EXCHANGE 
 
UNIVERSITY OF /PENNSYLVANIA 
 
 22 
 
 THE THERMODYNAMIC PROPERTIES 
 
 OF SOLUTIONS OF ONE-TENTH MOLAL 
 
 HYDROCHLORIC ACID, CONTAINING 
 
 CALCIUM, STRONTIUM AND 
 
 BARIUM CHLORIDES 
 
 BY 
 
 NORMAN JODON BRUMBAUGH 
 
 A THESIS 
 
 PRESENTED TO THE FACULTY OF THE GRADUATE SCHOOL IN 
 
 PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR 
 
 THE DEGREE OF DOCTOR OF PHILOSOPHY 
 
 IN CHEMISTRY 
 
 MARTIN & LYLE, PRINTERS 
 
 212 PENFIELD BUILDING 
 
 PHILADELPHIA 
 
 1922 
 
UNIVERSITY OF PENNSYLVANIA 
 
 THE THERMODYNAMIC PROPERTIES 
 
 OF SOLUTIONS OF ONE-TENTH MOLAL 
 
 HYDROCHLORIC ACID, CONTAINING 
 
 CALCIUM, STRONTIUM AND 
 
 BARIUM CHLORIDES 
 
 BY 
 
 NORMAN JODON BRUMBAUGH 
 n 
 
 A THESIS 
 
 PRESENTED TO THE FACULTY OF THE GRADUATE SCHOOL IN 
 
 PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR 
 
 THE DEGREE OF DOCTOR OF PHILOSOPHY 
 
 IN CHEMISTRY 
 
 MARTIN & LYLE, PRINTERS 
 
 212 PENFIELD BUILDING 
 
 PHILADELPHIA 
 
 1922 
 
The author desires to express his appreciation to Dr. 
 
 Herbert S. Harued, who suggested the general 
 
 plan of this investigation and from whom 
 
 valuable assistance and direction 
 
 were frequently received. 
 
; 
 
 THE THERMODYNAMIC PROPERTIES OF SOLUTIONS OP 0.1 
 
 MOLAL HYDROCHLORIC ACID CONTAINING CALCIUM, 
 
 STRONTIUM AND BARIUM CHLORIDES. 
 
 In several recent contributions, Harned (Jour. Amer. Chem. Soc. 37, 
 2460 (1915) ; 38, 1986 (1916) 43, 1808 (1920) from measurements of cells 
 of the type 
 
 H 2 |MeCl (c) in HC1 (0.1)| HgCl |Hg 
 and H 2 |MeCl (c) in HC1 (0.1)|Sat.KCl|HgCl|Hg 
 
 where Me represents potassium, sodium, or lithium, has attempted to com- 
 pute the independent hydrogen and chlorine ion activities of these 
 solutions. In all these cells the concentration of the acid has been kept 
 constant and the salt varied. Loomis, Essex and Meacham (Jour. Amer. 
 Chem. Soc. 39, 1133 (1917) and Ming Chow (ibid. 42,488 (1920), have 
 also measured cells of the same type containing hydrochloric acid and 
 potassium chloride, but in their measurements the total chlorine ion con- 
 centration was kept constant. 
 
 In the present investigation accurate measurements of the same types 
 of cells have been made, employing barium, strontium and calcium 
 chlorides in 0.1 M hydrochloric acid. The exact calculation of the in- 
 dividual activity coefficients of the ions in concentrated solutions is a 
 problem accompanied with great difficulties owing to liquid junction 
 potentials which cannot be accurately calculated. At the present time, 
 the only other method of value, besides calculations which are inexact, is 
 to eliminate as far as possible the liquid junction potential by the use of a 
 saturated potassium chloride solution. From previous results obtained by 
 Harned (loc. cit.) there is considerable evidence that the difference in 
 liquid junction potential between 
 
 HC1 (O.l)jSat. KC1 
 and HC1 (0.1) +MeCl |Sat. KC1 
 
 if present at all, is very small, probably amounting to less than a millivolt 
 when the MeCl is as concentrated as 2M. Although this error due to 
 liquid junction is appreciable, and the calculations cannot be regarded as 
 exact, it is thought that further experimental work of this nature is of 
 very great value, particularly since no other method has yet been found 
 which can approach it in accuracy. 
 
'4 * ' TMRMODYNAMIC PROPERTIES OF 0.1 M HC1 IN CaCh, SrCb AND BaCb 
 
 1. GENERAL THEORY. 
 
 If a process is carried out reversibly, the maximum work is inde- 
 pendent of the path. Hence, if the system passes from a state I to a state 
 II, the maximum work may be regarded as the difference in two quantities 
 
 AI and A 2 . Thus, 
 
 Maximum work = AI A 2 = (A 2 AI) = ( A A) 
 Now, take for example, the voltaic cell 
 
 ZnlZn** ||H + |H 2 
 and let the process 
 
 Zn+2H+ = ZnVH 2 
 
 take place reversibly at constant pressure producing the electrical work 
 W. W is not the quantity (-AA) for besides W there will be the work 
 PAV done by the production of 1 mol. of hydrogen. Hence, 
 
 W=(-AA)-PAV (1) 
 
 Let F=A+2pV 
 
 and AF = AA+2pAV (2) 
 
 AP will be the increase in free energy of the system. In the above 
 cell let nEF be the electrical work. Then, the total maximum work will 
 be (- A A) and 
 
 (-AA)=nEF+ P AV (3) 
 
 or from (2) and (3) 
 
 nEF=(-AA)-pAV=(-AF)* 
 *(See Lewis Jour. Amer. Chem. Soc. 35, 1 (1913) 
 
 Thus, the electrical work at constant pressure and temperature of a 
 reversible cell is equal to the free energy decrease. In order to calculate 
 AH, the increase in heat content function, from measurements of AF, 
 use will be made of the fundamental thermodynamic formula 
 
 AH=AF-Td (4) 
 
 The activity can be defined by the equation 
 
 F=RTlna+i (5) 
 
 where F is the partial molal free energy, i a constant, R the gas constant 
 and T the absolute temperature. 
 
