THE PORTAL OXIDATION POTENTIAL OF THE CERIC-CEROUS SULFATES By JOHN kcCALLULi A THESIS Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 19US ACKNOWLEDGMENT The writer wishes to thank Professor D. T. Ewing for his guidance and help in this in­ vestigation* His tolerance toward and faith in a young student is appreciated* ■JHHHfr -K-tt <- The Formal Oxidation Potential or the Ceric—Cerous Electrode in the Presence of Ammonium Sulfate The oxidation-reduction potential of ceric and cerous salts has been studied by Baur and Glaessner (1), Kunz (2), Noyes and Garner (3), Smith and Getz (U), and Sherrill, King, and Spooner ($)• Each of these authors has published one or more value, de­ pending on the anion and the amount of acid present. Thus Baur and Glaessner obtained values of 1.8U and 1.70 volts in nitric and sulfuric acids respectively. Kunz obtained values of l.UiU and 1.U60 in 1.0 and 0.5 molal sulfuric acid respectively. Noyes and Garner have published potential values of 1.610U, 1.6096, and 1.6085 volts for the cerous-ceric electrode in 2.0, 1.0, and 0.5 molal nitric acid respectively. Smith and Getz studied cerium chlorides, sulfates, nitrates, and perchlorates in the respective acids and obtained values in the order given ranging between 1.28 for chloride to 1.8k for perchlorate. Sherrill, King, and Spooner found the said standard potential, in perchlorate medium, to vary with the concentration of perchloric acid between 1 .6 U0 and 1 .7 3 1 volts. Ceric and cerous amnonium sulfates exhibit a greater solu­ bility and greater stability in sulfuric acid solutions. Further, cerium solutions are often used volumetrically in the presence of ammonium salts. For these reasons, Ewing and Saltonstall (6 ) have measured the potential of the ceric-cerous electrode in sul­ furic acid solution, utilizing double salts of cerium, ceric and -1 cerous ammonium sulfates, and with measurements at 15°, i'S*, and 3 5 °C have obtaiiied a temperature coefficient for this cell. Recent completely independent measurements of the ceric-cerous electrode made in this laboratory with ceric and cerous ammonium sulfates, have corroborated results obtained by Ewing and Salton— stall. The purposes of this investigation were, then, to measure the potential of the ceric-cerous electrode in sulfuric acid solu­ tion, utilizing double salts of cerium, ceric, and cerous ammonium sulfates; to determine the effect of the ammonium sulfate upon the potential of the electrode, and from these data to calculate the decrease in free energy and decrease in heat content for the reaction 4 Ce ^ ► Ce++'t' + H+ The cell measured was: Pt, H2 4 HgSO^CO.Sf), H2 SCW0.5f) + 2(NH^)2 SO^Ce(SO^)2 (c") 4 -2- (NH, )oS0. Oe (SO, ) (c*), Pt **■ 2 U 2 U 3 Apparatus and materials Preparation and Analysis of Solutions.-Ceric and cerous amnonium sulfates corresponding to the formulas 2(NHi )~S0. Ce(SO, ) 2H 0 and (NH ) SC Ce (SO, ) 8 h 0 were prepared * 2 k U 2 2 h 2 especially for this work (7). I 2 U 3 2 A saturated solution of each of these salts was made in 0.5m sulfuric acid. The ceric salt was reduced with 30 ;? hydrogen peroxide and an absorption spectrum was taken on each of these solutions using a 5 cm. cell in a Cenco-Sheaid Spectrophotelometer. Since no absorption bands could be found, other rare-earth salts were presumed to be ab­ sent. Lanthanum ammonium sulfate was added by increments to one of the cells until its concentration represented 10 ^ of the salts present. The effect of this added impurity could not be detected. A stock solution of 0.5000 t. 0.0005 molal sulfuric acid was made by diluting the acid with conductance water. The pre-cal- culated amounts of cerium salts needed were added to a portion of this acid. This solution was then analyzed according to the methods of Willard and Young (£), using o-phenathroline ferrous canplex as indicator. A correction was made for the ferrous