X/M obs. X/M calc. 9.44 7.50 ... 47.00 4.48 6.20 31.37 16.50 14-45 192.19 16.73 16.75 64.77 25.25 22.62 224.73 18.66 18.70 no.oo 33.66 30.73 407.88 27.70 28.99 169.13 41.88 39.01 575-32 34-17 37-05 299.78 55-54 53-91 671.95 37.41 41.20 448.60 67.17 67.99 567.52 75-07 77-81 692.20 82.16 84.36 The objectionable feature of the Freundlich equation, as well as to most all other adsorption formulas yet proposed, is that isotherms at many different temperatures have to be made in order to obtain the proper value of the constants to be used for adsorption values at any pressure and at any temperature. There is no way of predicting or even roughly ap- proximating what the adsorption would be at a temperature, say 40, knowing the adsorption at some other temperature, say o. This means that a very large number of experiments must be made on every system before it can be properly disposed of and cataloged. This point will be taken up more fully in the latter part of the paper. The accuracy of the measurements and the ease with which they can 1 Freundlich, "Kapillarchemie," p. 101. 30 be reproduced is clearly shown by Expts. XV, XVI and XVII, which were carried out on different dates with 2 . 1422 g., i . 5440 g. and 2 . 224 g. of gel, respectively. The values of X/M at equal pressures were cal- culated by the aid of the Freundlich equation. These calculations are found in Table IV. TABLE IV. X/M Calculated from i/n and a Values. P. Expt. XV. Expt. XVI. Expt. XXIV. (Cm.). June 26. July 4. Sept. 16. 5 58.45 56.70 59.36 10 78.68 77-33 79-86 15 93.63 92.73 94-97 20 105.91 105.48 107.40 25 113.90 116.55 118.16 30 126.03 126.47 127.75 35 I34-64 I35-5I 139.64 40 142.58 143.86 144.48 45 149-93 151-66 151.95 50 159-58 158.98 158.96 55 163-44 165.91 165.57 65 175-57 178.80 177-84 In Fig. 3 we have plotted log X/M against log p. If the equation held absolutely we would have a system of straight nearly parallel lines. This is not strictly true. There are deviations in both directions, but more noticeably so with those isotherms carried out at the extreme tempera- tures. This bending is concave towards the #-axis, and for high tempera- tures takes place at the extreme left, while at the lower temperatures it occurs at the extreme right. The first case is probably due to the slight pressure developed by the adsorbed air released on the introduction of the first amount of sulfur dioxide. This pressure, although extremely small in itself, is, in proportion to the pressure of sulfur dioxide realtively large at this part of the curve and hence would produce a noticeable effect. More will be said later in regard to this point. The bending in the case of the lower temperatures is easily accounted for. In that region the vapor pressure of the liquid is approached and deviations would not be surprising but expected. Others 1 have shown that where p/p ap- proaches unity the Freundlich equation is not applicable. The mere fact that a chemically inert substance like silica gel is found exhibiting such marked adsorptive properties is sufficient in itself to indi- cate that the cause of adsorption does not lie in the interaction of adsorbent and adsorbed substance. In making the above statement we do not mean to say that it covers all the cases of gas or vapor adsorption, for the fact of specific gas adsorbents would tend to disprove it, e. g., palladium for hydrogen. Perhaps it would be better to confine ourselves to the ad- 1 Titoff, Z. physik. Chem., 74, 641 (1910); I/. B. Richardson, /. Am. Chem. Soc., 39, 1828 (1917). sorption of vapors, although it will be seen that our analysis permits the extensions to regions that are ordinarily considered as gaseous. As an approximate line of division we might select the critical temperature and confine ourselves to a discussion of adsorption occurring below this tem- perature. It cannot be too strongly emphasized that we are dealing with phenomena that exhibit adsorption to a marked degree, and are not mani- festations of layers of a few molecules deep. It is our belief that the adsorption of gases or vapors, let us say at all temperatures below the critical temperature, may be predicted from a knowledge of the physical constants of the-gas or vapor alone. Further- more, the role of the adsorbent is simply that of a porous body, its chemical nature being a matter of indifference. (Cases of obvious chemical affinity are of course excluded.) Adsorbents differ in the extent of their total internal volume and also in the dimensions of the spaces, called pores for simplicity, that make up the internal volume. It is conceivable that 2 adsorbents may possess the same internal volume but show marked differ- ences in the adsorption of the same vapor due to differences in the distribu- tion of the pore sizes. If this is true the form of the adsorption curve expresses the distribu- tion of the internal volume as a function of the dimensions of the pores. An attempt was made to express this relation in terms of the Maxwell distribution law, but a moment's reflection will