 Thus, the free energies of an ion species in two states are related by 
 
 AF = F 2 -F 1 = RTln- (6) 
 
 ai 
 
 (6) will be the exact formula for the free energy change of a con- 
 centration cell. Consider the general reaction 
 
 aA-f-bB+.. . .=dD+eE.. 
 
THERMODYNAMIC PROPERTIES OF 0.1 M HC1 IN OaCb, SrCb AND BaCL 5 
 
 Let it take place electrically. Then it is easily proved (Lewis loc. 
 cit.) that 
 
 (-AF) = nEF = -RTln - (7) 
 
 a A a B 
 
 Two types of cells will be considered in the present investigation : 
 Type I H 2 | MeCl 2 (c) in HC1 (0.1) | HgCl | Hg 
 Type II H 2 | MeCl 2 (c) in HC1 (0.1) | Sat.KCl | HgCl | Hg 
 The electromotive forces of the above cells will be denoted by E(l), and 
 E(2) respectively. Also let E (l) equal E(l) when c = o; E (2) equal E(2) 
 when c = o. 
 
 2 E(1)F will be the free energy decrease ( AF) of the cell reaction. 
 
 H 2 +2 HgCl = 2 Hg-f 2 HC1 (c) 
 
 in the presence of HC1 (0.1M) and the acid-salt mixtures. Then 
 
 F[E (1)-E (l)] = (- 
 
 . . 
 
 where (_AF) j is the decrease in free energy of transfer of two mols of 
 
 hydrochloric acid from (MeCl 2 (c) + HC1 (0.1) to HC1 (0.1). (a H(s )) refers 
 to the activity of the hydrogen ion in the acid-salt mixtures.) 
 
 Further F[E (2)-E(2)] = (-AF) 2 = RT In -- 
 
 a H(0.1) 
 
 if, in the latter case, the potassium chloride solution eliminates the liquid 
 junction difficulties. 
 
 A further quantity which is often used is the activity coefficient 
 
 which for a single ion is defined by_ where c is the molal concentration of 
 the ion. c 
 
 2. EXPERIMENTAL. 
 a. Materials. 
 
 The various chemicals used in making the cells were carefully tested 
 as to their purity and most of the materials were prepared for this par- 
 ticular investigation from analyzed chemicals. The aim sought was to 
 avoid error in the electromotive force measurements from possible con- 
 taminating impurities in the stock materials. 
 
 The mercury used was distilled three times under reduced pressure. 
 During the distillation a stream of air was passed through the mercury 
 in the flask in order that all traces of zinc and cadmium might be oxidized 
 and thereby separated from the vaporized mercury. This purified mer- 
 cury was used in the calomel electrode chamber of all the cells. Also a 
 
6 THERMODYNAMIC PEOPEETIES OF 0.1 M HC1 IN CaCb, SrCk AND Bad* 
 
 portion of it was treated with a limited amount of nitric acid which had 
 been previously redistilled over solid potassium permanganate. From a 
 boiling solution of the mercurous nitrate thus formed, the calomel for the 
 cells was precipitated by the addition of redistilled hydrochloric acid. The 
 precipitated calomel was washed until all traces of hydrochloric acid had 
 disappeared, about forty times. The last two or three washings were made 
 with redistilled water. 
 
 All water used in making up solutions of the electrolytes had been 
 redistilled from an alkaline potassium permanganate solution through a 
 block tin condenser. 
 
 The barium chloride was prepared from commercial barium chloride 
 by three successive crystallizations, the last one being made from the con- 
 ductivity water. The salt thus obtained was analyzed. 
 
 A stock solution of strontium chloride of almost the maximum satura- 
 tion at 18 was made from a special grade of analyzed chemicals. The 
 purity of the strontium chloride in this concentrated solution was tested 
 by precipitating the chloride as silver chloride, and calculating the chloride 
 found in terms of the strontium content. The chloride analysis was 
 checked by an independent analysis of samples of the same solution by 
 precipitation of strontium sulphate from an aqueous alcoholic solution 
 and again calculating the resulting strontium sulphate as strontium. The 
 mean of the chloride analyses gave a strontium content of 33.820%, and 
 that of the sulphate analysis 33.740%, an actual difference of .08%, or a 
 precentage difference of a little over two-tenths of one per cent. The 
 strontium chloride was further tested spectroscopically and found to be 
 free of barium ; even sodium was present apparently in minute quantity. 
 
 Analyzed anhydrous calcium chloride was added to conductivity water 
 in excess. The solution was filtered, and to it, was added a slight excess of 
 the redistilled hydrochloric acid sufficient to overcome the alkaline reaction 
 of the original solution. This excess of hydrochloric acid was eliminated 
 by adding precipitated calcium carbonate to the solution and passing air 
 through the boiling solution to remove carbon dioxide gas. The solution 
 was then neutral. Three samples of the calcium chloride solution thus 
 prepared were treated with silver nitrate and from the weights of the 
 silver chloride, the calcium content was calculated, giving 4.163, 4.162 and 
 4.161 per cent, an average value of 4.162 per cent. Three other samples 
 of the same solution were evaporated to dryness with dilute sulphuric acid 
 and the calcium content was determined from the weights of the calcium 
 sulphate, the values being 4.152, 4.166 and 4.145 per cent, giving an aver- 
 age value of 4.154 per cent. The difference between this last value and the 
 
THERMODYNAMIC PROPERTIES OF 0.1 M HC1 IN CaCb, SrCb AND Bad* 7 
 
 average value for the calcium content by the chloride method is 0.008%, or 
 in terms of the mean calcium content, 4.158, the difference is a little less 
 than two-tenths of one per cent. 
 
 b. Apparatus. 
 
 Measurements of this type have been made by numerous investigations 
 ( Acree Am. Chem. J. 46, 632, 1911 ; Harned, J. A. C. S. 37, 2460, 1915 ; 
 Ellis, J. A. C. S. 38, 737, 1916 ; Lewis, Brighton & Sebastian, J. A. C. S. 
 39, 2245, 1917), but the cells employed here differed in some respects from 
 any previously described. One type of cell was employed for the meas- 
 urement of the combination 
 
 H 2 I MeCI 2 (c) in HC1 (0.1) | HgCl | Hg 
 
 It was an H shaped cell and is shown in Fig. 1. 
 