iron present in the indicator. The ferrous sulfate solution was standardized immediately before use with a ceric sulfate solution which had been standardized against a Bureau of Standards sodium alate. The method of Walden, Hammett, and Chapman (9) was followed. Analyses for ceric and cerous cerium were made before and after a potential measurement and the latter analyses were used in calculations* Weight burettes were used throughout* All cerium concentrations are expressed in millimoles of cerium per thousand grams of solution. The Electrolytic Cell*-The assembled cell consisted of four electrodes. Each half-cell, constructed from pyrex tubing, was closed by a ground glass joint bearing platinum electrodes* Each cerium electrode is connected to each hydrogen electrode through a flowing junction (10). This design permits the potential to be measured four ways and all values given are the average of four such measurements* J{ydrogen for the reference electrode was generated by electrolysis of a 15% solution of sodium hydroxide between nickel gauze electrodes* The gas was passed over a heated platinum spiral and through a saturating vessel containing sulfuric acid of the same concentration as that used in the half—cell* Nitrogen was passed through the cerium solution to exclude air and to gently agitate the solutions. Tank nitrogen was used after purification by bubbling through alkaline pyrogallol solution, washing with water, and passing over a heated copper gauze in a combustion fur­ nace. The gas was passed through a saturator prior to entry into the cerium half-cells* Vapor traps assured a hydrogen, or a nitro­ gen, atmosphere and the entire apparatus was immersed in a bath maintained at 1 5 *0 0 , 2 5 .0 0 or 3 5 .0 0 1 0 .0 1 ° C. -U- Platinum electrodes in the cerium half-cells were bright while those in the hydrogen half-cells were prepared according to the directions of Popoff, Kunz, and Snow (11) with the exception that they were not gold-plated. Method of Potential Measurements.-Early measurements were carried out with a Queen Standard potentiometer, Model E—30 I4.O, in conjunction with a Leeds and Northrup Type R galvanometer. Recent duplicate values were obtained with a Wolff potentiometer, No. 7012, and a similar galvanometer. The system was shielded in the manner recommended by White (12). An Eppley standard cell, measured and certified by the U. S. Bureau of Standards, was the standard of e.m.f. The cerium half-cells were flushed out with purified nitro­ gen for a time and hydrogen half-cells were flushed with puri­ fied hydrogen. The half-cells, the inlet tubes and traps, and the corresponding half of the flowing junction were rinsed several times with the solutions to be studied before filling. The complete cell unit was inserted in the constant temperature bath with very slow flow of hydrogen and nitrogen. The flowing junction was operated only a few minutes before taking a measure­ ment. Readings were taken every one or two hours until equilib­ rium values reoccurred. Only those values which checked four ways, i.e., against both hydrogen electrodes, were accepted as equilibrium values. The partial pressure of the hydrogen gas was calculated as outlined by Ellis (13) except that no allowance was made for the variation of gravity at this latitude. The Observed and Computed Electromotive Forces In Table I are recorded the electromotive forces at various concentrations and at three temperatures. The formal oxidation potential e £ has been derived with the electrode potential equa­ tion and the following considerations. The change of state in the cells considered and for the passage or one faraday may be represented by Ce r H Ce -- and the electromotive force is given by E _ E° - 2 -3°3RT 1 x AH* aC e ^ " x where a denotes activity. PH2 Nothing is known of the activities of the ceric and cerous ions so that, in conformity with