convince one that there is no reason to expect the pore sizes to be distributed according to the laws of probability. The pores in the silica gel exist as the result of the juxtaposition of colloidal particles which are approximately all of equal dimensions and are, therefore, probably V-shape in cross section, or at any rate may be designated as tapering. It is at once evident that if the adsorption curve simply shows the man- ner in which the various sized pores are distributed that go to make up the internal volume of the adsorbent, then, instead of seeking a relation between weight of adsorbed gas and the equilibrium pressure we should at once turn to the volume occupied by the adsorbed gas. As a matter of fact, if we express our isotherms of sulfur dioxide adsorption with volume of liquid sulfur dioxide as ordinates instead of weight, the curves are brought closer together. Our next consideration is, of course, to express the abscissas of our isotherms not as simple equilibrium pressures but as corresponding condensation pressures. It has long been known that the properties which determine the ease of condensation of a gas or vapor are closely connected with the physical constants of the gas or vapor which are of importance in determining the magnitude of the adsorption. It is well known that condensations of vapors occur with greater ease in capillary tubes than on a level sur- face, provided the liquid wets the capillary wall. This phenomenon has been long studied and the lowering of the vapor pressure of a liquid in a capillary in terms of the ordinary vapor pressure of the liquid P is given by the following relation: where a is the surface tension, d the density of the saturated vapor, D the density of the liquid and r the radius of the capillary. With the aid of this relationship we can readily derive the fact that the radius of the tube must be very small in order to have an appreciable effect on the vapor pressure of the liquid inside. It is not until we get to tubes of less than o.ooi mm. in diameter that we begin to affect the vapor pressure. From this it is clear that if we wish to account for the marked lowering of the vapor pressure in the case of adsorption, pores approaching molecu- lar magnitude must be assumed. It is our feeling that such a wide ex- trapolation of the above formula is not justified and in the present anal- ysis we shall not consider the question of absolute diameter of pores. If we wish to compare the adsorption of a particular adsorbent for a gas or vapor at various temperatures, it is evident that the comparison must not be made at the same pressure, but rather at some corresponding pres- sure. As suggested by Williams and Donnan 1 the value of p/p may be selected for this purpose (p is the vapor pressure of the condensed vapor) . In Fig. 8 we have plotted the logarithms of the volumes of condensed sulfur dioxide (obtained by dividing the weight of sulfur dioxide by the density of liquid sulfur dioxide at the corresponding temperature) as ordinates against the values of logarithm p/p as abscissas. It will be noted that greater volumes are taken up at lower temperatures at the same corre- sponding pressures. Furthermore, it is to be noted that all the adsorption isotherms are brought much closer together. When P/Po equals unity the same volume of sulfur dioxide is taken up at all temperatures. At the higher temperature we were unable to work with pressures sufficiently great to enable us to realize the value of unity for p/p ot however, the slope of the log curves is such as to bring all curves together at the point p/po = i. An approximate idea of exactly what this volume is may be grasped by 1 Williams and Donnan, Trans. Faraday Soc., 10 (1914). 33 reference to Fig. 9. Here are plotted on a larger scale the results ob- tained at the lower temperatures, in fact those temperatures where the saturation point was reached. This point is easily fixed by the very sharp break in the curve. Introduc- ing density correction, these values become almost identical. Table V gives these results, corrected and uncorrected, as well as the saturation value of the isotherm at o calculated from the adsorption equa- tion. The accuracy of the Freundlich equation does not permit calculation of the saturation points at the higher temperatures as a wide deviation would be expected. TABLE V. Temperature 80 Vol. gas phase, cc 232 Vol. liquid phase, cc. (or internal vol. of gel) . o . 4073 54" 228 0.4168 34-0' 216 0.4039 209 0.4167 Similar results with silica gel were obtained by Bachmann. 1 This in- vestigator showed that with the same sample of gel at the saturation pressure, that is the vapor pressure of the liquid at that temperature, the same volume of different liquids was taken up. Some experiments were carried out in which the liquid was introduced through the gas phase; others where the gel was introduced directly into the liquid. In this latter case the surface was carefully wiped with filter paper and possi- ble errors from this source minimized. The author states that no correc- tion for contraction or other volume change resulting from possible forces acting within the gel structure was considered in the calculation. A few determinations are given. 