 FIG. 1 
 
.8 THERMODYNAMIC PROPERTIES OF 0.1 M HC1 IN CaCfe, SrCb AND BaCL 
 
 The side marked C is the calomel electrode. In the first cells contact 
 011 the calomel electrode side was made through a glass tube fixed in a one- 
 hole rubber stopper in the end of which tube was sealed a platinum wire 
 similar to the arrangement shown in the calomel side, C, of Fig. 2. It 
 sometimes happened, however, that when the rubber stopper holding the 
 glass tubing was inserted into the calomel limb of the cell, air pressure 
 was produced in the calomel chamber above the solution. When the 
 stopcock S was subsequently opened for a measurement a certain amount of 
 calomel, lodged between the points A and S, would be suddenly carried 
 through to the hydrogen electrode side. The lead wires for the calomel 
 electrode were therefore thrust into mercury in the small side tube shown 
 to the left of C which, in turn, was in contact with the calomel electrode 
 through a platinum wire fused into the bottom of the cell. The stopcock 
 shown above C was always kept open until the rubber stopper in which 
 the former was fixed had been securely inserted into the top of the tube. 
 By following this procedure no calomel was forced into the hydrogen com- 
 partment. 
 
 In the first cells used the connecting tube of the cell AB, Fig. 1, was a 
 piece of straight side glass tubing. Frequently, however, air bubbles col- 
 lected near the stopcock S and very persistently remained there. By re- 
 placing the straight side tubing with a tubing flared at either side of the 
 stopcock S, as shown by AB, Fig. 1, any bubbles which were present when 
 the cell was set up were very easily removed. 
 
 As mentioned later, it was customary to shake the cell until its elec- 
 tromotive force had attained a constant value. This shaking invariably 
 caused some calomel to lodge even in the flared tube between the points 
 A and S ajs a result of which, if the stopcock were opened for some time, 
 a certain small amount of calomel might be carried into the hydrogen 
 electrode chamber. In order to eliminate this, a connecting tube of the 
 shape indicated by A' B' was tried. A certain amount of calomel, it was 
 observed, still lodged near the stopcock just above the elbow of the tube. 
 Moreover, at the same point in the tube A'B' a bubble would collect which 
 was difficult to dislodge. Finally, therefore, a connecting tube of the type 
 shown at A"B" was used. By pouring the electrolyte into the tube first 
 until the side SB" was completely filled, and then adding the calomel, the 
 presence of air bubbles near the stopcock was entirely avoided. The cal- 
 omel here used had previously been equiliberated at 25 with a solution of 
 the particular chloride of a definite concentration for several days. This 
 arrangement of the connecting tube A"B" at an angle of about 45 to the 
 limbs of the cell had the marked advantage that no calomel would lodge 
 near the stopcock, for after each shaking it would roll to the bottom of the 
 calomel electrode chamber. 
 
THERMODYNAMIC PROPERTIES OF 0.1 M HC1 IN CaCL, SrCfc AND BaCb 9* 
 
 The hydrogen electrode was kept always completely immersed in the 
 electrolyte and placed in such a position that the hydrogen bubbles coming 
 from the equiliberating chamber M would be divided by the platinum foil. 
 The hydrogen electrode chamber was provided with a trap T permanently 
 inserted in the rubber stopper which closed the tube. By having the end 
 of the small escape tube of the trap under the surface of the electrolyte in 
 the bowl of the trap, the space above the surface of the liquid in the 
 hydrogen electrode chamber was kept filled with hydrogen. 
 
 The hydrogen was first passed through a solution of the electrolyte in 
 the equiliberating tube M, thereby becoming saturated before coming into 
 contact with the solution in the hydrogen electrode chamber, and thus 
 preventing any evaporation in the chamber. It has been determined that 
 equiliberating tubes of the above type (M in Figs. 1 & 2) are satisfactory 
 for saturating the hydrogen. 
 
 After each measurement the hydrogen electrode was removed, any 
 possibly adhering calomel (indicated by a gray color instead of the intense 
 black of the platinum sponge) was dissolved by immersing the electrode 
 in nitric acid. After rinsing with distilled water the electrode was recoated 
 by making it the cathode in a chlorplatinic acid solution, from twenty to 
 forty-five minutes, the current density being from 20 to 50 milli-amperes. 
 H 2 | MeCl 2 (c) in HC1 (0.1) | KCl(Sat.) | HgCl | Hg 
 
 Fig. 2 represents the potassium chloride cell. 
 
 FIG. 2 
 
10 THERMODYNAMIC PROPERTIES OF 0.1 M HC1 IN CaCh, SrCb AND BaCh 
 
 Calomel previously equiliberated for several days with a solution of 
 potassium chloride saturated at 25 was poured into the calomel chamber 
 C along with the mercury. The bridge RR was then carefully filled with 
 the same potassium chloride solution, as well as the cup P. At the bottom 
 of the cup a few crystals of potassium chloride were always present. The 
 bulb I/ was likewise filled with the solution. The equiliberating tube M, the 
 hydrogen electrode chamber II , the bridge R', as well as the bulb L, were 
 all filled with a solution of the particular electrolyte being measured, that 
 is with MeCl 2 (c) in IIC1 (0.1). This electrolyte filled the capillary 
 tubing Y the end of which dipped into the saturated potassium chloride 
 solution in the cup P when a measurement was being made. 
 
 When no measurements were being taken, a cup, really a short test 
 tube of heavy glass fitted over the rubber stopper on the end of the capil- 
 lary Y where previously the cup P had been. By means of this device the 
 saturated potassium chloride half of the cell, C RP, would be successively 
 attached to any number of half cells, YR'HM. After each measurement 
 the solution from the reservoir bulb L i was run through the capillary and 
 the potassium chloride carefully removed from the outside surface of the 
 capillary tubing by bibulous paper. Similarly, the potassium chloride solu- 
 tion was renewed by opening the stopcock below the bulb. 
 