current methods for estimating oxidation-reduction potentials, concentra­ tions are used in place of activities; that is, the ratio of the activity coefficients of the cerous and ceric ions is assumed to be unity. The activity coefficient of the hydrogen ion is constant in all cells since the sulfuric acid concentration is constant. This quantity is difficult to estimate since it arises from an unsymetrical electrolyte and non-thermo-dynamic assumptions be­ come necessary. For these reasons, the correction is not made. -6- Thus all values are referred to the hydrogen electrode in 0.5 molal sulfuric acid. This method of calculation allows direct comparison of our data with values published by Kunz (2), who performed similar experiments with the ordinary ceric and cerous sulfates. At the same time sufficient data is included to allow future correction for reference to the standard hydrogen elec­ trode. Mean activity coefficients of sulfuric acid are now available but their use in cases such as this is questionable. This point is under consideration. The last column of Table I is thus calculated with the Equation* ^observed) = Ef ~ £^2|£2_log --CCer *** x H Those cells marked 11S" are measurements of Saltonstall (6 )j those marked "L” are measurements of LlcCallum (19U7). -7- TABLE I Observed and Corrected E3e ctrcmotive Forces at 15, 25, and 35°C Temp. Cell # Ce++*++ Ce Ce /Ce E (observed) I5°c. 1*M 2S Us 11S im 15s 22S 25s 28S 25°C. 5m 3S 5s 13S 2M 19S 2US 27S 35°c. 6l: is 7S 9S 31' 2OS 23S 26S 20.28 19. 8U 15.86 12.00 11.9U 8.059 5.?96 U.0U2 2.025 1.01U 1.013 20.28 19.85 16.05 11.9U 11.9U 7.95U 5.323 2.007 1 .011* 20.28 19.86 16.00 12.08 11.9U 7.962 5.299 2.012 1.013 1.025 1.012 1.03U 1.699 1.051 1.055 1.013 1.016 1.012 1.012 1.021 1.692 1.U603 1.U60U 1.U608 1.U616 1.1*623 1.U618 1.U502 1.U623 1.1*630 1.1*610 1.1*612 1.U617 1.U62U 1.1*631 1.1*631 1.U639 1.U6U1 1.1*61*9 1.U570 1.U569 1.U578 1.1*583 1.U592 1.U591 1.U577 1.1*582 1.1*589 1.U595 1.1*595 1.U60U 1.U610 1.U619 1.UU68 1.057 1.U597 l.oiU 1.U5U1 1.1*532 1.U551 1.U555 1.1*562 1.1*563 1.1*1*36 1.1*570 1.020 1.007 1.027 1.012 1.026 1.701 1.058 E° (volts) 1.U5U7 1.1*558 1.1*565 1.U572 1.U576 1.U562 1.U586 1.U596 Summary and Discussion It may be seen from Table I that the formal oxidation poten­ tial, E°, is decreased by an increase in the concentration of the cerium salts. This effect is opposite to that observed by Kuna. o At 25 C. an extrapolation to zero concentration of cerium leads to a value of 1.1*626 volts. This is the value which should in­ clude no liquid-junction potential and may be compared with Kunz's formal oxidation potential of 1.1*602 volts. The effect of ammonium sulfate upon the formal oxidation potential of the ceric-cerous electrode in sulfate medium is small (at most U.Omv in the range studied.) Its presence, however, tends to decrease the observed electro-motive forces. Kunz has demonstrated that a decrease is also produced by additional sul­ furic acid. Table II has been obtained by a graphical extrapolation to zero cerium concentration. The formal oxidation potentials thus obtained were used in the calculation of the temperature coeffi­ cient of the cell, the decrease in free energy (-AF), and the de­ crease in heat content (-4 H) for the reaction ^H^Cl atm.) + Ce*'*'4‘+ — Ce"4-*4, ■+ H+ in 0.5 molal sulfuric acid. The Gibbs- Helmholtz equation was used for the calculation of -fiH. -5- TABLE II Temp. (°C) 15 25 35 Temperature Coefficient (Volts/degree) -0.00033 -0 .0 0 0 2 7 -0 .0 0 0 2 0 - AF (calories) 36,033 35,5U7 3 5 ,0 5 0 -10- -AH (calories) E? (volts) 33,795 33,726 33,673 1.1*656 1.1*626 1.1*603 REFERENCES (1) E. Baur and A. Glaessner, Z. Elektrochem, 9, 53U (1903) (2) A.H. Kunz, J. Am. Chem. Soc., 53, 96 (1931) (3) A.A. Noyes and C. S. Garner, ibid., 58, 1265 (1936) (U) G.fT* Smith and C. A. Getz, Ind. Eng. Chem., Anal. Ed., 10, 191 (1936) (5) M. S. Sherrill, C. P. King, and