2 18. Sample 2. 0.3572 g. gel. Wt. absorbed. Liquid. G. H 2 0.2276 CH 6 0.8791 C 2 H 2 Br 4 0.6720 Vol. per g. of gel. Cc. 0.6210 0.6270 0.6210 1 W. Bachmann, Z. anorg. Chem., 79, 202 (1913). 2 Other gel samples gave consistent although different values from the above, e. g., Sample 5 vol. = 0.3621 cc.; loc. cit. 34 The absolute value is not in agreement with that found in this investiga- tion, but it must be remembered that the experimental method as well as the gel sample itself was different. The main point is that with the same gel sample there is an equal volume of the liquid adsorbed, no matter what the liquid or what the temperature. Up to this point we have considered the lowering of the vapor pressure from the simple standpoint as being due to the rise in a capillary tube. Clearly, in our case the effect is not due to a difference in level, nor is it certain that we are dealing with tubes opened at both ends. For our purpose it is better to consider the lowering of the vapor pressure of the liquid in a pore as due to a negative tension exerted on the liquid around the meniscus. Thus this pull has its origin in the tendency of films which wet the walls to contract so as to expose as little of surface as possible. Looking at the adsorption of vapors in this light, it is seen that the con- densed vapor is under a tension rather than a pressure. Furthermore, it is a simple matter to calculate the magnitude of this negative pressure. Using the well-known Gibbs relation, where dp = change in the vapor pressure, dP = change in the hydrostatic pressure, V = volume of the condensed phase, and v volume of the gas phase, expressing the variation of vapor pressure with the hydro- static pressure, we can calculate that liquid sulfur dioxide at 30, having a vapor pressure of 3496 mm., when in a capillary tube under a vapor pressure of 9.55 mm., is subject to a tension of about 530 atmospheres. When the pressure over the condensed liquid sulfur dioxide has risen to 706 mm. by the above relationship it can be shown that the negative pressure has fallen to 420 atmospheres. It is evident that we are in a position to calculate the negative pressure on any liquid provided we know the lowering of the vapor pressure, and the density of the condensed phase. (It is assumed that the vapor obeys the gas laws.) If the liquid is in a closed tube this pull must occasion a dilation of the same to an extent that is proportional to the compressibility of the liquid. Worthington 1 has stated that the volume changes caused by negative pressure may be calculated with the aid of the compressibility coefficient. Unfortunately, we have no direct measurements of the compressibility of liquid sulfur dioxide and are, therefore, unable to evaluate quantitatively the volume change. It is known that in some cases 2 the relation & */* I/" Lj{f SB jfx 1 Worthington, Trans. Roy. Soc. (London), iSsA, 355 (1892). 2 Richards, J. Am. Chem. Soc., 40, 59 (1919). 35 holds good, but it has only been tested over a narrow range of a and many exceptions have been noted. We can, however, say that liquids of high surface tension have smaller compressibilities than liquids of low surface tension. Here we have a possible explanation for the fact that the volume of sulfur dioxide at corresponding pressures are smaller at high than at low temperature. At the higher temperature the condensed phase is more compressible, cr, being smaller, and in addition the negative pressure is greater. In other words, we do not know the actual density of the con- densed phase in the gel, but in all cases it is lower than the normal density which it approaches when p/po = i. Expt. XII Expt. XXIII. 100. 30. = 2114.3 cm. a = 22.75, D = L3556, Po = 349.6 cm. log V. log P/po. log PV/PO. log V. 103 P/Po. log pff/po. 2.49183 5.03643 7.00257 2-39811 3.33415 2.69113 2 .66113 2.27363 7.23977 z . 73466 2.06453 7.42151 2-75343 2.41060 7.37674 i. 88680 2.37194 1.72892 2 . 80302 2.50189 i . 46803 00355 2 . 60706 7 . 96404 . 11206 2.83983 0.09681 .21380 7.067II 0.35698 .28652 7.22883 0.58581 .32130 7.3O30I 0.65999 Expt. XVIII. 40. tr = 21.0, D = 1.3111, po = 471.2 cm log V. log p/po. log Pff/po. 2.21395 3-30176 2.62398 2.55637 3-82330 7.14552 2.74H5 2.13816 7.46038 2.86600 2.36818 7 . 69040 2" . 96090 2.55501 1.87723 7.08350 2.80359 0.12581 7.16607 2.97865 0.30087 7.21436 7.08077 0,40299 1-25355 7.16702 0.48944 Expt. XXVI. -54. = 39-0 1 ? = 1.565, Po = 88.3 mm. log V. log P/po. log pff/po. 2.75603 3.65610 7.24716 7.16510 5.67313 0.26419 7.30525 7.04748 0.63854 1.41792 7.29832 0.88938 7.49483 1-49337 1.08443 1.57984 i - T0435 1-29541 Expt. XIX. 80. o- = 13.1, D = 1.192, po = 1368 cm. log V. log p/po. log Pff/po 2.60374 2.14764 ".26491 2.65H5 2.21557 "-33284 2.82272 2.47444 .59171 2.91388 2.62382 ".74109 2.95323 2.69124 ".80851 Expt. XXV. 80. 1.6295,