 The hydrogen was generated electrolytically by passing the current 
 through a 10% solution of sodium hydroxide. A current of about two 
 amperes was used. A 20% sodium hydroxide solution was first tried but 
 this attacked the electrodes. Even with a 10% solution it was found that 
 copper in contact anywhere with the sodium hydroxide solution was 
 attacked. Finally a platinum anode suspended by a nickel wire and a 
 nickel cathode held in place by a wire of the same material were used in 
 the generator. A cell thus built seemed to be able to supply hydrogen 
 continuously and for an indefinitely long' time. Finally, the glass vessels 
 which contained the alkali solution were attacked to some extent. In order 
 to maintain a constantly uniform gas pressure, each cell was provided 
 with its own hydrogen generator. During the greater part of the inves- 
 tigation three cells were being measured simultaneously ; for a short time 
 four cells were set up. 
 
 To prevent any admixture of the hydrogen with oxygen the tube in 
 which the anode was suspended extended almost to the bottom of the vessel 
 containing the electrolyte. The electrolyte was forced up into this same 
 tube by the back pressure of the generated hydrogen. The level in this 
 tube was regulated by the stopcock attached to the tube M (Figs. 1 & 2), 
 and was maintained at such a height that the hydrogen bubbled regularly 
 and continuously through the hydrogen electrode compartment, H. Be- 
 
THERMODYNAMIC PROPERTIES OF 0.1 M HC1 IN CaCk, SrCb AUD BaCL* 11 
 
 tween the hydrogen generator an^ the cell there was placed first in the 
 hydrogen line a Dreschel wash bottle containing concentrated sulphuric 
 acid. The hydrogen was then led through a tower containing sticks of 
 fused sodium hydroxide, after which it entered the equiliberating vessel 
 M The electromotive force of the cells was measured on a Wolff poten- 
 tiometer having a total resistance of 15,000 ohms. A null point was ob- 
 tained by balancing the cell against two large Weston cells (Hulett 
 Physical Review 1909) in series. Before and after each measurement the 
 latter were compared with a standard Weston cell. The latter in turn was 
 occasionally compared with a new Weston certified by the Bureau of 
 Standards in 1921. 
 
 Immediately before taking a set of readings the stopcocks S, Fig. 1, on 
 all the cells were opened, the large Hulett design Weston compared with 
 the standard, after which the cells were read in rapid succession. Each 
 cell had its own lead wires to a three way cup switch placed beside the poten- 
 tiometer. Finally the large working cells were rechecked and the stop 
 cocks closed. 
 
 The temperature of the bath was controlled, to within -f.05 by means 
 of a very large vessel filled with toluene whose volume, changing with the 
 temperature, moved a thin mercury column in immediate contact with the 
 toluene. The mercury made electrical contact with a platinum wire and 
 thereby opened and closed the electric heating circuit. 
 
 c. Measurements. 
 
 All of the electrolytic solutions were made up on the basis of a frac- 
 tional or multiple part of a mole per 1000 grams of water. The amounts 
 of the constituents of each solution were determined by weight; in no 
 single instance were volumetric methods employed. Temperature coeffi- 
 cients were thereby eliminated. The strengths of the stock solutions of 
 hydrochloric acid, calcium chloride and strontium chloride were determined 
 by precipitation of silver chloride. 
 
 For weighing substances up to about 70 grams, a balance with a sen- 
 sitiveness of two ten thousandths of a gram per division of pointer scale was 
 used ; for larger quantities a beam balance with a sensitiveness of approxi- 
 mately two one hundredths of a gram per scale division was available. 
 The stock solution of redistilled hydrochloric acid analyzed for its acid con- 
 tent at the beginning of the investigation had a mean value of 7.3237% 
 for four samples, with a maximum deviation from the mean for any one 
 sample of 0.0057%, and a maximum difference for any two samples of 
 0.010%. Because the hydrochloric acid present in the cells was the most 
 
12 THERMODYNAMIC PROPERTIES OF 0.1 M HCl IN CaCb, SrCb AND BaCU 
 
 important constituent of the electrolyte, the stock solution was reanalyzed 
 at the end of the investigation and found to have an acid content of 7.3335% 
 with a maximum difference of 0.0082% and a maximum deviation of 
 -{-.0051%. The change had been negligible. The values of several cells 
 were checked with solutions having the slightly different acid factor, and 
 found to be practically unchanged. Two samples of the calcium chloride 
 solution gave a mean value of 31.847% content with a difference of 0.005%, 
 and two analyses of the strontium chloride solution indicated that 19.284% 
 of the compound was present. In the latter analysis the difference was 
 0.024%. It might be noted that in order to secure concordant results of 
 these almost saturated salt solutions, it was found necessary to wash the 
 precipitated silver chloride at teast ten times with acidulated water. 
 
 From the determination of the concentration as described above, the 
 molal content of each solution was obtained by dividing the strength of 
 the solution expressed in per cent by the molecular weight of the particular 
 salt. Since it was necessary to know the weight of the solution containing 
 one molecular weight of the salt the molar strength as found above was 
 divided into the per cent of water present with the salt. This latter num- 
 ber was obviously obtained by subtracting the salt concentration expressed 
 in per cent from one hundred. The result multiplied by a hundred an$ 
 added to the gram molecular weight of the particular chloride gave the 
 total weight of solution per mol. of salt. For fractional molar solutions, 
 proportional parts of this number were taken. 
 
 The amount of water to be added was easily found from the above 
 calculation. The water present with the one-tenth molal hydrochloric acid 
 also decreased by its weight the water necessary to make the one thousand 
 grams present with the salt. In the barium chloride solutions fractional 
 parts of the two molecules of water of crystallization were regarded as a 
 part of the water of dilution. 
 