R. C. Spooner, J. Am. Chem. Soc., 65, 170 (19U3) (6 ) R. E. Saltonstall, Ph. D. Thesis, Michigan State College (1935) (7) Oscar T. Coffelt, Jackson, Michigan (6 ) H. H. Willard and P. Young, J. Am. Chem. Soc., 50, 1322, 1379 (1926) (9) G. H. Walden, Jr., L. P. Hammett, and R. P. Chapman, ibid., 55, 2U69 (1933) (10) A. S. Lamb and A. T. Larson, ibid., U2, 229 (1920) (11) S. Popoff, A. H. Kunz, and R. D. Snow, J. Phys. Chem., 32, 1056 (1928) (12) W. P. White, J. Am. Chem. Soc., 36, 2011 (191U) (13) J. H. Ellis, ibid., 38, 737 (1916) -11- The Formal Oxidation Fotential of the Ceric-Cerous Sulfates Oxidation—reduction potentials of ceric-cerous salts have been reviewed in our previous paper (1). All these previous determinations have been carried out in solutions with relatively high acid concentrations. Kunz (2) measured the potentials in 0.5 and 1.0 molal sulfuric acid. Noyes and Garner (3) made measurements in 0.5, 1.0, and 2.0 molal nitric acid. Smith and Getz (U) extended the measurements to acid concentrations as high as 8 normal. Sherrill, King, and Spooner (5) have measure­ ments in perchloric acid from 0.2 to 2.U molal. In all these studies, the concentration of the cerium salts was of the order of 0 .0 0 1 to 0 .1 molal. Kunz, and Noyes and Garner, found little change in poten­ tials for different acid concentrations in sulfate or nitrate solutions, but Smith and Getz and Sherrill, King and Spooner found the potential to increase over 1 0 0 millivolts as the con­ centration of perchloric acid increased* This effect is opposite to that observed in sulfate medium where Kunz has shown an increase in concentration of sulfuric acid produces a decrease in the com­ puted e.m.f. Ceric salts hydrolyze easily but extended measurements to the more dilute acid concentrations should provide additional insight to the discrepancies that exist in ceric-cerous systems. To this end two series of measurements have been carried out in -12- the more dilute solutions; one in which the concentration of cerium sulfates iras kept constant and the sulfuric acid content was lowered and a second in which the concentration of all con­ stituents was decreased by the simple addition of water. Measurements were made on cells of the type, (1) Pt, Hg+HgSO^n^), H2 S0^(ml )+Ce2 (S0li)3 (m2 )+CeCS0^)2 (m^), Pt The measurements on Series II have been carried out at three temperatures • Apparatus and Materials Preparation and Analysis of Solutions.-Cerium salts pur­ chased frcoi the 0. F. Smith Chemical Co. were used* Ceric hydrogen sulfate, calculated as Ce(HSO, ) , was analyzed to be U I4, 91% pure* This salt was used without further purification* The cerous sulfate was heated at UOO-U500 C according to directions by Mellor (6 )* This dried salt, calculated as Ce2 (SO^)^, was analyzed to be 90% pure and was used in this form. A saturated solution of each of the salts was made in 0.5m sulfuric acid* The ceric salt was reduced with C* P. 30% hydrogen peroxide and an absorption spectrum was taken on each of these solutions using a 5cm. cell in a Cenco-Shear Spectraphotolcmeter* Since no absorption bands could be found, the remaining percentage impurities of the above cerium salts was assumed to be water. The cell solutions for the rirst series of measurements were made up as follows. A stock solution of 0,5000 i 0.0005 molal. sulfuric acid was made by diluting the acid with a good grade of conductance water* For the first cell, the pre—calcu­ lated amount of cerium salts needed to make the solution 0 .005 m with respect to Ce(S0 ^ ) 2 and 0 .0025 m with respect to 0 6 2 (8 0 ^)^ were added to a portion of this acid. This solution was then analyzed according to the methods of Willard and Young (7) using o—phenanthroline ferrous complex as indicator* -1U- In this and subsequent cells, a correction was made for the ferrous iron presei+ in the indicator. The ferrous sulfate solution was standardized immediately before use with a ceric sulfate solu­ tion which had been standardized against a Bureau of Standards sodium oxalate. was followed. The method of "Walden, Hammett, and Chapman (8) Analyses for ceric and cerous cerium were made before and after a potential measurement and the latter analyses were used in calculations. For the remaining cells of this first series, a portion of the stock acid was diluted with con­ ductance water and standardized. The resulting acid solution was then divided, cerium salts being added to half, as above, while the other half was used for the hydrogen electrode. The cell solutions for the second series of measurements were obtained from two stock solutions. These solutions were prepared by making a large quantity of approximately 0 .5>m sul­ furic acid. This was standardized and divided* To half was added cerium salts as for cell #1 in the first series* A portion of each stock solution was then diluted with water in exactly the same manner so that the sulfuric acid content in each solu­ tion would be the same. Standardization of each was carried out before and after a measurement at each temperature and the average of all analyses were used in the calculations. The Electrolytic Cell and Method of Potential Measurements are exactly the same as described in our previous paper (1 ) to which the reader is referred for details. -15- For observed potentials beyond the range of the potentiometer, a secondary standard cell was placed in series. The Observed and Computed Electromotive Forces The change of state for the passage of one Faraday through cell (1 ) may be represented by (2) £h * Ce^*4,— ce**4’ * H+ and the electromotive force is evaluated by the thermodynamic equation (3) E = E° - + F aCe+* ^i*xP2H 2 where arises from the small amount of cerium present in one half-cell, and a denotes activity. As nothing is known of the activity of the cerous and ceric ions and since the activity of the hydrogen ion in sulfuric acid is unknown, current methods for estimating oxidation-reduction potentials employ a quantity known as the "formal" oxidationpotential, E°(formal). hibited when This is taken to mean the potential ex­ all constituents are present in theamount formula weight per thousand grams ionization. of one ofsolvent withoutregard to Further, Kunz, Noyes and Garner, and our previous paper have shown that El of equation (3 ) is practically negligi­ ble so that under these conditions (U) E°(formal) - E + 21 1 _ F »Ce ^ ^ * P 4 H 2 -16- The electromotive forces at various concentrations of total cerium and sulfuric acid are recorded in Table I. The last column, E°(formal) was calculated by means of equation (1*). The molality of the hydrogen ion is taken to be twice that of the sul­ furic acid. TABLE I Observed and Computed Electromotive Forces Series Temper­ Cell m Ce^ ature § § xlO I 25°C. 6 7 8 9 II 25°C. 15°C. 5.081 13 16 17 5.738 5.735 2.808 2 .8 9 6 27 1.971* 1.182 0.7336 0.3718 11 5.738 1 .8 8 6 1.079 0.6735 0.3056 .2026 1 .0 0 3 2 0.1*970 .3300 .1967 .1 2 2 2 .0613U 1.1*619 1.1*767 1.1*867 1.1*990 1.1*625 1.1*615 1.1*599 1 .1*602 1.1*589 1 .1*526 .9505 .9562 .91*82 .9526 .91*25 .9631* 0.9363 .9355 .9363 .9237 .9176 .1 2 2 2 .06131* .9328 1.1*596 1.U73U 1.U835 1.1*956 1.5061 1.5089 5.738 5.735 1 .0 0 3 2 15 19 2 .8 9 6 2 .8 0 8 20 1 .1 8 2 0.1*970 .3300 .1967 -17- 1 .5 1 0 1 1.5185 .06131* 12 25 28 0 .9 5 2 2 .9 6 2 1 26 1.986 1.078 0.7336 0.6735 0.3718 0.3058 1.1*617 1.1*605 1.U567 1 .U521 1.1*1*28 .1 2 2 2 1.079 0.6735 0.3058 1.971* 1.1*609 1,1*711* 1.1*690 1.1*81*1 1.1*836 1.1*61*7 1.1*809 1 .1*900 1.5020 1.513U 1.5255 2 .8 9 6 23 E°(formal) E (observed) (volts) 0.9500 .951*9 .9550 .9500 .91*80 0.9537 0.1*970 .9696 .3300 .9778 .9711 .1967 1.971* 1.182 0.7336 0.3718 1 .8 8 6 2 1 .0 0 3 2 5.735 2.808 22 35°c. 5.31*6 1 .0 0 0 0 5 .2 2 0 5.035 0 .6 ll*2 8 .11*1* 