 The calomel which was to be used for the cells was shaken at least 
 eight times with separate portions of the particular solution after which 
 it was allowed to stand in the thermostatic bath at 25 for some hours 
 before using. A cell did not attain its maximum voltage until the hydrogen 
 electrode had been exposed to the stream of hydrogen for about six hours. 
 Before a reading was taken the stopcock S, Fig. 1, was opened, then closed, 
 and the cell shaken. After the calomel had settled the reading of the electro- 
 motive force of the cell was checked. This procedure was continued until 
 the cell had acquired a relatively constant voltage. In the case of the 
 concentrated potassium chloride cells, Fig. 2, the calomel electrode side of 
 which was attached in turn to each salt-acid hydrogen electrode half as 
 
THERMODYNAMIC PROPERTIES OF 0.1 M HCl IN CaCb, SrCl* AND BaCI* 13 
 
 previously mentioned, this shaking process was discontinued after a con- 
 stant and correct value for the combination 
 
 H 2 | HCl (0.1) | KC1 (Sat.) | HgCl | Hg 
 
 had been secured. The value regarded as correct was that obtained by 
 Fales and Vosbufgh (loc. cit.) namely 0.3103. The value here found as a 
 result of fifty checked and separate groups of readings was 0.3100, which 
 is practically within the limit of error as given by the investigators referred 
 to above. The HCl (0.1) side of a cell wa!s kept in the bath and used as 
 a check on the elSectrojmotive force values o| the- salt>-acid cells. 
 
 ; i .'!'";:' ( I 
 
 After the double! cell' (Fig. 1) had attained constant value at 25 P the 
 
 temperature of the thermostatic bath was changed to either 18 or 30, 
 the stopcock opened and the voltage read. The cell was then shaken, and, if 
 a change in value occurred, repeatedly shaken until constancy was obtained. 
 Then the bath was brought back to its initial temperature and the cell 
 again tested. The differences in voltage between the averages of the values 
 thus obtained were used for the determination of the temperature coeffi- 
 cients. (Table III.) 
 
 The mean values for the electromotive force readings of the double 
 cells are given in Table I. 
 
 TABLE I. 
 
 25 VALUES E. M. F. DOUBLE CELLS 
 
 c BaCl 2 SrCl 2 CaCl 2 
 
 0.00 0.39898 0.39898 0.39898 
 
 0.10 0.37530 0.37500 0.37462 
 
 0.20 0.36337 0.36318 0.36305 
 
 0.30 0.35503 0.35449 0.35326 
 
 0.50 0.34155 0.34031 0.33986 
 
 0.75 0.32786 0.32630 0.32529 
 
 1.00 0.31678 0.31471 0.31176 
 
 1.3 0.30358 0.31280 
 
 The object of the investigation was not primarily to establish the elec- 
 tromotive force value of any one particular strength of a single salt but to 
 determine the relative values for the different strengths of all three salts. 
 Therefore, at first, cells of different solution strengths of the same salt were 
 measured and the results plotted. 
 
14 THEBMODYNAMIC PROPERTIES OF 0.1 M HC1 IN CaCb, SrCb AND BaCh 
 
 /SO 
 
 
 
 '0 C 
 
 FIG. 3 
 
 Where the values were obviously incorrect in comparison with neigh- 
 boring points on the graph of the same salt or of the other two salts, new 
 cells of that strength were placed in the bath and kept there until the value 
 of the electromotive force was established beyond doubt. Thus it followed 
 that certain cells were read but a few times while the mean value for 
 others was the result of numerous sets of readings. The value of the l.M 
 strontium chloride cell is the mean of more than fifty readings, the l.M 
 calcium chloride of over twenty readings and that of the three-fourths 
 strontium chloride of some forty readings ; no cell was read less than four 
 times at each temperature. 
 
 It is thus evident that the control of the work depended upon the 
 graphs, Figs. 3 & 4. While some of the values depicted upon the graphs 
 are the results of less than a dozen readings, it should be noted that neigh- 
 boring points on the same smooth line are established by many readings. 
 These latter values may therefore be regarded as control points or control 
 values. One cell only of each kind was set up in the bath at any one time. 
 The mean values in Table I are therefore dependent upon readings taken 
 on different days. It should be added that all the cells except those noted 
 below were read over a period of at least three days and frequently a week. 
 The values for the one-tenth molal strength of the double cells are the only 
 ones which depend upon one day 's readings. It is apparent that the values 
 obtained represent readings which were made at different times over a 
 considerable period and should therefore be easily reproducible. 
 
THERMODYNAMIC PROPERTIES OF 0.1 M HC1 IN CaCh, SrCb AND BaCb 15 
 
 The variation in the e. m. L values of ten of the cells amounted to 
 approximately one-tenth of a millivolt. In six, the variation ranged from 
 two-tenths to five-tenths. In the case of the three-tenths barium chloride 
 and of seventy-five hundredths calcium chloride the values given in Table I 
 are each the result of two sets of independent readings which varied by one 
 millivolt but these values are the only ones of the kind in the table. It 
 is believed that the cells were reproducible to within 0.2 of a millivolt. 
 
 The values found for the temperature coefficients are given in Table 
 
 III. 
 
 TABLE III. 
 
 AE 
 AT 
 
 BaCl 2 
 25-ll8 ; 30-25 
 
 DOUBLE CELLS 
 
 SrCl 2 
 25-18 ' ' 30-25 
 
 CaCl 2 
 25-18 36-25 
 
 .1 
 
 .2 
 .3 
 .5 
 .75 
 1.00 
 1.3 
 
 +0.000125 +0.000098 
 +0.000092 +0.000069 
 +0.000064 +0.000044 
 +0.000018 +0.000000 
 -0.000028 -0.000046 
 -0.000070 -0.000089 
 -0.000120 -0.000140 
 
 +0.000108 +0.000083 
 +0.000062 +0.000044 
 I +0,000027 +0.000012 
 -0.000025 -0.000040 
 -0.000076 -0.000095 
 -0.000120 -0.000146 
 
 +0.000098 : +0.000070 
 +0.000049 +0.000019 
 +0.000010 -0.000020 
 -0.000053 -0.000082 
 -0.000117 -0.000145 
 -0.000172 -0.000200 
 
 These values were obtained by plotting the differences in voltage at 18, 
 25 and 30 and continuing the measurements until acceptably constant 
 results were obtained. In certain cells, notably the calcium cells, the var- 
 iation was remarkably small, in fact so little as 0.003 millivolt. In other 
 cells the variation was larger. It is believed that the temperature coeffi- 
 cients are reproducible to within zt 0.005 millivolt. 
 
 TABLE II. 
 
 E. M. JF'S. FOR CON. KCl CELLS 25 
 
 0.1 
 
 0.2 
 
 0.3 
 
 0.5 
 
 0.75 
 
 1.00 
 
 1.30 
 
 BaCl 2 
 
 0.00140 
 0.00301 
 0.00480 
 0.00882 
 0.01432 
 0.01989 
 0.02658 
 
 SrCl 2 
 
 0.00160 
 0.00337 
 0.00530 
 0.00959 
 0.01531 
 0.02141 
 
 CaCl, 
 
 0.00194 
 0.00390 
 0.00599 
 0.01041 
 0.01641 
 0.02310 
 
16 THERMODYNAMIC PROPERTIES OF 0.1 M HC1 IN CaCh, SrCb AND BaCl* 
 
 The voltage values for the half cells (Fig. 2), subtracted from the 
 HC1 no salt value mentioned above (0.3100), are given in Table II, and 
 are plotted in Fig. 4. 
 
 F 'IG. 4. 
 
 ff?ATE 
 ClLO#/t 
 
 f Cr, 
 
 00O8 ffO/O 00'? 
 
 FIG. 4 
 
 The electromotive force readings were corrected for partial hydrogen 
 pressure by direct reading of the correction from graphs showing varia- 
 tion of voltage with barometric pressure for each one of the three temper- 
 atures at which measurements were made. The values for the e. m. f. 
 indicated on the chart were derived from the expression (Harned loc. cit.) 
 
 RT 
 E = In 
 
 760 
 
 PP-PH.O 
 
 It should be stated that considerably more difficulty was experienced 
 in measuring the concentrated electrolytes than with the more dilute, both 
 in establishing electromotive force values and in determining temperature 
 coefficients. It is here suggested that this difficulty was possibly caused by 
 an appreciable solubility of the calomel electrode in the concentrated solu- 
 tions of the salts under consideration. 
 
THERMODYNAMIC PROPERTIES OF 0.1 M HC1 IN OaCb, SrCh AND Bad* 17 
 
 
 III. (a) THE FREE ENERGY AND HEAT CONTENT 
 INCREMENTS OF THE CELL REACTION. 
 
 The decrease in free energy resulting from the reaction in the cell of 
 
 2 HgCl+H 2 = 2 Hg+2 HC1 (0.1M) 
 
 has been computed from the values for the electromotive force given in 
 table IV for 18, 25 and 30 by multiplying each value there given by 
 2 x 96500. 
 
 TABLE IV. 
 
 c 
 
 Bad, 
 0.00 
 0.1 
 0.2 
 0.3 
 0.5 
 0.75 
 1.00 
 1.3 
 
 0.39785 
 0.37443 
 0.36273 
 0.35458 
 0.34142 
 0.32806 
 0.31727 
 0.30442 
 
 E 2B 
 
 0.39898 
 0.37530 
 0.36337 
 0.35503 
 0.34155 
 0.32786 
 0.31678 
 0.30358 
 
 0.39963 
 0.37579 
 0.36372 
 0.35525 
 0.34155 
 0.32762 
 0.31633 
 0.30288 
 
 SrCI 2 
 
 0.1 
 
 0.2 
 
 0.3 
 
 0.5 
 
 0.75 
 
 1.00 
 
 0.37424 
 0.36265 
 0.35429 
 0.34049 
 0.32683 
 0.31555 
 
 0.37500 
 0.36318 
 0.35449 
 0.34031 
 0.32630 
 0.31471 
 
 0.37544 
 0.36340 
 0.35455 
 0.34011 
 6.32581 
 0.31398 
 
 CaCl, 
 
 0.1 
 
 0.2 
 
 0.3 
 
 0.5 
 
 0.75 
 
 1.00 
 
 0.37393 
 0.36271 
 0.35319 
 0.34022 
 0.32612 
 0.31296 
 
 0.37462 
 0.36305 
 0.35326 
 0.33986 
 0.32529 
 0.31176 
 
 0.37497 
 0.36315 
 0.35316 
 0.33929 
 0.32456 
 0.31076 
 
18 THERMODYNAMIC PROPERTIES OF 0.1 M HC1 IN CaCb, SrCb AND BaCb 
 
 The decrease in free energy thus determined for 18, 25 and 30 degrees 
 is given for each concentration of the salts in Table V, columns 2, 3 and 
 4. 
 
 BaCl 2 
 
 0.00 
 
 0.10 
 
 0.20 
 
 0.30 
 
 0.50 
 
 0.75 
 
 1.00 
 
 1.3 
 
 SrCl 2 
 
 0.1 
 
 0.2 
 
 0.3 
 
 0.5 
 
 0.75 
 
 1.00 
 
 CaCl 2 
 
 0.1 
 
 0.2 
 
 0.3 
 
 0.5 
 
 0.75 
 
 1.00 
 
 (-AF), 
 
 76785. 
 72265. 
 70007. 
 68434. 
 65894. 
 63316. 
 61233. 
 58753. 
 
 72228. 
 69991. 
 68378. 
 65715. 
 63078. 
 60901. 
 
 72168. 
 70003. 
 68166. 
 65662. 
 62941. 
 60401. 
 
 TABLE V. 
 
 (-AF) 25 (-AF) 30 
 
 AF 
 AT 
 
 C-AH) 
 
 77003. 
 72433. 
 70130. 
 68521. 
 65919. 
 63277. 
 61139. 
 58591. 
 
 72375. 
 70094. 
 68417. 
 65680. 
 62976. 
 60739. 
 
 72302. 
 70069. 
 68179. 
 65593. 
 62781. 
 60170. 
 
 77129. 
 72527. 
 70198. 
 68563. 
 65919. 
 63231. 
 61052. 
 58456. 
 
 72460. 
 70136. 
 68428. 
 65641. 
 62881. 
 60598. 
 
 72369. 
 70088. 
 68160. 
 65483. 
 62640. 
 59977. 
 
 +29.0 
 + 21.00 
 + 14.50 
 + 9.50 
 + 1.30 
 - 7.00 
 -15.50 
 -25.00 
 
 + 19.00 
 + 10.80 
 + 4.03 
 - 6.40 
 -17.50 
 -27.50 
 
 + 15.00 
 + 5.02 
 - 2.30 
 - 14.00 
 -25.50 
 -35.50 
 
 68361. 
 66175. 
 65809. 
 65690. 
 65474. 
 65363. 
 65758. 
 66041. 
 