5.285 .3928 1*.972 5 .2 21* .2931* 1*.996 ll* 18 II “h 5-U7U 10 21 21* II Ce^ xlO 1 .1*652 1 .1*658 1.1*639 1.1*61*3 1.1*639 1.1*616 1.1*601* 1.1*577 1 .1*562 1.U559 1.1*538 1.1*1*09 Discussion and Suranary Two cells shown in Table I showed visible evidence of hydrolysis* we see These are Cells #10 and #28. Excluding these values, thatthe formal oxidation potential is practicallyconstant over a 15 fold change of concentration of any or all constituents. There is a tendency for E°(formal) to decrease as the amount of acid decreases. However, neglecting this trend for the time being, we obtain the following averages: 15° E°(formal) . l.i*63U t 0.003 volts 25° E°(formal) « 1.U587 1 0.006 35° E°(formal) « 1.U566 ± 0.001* These values may be compared with values obtained by Kunz and in our previous paper when calculated with equation (U): Kunz J(25° < 1J?5° /^15° Ewing, ' Saltonstall, * 250 and kcCallum .35° 0.5ni HpSC) E°( formal) * 1.U603 1 .0 m H2 S0 ^ E°(formal) . 1 .U611 0.5m H9 S0, ^ u n E°(formal) - 1.1*656 n E°(formal) - 1.1*603 E°( formal) — 1 .1*626 The above values are seen to be well within the limits indi­ cated and thus extend the range of applicability of equation (1*) over a concentration range greater than thirty fold. The greatest discrepancy, however, is the constancy with which the formal poten­ tials increase with increasing acid concentration. This effect corroborates that observed by Sherrill, King, and Spooner in -18- perchlorate medium and is opposite to the lowering of potential which is often inferred from Kunz's data. Equation (U) and "formal" oxidation potentials in general are non—thermodynamic in that no allowance is made for incomplete chemical dissociation, activities, or the liquid junctions which are usually present. Such potentials are, however, of great practical use and the above data does show that equation (U) gives practically constant values over a wide range of concentrations. - 19 - REFERENCES (1) D. T. Ewing, R. B. Saltonstall, and J. mcCallum, (Unpublished Paper) (2) A. H. Kunz, J. Am. Chem. Soc., ibid., 53, 98 (1931) (3) A. A. Noyes and C. S. Garner, ibid., 58, 1265 (1936) (U) G. 7. Smith and C. A. Getz, Ind. Lng. Chem., Anal. Ed., 10, 191 (1938) (5) M • S. Sherrill, C. B. King, and R. C. Spooner, J. Am. Chem. Soc., 65, 170 (191*3) (6 ) J* W. Mellor, "A Comprehensive Treatise on Inorganic and Theoretical Chemistry," Vol. 5, P» 650, Longmans, Green, and Co., London, (192U) (7) H. H. Willard and P. Young, J. Am* Chem. Soc., SO, 1 3 2 2 , 1379 (1 9 2 8 ) (8 ) G. H. Walden, Jr., L. P. Hammett, and R. P. Chapman, ibid., 55, 21*69 (1933) -20- STANDARD "OXIDATION-REDUCTION" POTENTIALS ”Oxidation-reduction" potentials are usually restricted to those occurring when two soluble components are in contact with an inert electrode. A great many researches in this field have been carried out but results do not compare with other branches of electrochemistry. This is due primarily to two causes (1) oxidation-reduction potentials have been measured in concentrated solutions which usually involve the two soluble components plus an acid, multivalent ions, or chemical complexes. (2) Calcula­ tions are based on stoichiometric ionic concentrations without regard to dissociation, activity, or anions common to all con­ stituents. Thus studies of the ceric-cerous electrode have been made on ceric and cerous sulfates, nitrates, and perchlorates in the respective acids and calculations have been based on stoichio­ metric concentrations of the ceric, cerous, and hydrogen ions. In some systems an allowance is made for the activity of the hydrogen ion. In other less complicated systems such as the mercuric-mercurous electrode an allowance is made for the activ­ ity of the mercuric, mercurous, and hydrogen ions. But in no case, to our knowlede, is allowance made for the effect of the anion. This is contrary to methods in which