 66713. 
 66935. 
 67225. 
 67557. 
 68191. 
 68934. 
 
 67832. 
 68579. 
 68864. 
 69646. 
 70386. 
 70749. 
 
 In determining the heat content function ( AH) column five, table 
 V, the expression 
 
 (-AH) = (-AF)-Td 
 
 (-AF) 
 dT 
 
 was used. But it was found at least to be impracticable if not impossible 
 to express AF) as a function of T and subsequently to differentiate the 
 equivalent expression 
 
 d(AF) AH 
 dt " T 2 
 
 and from this differentiated expression to calculate the numerical value 
 of (_AH). For it was evident that AF==f(T) varied markedly for various 
 concentrations of the three different salts. The values for 
 
 -AF } 
 
 Td 
 
 dT 
 
THERMODYNAMIC PROPERTIES OF 0.1 M HC1 IN CaCb, SrCb AND BaCh 19 
 
 were therefore determined by, a graphic method. The values of 
 the free energy decreases as given in columns 2, 3 and 4, Table V, 
 were plotted against their respective temperatures and a smooth curve 
 was drawn through the three points thus determined. The scales used for 
 plotting differed for the various groups of free energy values. In general, 
 when the variation of free energy with the temperature was slight, a large 
 scale was employed. Thus, in the case of five-tenths barium chloride and 
 of three-tenths calcium chloride a scale of five-tenths of a centimeter per 
 joule and of 2 centimeters per degree was used. For most of the concen- 
 trations, however, a scale of one-tenth or of one-fifth of a centimeter per 
 joule and of 1 centimeter per degree was found to be satisfactory. The 
 increase or decrease in energy for one-half of a degree on either side of 
 the 25 value was scaled off on the curve. The values thus obtained are 
 given in column five, Table V. 
 
 In order to check the values for 
 
 column five, Table V, each one of these values was plotted against the 
 corresponding salt concentration. All of these points should exactly deter- 
 mine a curve which should be perfectly smooth and give no evidence of 
 discontinuities. All points were directly on such curves except those for 
 five-tenths barium chloride and three-tenths calcium chloride; values for 
 these concentrations given in column 5, Table V, were scaled from the 
 last mentioned curves. These values did not lie directly on their respective 
 curves because it is evident from their free energy values for 18, 25 
 and 30, Table V, that each has a maximum free energy value between 
 18 and 25 which value could not be determined unless the temperature 
 coefficients for that particular temperature were known. 
 
 * -p 
 
 By multiplying each one of these values for by the value of 
 
 AT 
 
 T (=298) and subtracting the result from the corresponding value for 
 the free energy at 25, Table V, columns 2, 3 and 4, the values in joules 
 of the change in heat content function are determined. They are tabulated 
 in column five, Table V. 
 
20 THERMODYNAMIC PROPERTIES OF 0.1 M HC1 IN CaCb, SrCb AND BaCb 
 
 b. THE FREE ENERGY AND HEAT CONTENT DECREASE OP 
 
 TRANSFER OF 2 MOLS. OF HC1 FROM MeCl 2 (0) IN HC1 
 
 (0.1M) to HCL (0.1M). 
 
 The free energy and heat content function of the transfer of two gram 
 ions of hydrogen and chlorine are given in Table VI. 
 
 TABLE VI. 
 
 c 18 25 30 (-AH) 26 
 BaCl 2 
 
 0.1 4520. 4570. 4602. 2186. 
 
 0.2 6778. 6873. 6931. 2552. 
 
 0.3 8351. 8482. 8566. 2671. 
 
 0.5 10891. 11084. 11210. 2887. 
 
 0.75 13469. 13726. 13898. 2998. 
 
 1.00 15552. 15864. 16077. 2603. 
 
 1.3 18032. 18402. 18673. 2320. 
 SrCl 2 
 
 0.1 4557. 4628. 4669. 1648. 
 
 0.2 6794. 6909. 6993. 1426. 
 
 0.3 8407. 8586. 8701. 1136. 
 
 0.5 11070. 11323. 11488. 804. 
 
 0.75 13707. 14027. 14248. 170. 
 
 1.00 15884. 16264. 16531. -573. 
 
 0.1 4617. 4701. 4763. 529. 
 
 0.2 6782. 6934. 7041. -218. 
 
 0.3 8619. 8824. 8969. -503. 
 
 0.5 10923. 11410. 11646. -1285. 
 
 0.75 13844. 14212. 14489. -2025. 
 
 1.00 16384. 16833. 17152. -2388. 
 
 They were obtained by subtracting the values for the decrease in free 
 energy for each salt concentration (Table V) from the value for the free 
 energy given at the top of Table V, at salt concentration 0.00. In a similar 
 manner the heat content function values were obtained from Table V and 
 are given for 25 in the last column of Table VI. 
 
 c. INDEPENDENT ACTIVITIES OF IONS. 
 
 Maclnnes (loc. cit.) first clearly pointed out that in solutions of 
 different electrolytes having a common ion, the latter may have the same 
 activity independent of the accompanying ions. In particular the ratio of 
 
THERMODYNAMIC PROPERTIES OF 0.1 M HC1 IN CaCh, SrCb AND BaCb 21 
 
 the activity of the chloride ion in a given concentration of the latter to a 
 constant concentration of the same ion should be identical for barium, 
 strontium and calcium chlorides. The data obtained in this investigation 
 affords further proof of this theory. (Earned, J. A. C. S., 43, 1814, 
 1920.) 
 
 Mathematically the above mentioned ratio may be obtained by using 
 equations (8) and (9) of this paper. If (9) is subtracted from (8) we 
 have 
 
 that is, 
 
 - F[E (2) - E(2)l = RTl 
 
 _ [Eo (2) - E(2)] = 
 
 11 "" 
 
 a H(0.1) a C(0.1) 
 
 a H(0.1) 
 
 which reduces finally to 
 
 * a H(0.1) a Cl(0.1) 
 
 a H(0.1) 
 
 - [E (2) - E(2)] 
 
 a Cl(0.1) 
 
 Values for E (l) E(l) can be readily obtained from Table I by 
 subtracting the values for each concentration of the three chlorides from 
 the electromotive force value given at the head of the table as concen- 
 tration 0.00. These values are given in the first part of Table VII. 
 