other electromotive force problems are handled. -21- It was Taylor (1) who first pointed out that the E.M.F. of a cell with transference is solely a function of molecular free energies and not a function of ionic free energies. His con­ clusion is based on the fact that the activity or chemical poten­ tial of an individual ion cannot be accurately determined because of the existence of liquid junction potentials whose magnitude cannot be computed without a previous knowledge of the individual ionic activities that one wishes to measure. Later Guggenheim (2) extended this concept to all physicalchemical measurements by pointing out that the chemical potential of an individual ion has never been defined in terms of physical realities and therefore is without physical significance. How­ ever, he does conclude, "the ’mean activity coefficient* of a salt is defined, as is also the ratio of the activities or activ­ ity coefficients of two ionic species with the same charge". The"mean activity coefficient" of a salt, t z on the molal scale, is defined as (1 ) where V - Ifi- + V_ and V+ and \T _ are the number of positive and negative ions respectively into which the salt dissociates. Similarily the mean concentration, m^ on the molal scale, is defined as (2 ) where m is the molality of the salt. of a salt, as, is defined as -22- So that the mean activity (3) aa = - { V * * V-'*' » m/n*'" It follows from these fundamental definations, that the use of "mean activity coefficients" requires a knowledge of how a salt chemically dissociates. It is this fact, in turn, that has prevented their use in oxidation-reduction calcula­ tions, For example, most of the heavy metals hydrolyze easily and in most cases the required hydrolysis constant is unknown. In fact Swift (3) goes so far as to say that because the neces­ sary dissociation or hydrolysis constants are unknown, only "formal" oxidation-reduction potentials are of practical signifi­ cance. It is the purpose of this paper to treat certain available data in terms of "mean activity coefficients" and to show there­ by (1) the order of magnitude of difference between "formal" and "standard" cocidation-potentials and (2) that certain regularaties result through the use of mean activities which may, in turn, be used to interpret the chemical state of solutions. -23- Calculations.—As our first case let us take the eerie—cerous electrode in sulfate medium. Such a cell is represented by (h) Pt, H2(l atm.) + HgSO^n^), HgSO^n^) + Ce^SO^) + GeCSC^^n^), Pt and the change of state in terms of molecular species and for passage of one faraday is (5) H2 (l atm.) * Ce(SOu )2 (m3 ) ^Ce^SO^) (n^) + At 25°C. the potential of cell (U) is given by the electrode potential equation and equatioj^ (5) as (6) E a E° - O.^lElOg A C»2(80^)3 X AH? S0lf A Ce(SO^)2 Now let us assume 1CX)^ ionization of these constituents to give Ce , Ce , SC^ and H ions. We know this is not true (HSOj^ ions for example) but this point will be clarified later. (7\ (7) With this assumption and equation (3) we have *2 ACe(SOu)3 = A± A2 H2S0[^ = A i ' Y' $/2 = C2 - 3 > -2 (22 9± I'^'rj^Lul tc*2(SOk )3 V u '6 2 ACe(SOi,), = * ”♦ h 2 I4. <1 X.2 2) .11, y- 3 3 Ce(SOu )2 Substituting equations (7) in equation (6) we have (P) ^ E - E° - Q.O^l^ln.g H^S), M3 ' f 3 P Ce(SO^)2 m^, m2, and E are experimentally determined quantities. —21*.— (SQ).)•*. ^ \ S% iS avai^able ^ literature (U) and its value includes the allowance necessary for the incomplete dissociation of sul­ furic acid. (9) Collect all these known quantities together and call F.» » E r 0.059l5logV_ ^ 2 A1 ^ H2SCU ^ = 1,13 .5/2 E° - O.OS^l^log^Ce^CSOjJt^ ^Ce(SCu)2 The mean activity coefficients on the right-hand side of this equa­ tion may he obtained from a suitable form of the Debye—Huckel equations, namely (10) loe)fsalt= o salt 1 + where z^. and z.. are the charges on the positive and negative ions respectively, without regard to sign, A, ^ , and a are constants, and JA is the ionic strength. (11) In our case, by equation (10), lo6 ifCe2(S0j,)o= l o £^Ce(Sdh)o = ---- ------------ ------ --------------- l a (J.a.