 TABLE VII. 
 
 c 
 
 0.1 
 0.2 
 0.3 
 0.5 
 0*75 
 1.00 
 1.3 
 
 01 
 
 0.2 
 
 03 
 
 05 
 
 075 
 
 1.00 
 
 1.3 
 
 BaCl 2 
 0.02368 
 0.03561 
 0.04395 
 0.05743 
 0.07112 
 0.08220 
 0.09540 
 
 0.02228 
 0.03260 
 0.03915 
 0.04861 
 0.05680 
 0.06231 
 0.06882 
 
 SrCl 2 
 0.02398 
 0.03580 
 0.04449 
 0.05867 
 0.07268 
 0.08427 
 
 0.02238 
 0.03243 
 0.03919 
 0.04908 
 0.05737 
 0.06286 
 
 CaCl 2 
 0.02436 
 0.03593 
 0.04572 
 0.05912 
 0.07379 
 0.08618 
 
 0.02242 
 0.03203 
 0.03973 
 0.04871 
 0.05728 
 0.06308 
 
 The values for E (2)-E(2) are those given in Table II. The dif- 
 ference between these two sets of values is shown in the second part of Table 
 VII. The maximum difference for any one concentration is 0.00058 volts 
 and the average difference for the six concentrations given is but .00041 of 
 
22 THERMODYNAMIC PROPERTIES OF 0.1 M HC1 IN CaCk, SrCk AND BaCk 
 
 a volt. This is very small considering the high concentrations of the solu- 
 tions. The slight deviation still further substantiates the belief that com- 
 mon ion activities under the same conditions are identical. Harned in his 
 work with the alkaline metal chlorides (loc. cit.) likewise found that the 
 deviation present was well within the probable experimental errors. 
 
 d. THE CALCULATION OP THE ACTIVITY COEFFICIENTS OF 
 THE HYDROGEN ION AND THE CHLORINE ION AT 25 IN 0.1M 
 HYDROCHLORIC ACID CONTAINING BARIUM, STRONTIUM AND 
 CALCIUM CHLORIDES AT CONCENTRATIONS UP TO 1. M. 
 
 As shown above under the reaction of Independent Activities of Ions 
 [Bo(D - E(l)l - [E (2) - E(2)] = 5 
 
 a Cl(O.l) 
 
 The values in volts for the first member of the above equation are 
 given in the second part of Table VII. The value for a C i (0 .i) has been de- 
 termined by Harned (J. A. C. S., 44, 252, 1922), and calculated as .0779. 
 From the same source the value for a H is derived as 0.0868. Substituting 
 numerical values in the above equation and solving for a cl there is given 
 
 log a c . = log .0779 + 
 
 .05915 RT 
 
 where the constant .05915 represents the numerical values of x 
 logarithmic conversion factor. 
 
 In a similar manner the expression for an is 
 log a H = .o g . 07638+^ 
 
 The values of e. m. f. for a cl were obtained from the first part of 
 Table VI and those for an from Table II. The values for a c i and a H 
 as calculated above are given in Table VIII. 
 
 TABLE VIII. PART 1. 
 
 Values of 
 
 c BaCl 2 SrCl 2 CaCl 2 
 
 0.1 0.18544 0.18617 0.18645 
 
 0.2 0.27712 0.27530 0.27105 
 
 0.3 0.35760 0.35817 0.35746 
 
 0.5 0.51684 0.52638 0.51883 
 
 0.75 0.71090 0.72684 0.72414 
 
 1.00 0.88097 0.90003 0.90790 
 
 1.3 1.13508 
 
THEBMODYNAMIC PROPERTIES OF 0.1 M HC1 IN OaCl, SrCb AND BaCh 23 
 
 TABLE VIII. PART 2. 
 
 Values of (EH) 
 
 c Bad, SrCl 2 CaCl 2 
 
 0.000 0.0868 0.0868 0.0868 
 
 0.100 0.0969 0.0974 00987 
 
 0.200 0.1029 0.1042 0.1064 
 
 0-300 0.1102 0.1127 01151 
 
 0.500 0.1290 0.1332 01371 
 
 0.750 0.1599 0.1661 0.1735 
 
 1-000 e 0.1984 0.2105 0.2248 
 1.3 0.2577 
 
 SUMMARY. 
 
 1. Measurements of the electromotive forces of the cells 
 
 H 2 I MeCl 2 (c) in HC1 (0.1) | HgCl | Hg 
 
 at 18, 25 and 30 containing barium, strontium and calcium chlorides, 
 have been made. 
 
 2. Measurements of the cells 
 
 H 2 | MeCl 2 (c) in HC1 (0.1) | KC1 (Sat.) | HgCl | Hg 
 
 at 25 containing barium, strontium and calcium chlorides, nave also been 
 made, 
 
 3. Values for the cells 
 
 H 2 | HC1 (0.1) | HgCl | Hg 
 and H 2 | HC1 (0.1) | KC1 (Sat.) | HgCl | Hg 
 
 at 25 were checked with values of the same cells found by other investi- 
 gators. 
 
 4. The values for the free energies and heat content decreases of the 
 cell reaction 
 
 H 2 f 2 HgCl = 2HCl (0.1)+2Hg 
 
 in the presence of barium, strontium and calcium chlorides, respectively, 
 have been computed. 
 
 5. The decrease in free energy and heat content function of transfer 
 of the chlorine and hydrogen ions respectively from MeCl 2 (c) in HC1 
 (0. 1M) to HC1 (0.1) have been compiled. 
 
 6. The independent chloride ion activity in the various salt solutions 
 proposed by Maclnnes and found to hold within narrow limits by Harned, 
 has been further substantiated. 
 
 7. The activities of the hydrogen ion and the chlorine ion at 25 in 
 0.1M hydrochloric acid containing barium, strontium and calcium chlorides 
 at concentrations up to l.M have been found. 
 
< -ay lord Uros. 
 
 Makers 
 
 Syracuse, N. Y. 
 PAT. JAN, 21, 1908 
 
 494210 
 
 UNIVERSITY OF CALIFORNIA LIBRARY