^ Combining equations (11) and (9) and rearranging terms we obtain (13) E* s E° — 0.5326A tffl 1. ■+ ^ a "a" is assumed to be a constant but its value is unknown. However, for aqueous solutions at 25°C, A = 0.5091 and ^ = 3»286xl0^. Sub­ stituting these values in equation (13) and rearranging terms, we have -25- (1U) E» f 0.2711 vV L° 3.309x10 The constants of equations (15), (16), and (17) are based on revised values of constants given by Van P.usselberghe (6) and Birge (7). tablec Values of given by Harned and Hamer (5). -26- TABLE I Series Cell # iff II (I5°c) II (25°c) II (35°c) “1 m2 xlO 3 m xlO^3 11 1U 18 22 23 26 0.5C16 0.21*58 0.1650 O.C5835 0.06112 0.03067 13 16 17 21 2h 27 0.5C16 0.21*58 0.1650 0.09635 0.06112 0.03067 2.665 1.10*8 0.5670 0.5910 0.3666 0.1855 5.735 2.608 1.886 1.075 0.6735 0.3058 12 15 1° 20 25 28 0.5016 0.21*56 0.1650 0.09835 0.06112 0.03067 2.869 1.10*8 0.9870 0.5910 0.3666 0.1659 5.735 2.808 1.886 1.079 0.6735 c.3058 2.869 1.1*1*8 0.9870 0.5510 0.3668 0.1655 5-735 2.808 1.68 6 1.075 0.6735 0.3058 E Ioiiic (volts) Strength 1.1*653 l.lt613 1.1:903 1.502U 1.5139 1.5260 E» (&q.l6) 1.617 1.1*355 0.8009 1.1*1*58 C.5321* 1.1*502 O.3 I66 1.1*586 0.1970 1.1*61*7 0.09667 1.1*761* (Eq. 9) i.hezs 1.617 1.1*279 1.1*776 0.8009 1.1*363 1.8673 0.5321* 1.1*1*20 1.1(697 0.3169 1.1*508 1.5107 0.1670 1.1*559 1.5153 0.0981*7 1.1*61*0 (Eq 17) 1.1*210 1.1*605 1.617 1.1*71*3 0.8009 1.1*289 1.1*61*1* 0.532U 1.1*31*1 1.8.567 0.3169 1.1*1*32 1.5072 0.3970 1.1*1*61 1.5098 0.0981*7 1.1*512 -27- E" (E°-E? xlO- (Eq.16) E°=l.f 1.7621* ill*.5 1.6758 71.32 51*.5! 1.6377 1.6032 37.& 1.5768 2 6 .9f 1.5570 15. 1*3 (Eq.15) 1.7727 1.6789 1.6398 1.6031* 1.5762 1.51*91 (Eq.3 7) 1.7850 1.6650 1.61*29 1.601*3 1.5751 1.51*10 E°=l.f 111.1; 70.81 53.6J 3 6 . hi 2 6 . hi 16.11 E°=l-f 110.7 70.75 53.92 36.1*f 26.51 17.82 o Vy ClJ o s.^ l~f^y.tr^poUt< oh to oht<\ a = 7.150^. The data frcoi Series II used for these calculations is uni­ que in that the ratio, m^sn^sm^ is practically a constant. It may be easily shown from existing data that any other ratio of these constituents will give points which do not lie on these lines. This does not mean, however, that the above method of calculation is without value. This discrepancy does indicate (1) that the eerie and cerous sulfates are probably not present as such but exist in some complex form that depends on the ratio (2) that Ce44**, Ce444, h "*, and SO^ ions are pre in the solution, and (3) that the actual concentration of these ions is directly proportional to their stoichiometric concentra­ tions, for a given ratio There are at least two ways in which the given method of calculation may be verified. One is to apply the method to an entirely different oxidation-reduction cell. A second way is to test the "a" parameter, already obtained with the "extended" Debye—Huckel theory for unsymetrical electrolytes as developed -29- by Lalier, Gronwall, and Grieff (8)* Unfortunately, available data for oxidation-reduction cells are at concentrations too great for direct use of the Mextended" theory tables. a preliminary test was made in the following manner: (15) was assumed to be valid. However, Equation An ionic strength was assumed such that the "extended'1 theory tables might be used. The con­ stants obtained frau equation (15) and Fig. 1, were substituted in the extended theory and an E° calculated. Results were somewhat unsatisfactory but did indicate that (1) the E° of cell (i±) is of greater magnitude than given by equation (15) and (2) the "a" parameter is larger than indicated above. The validity of equation (15) may also be tested with the mercuric-irercurous oxidation-reduction cell. (18) Pt, H2(l atm.) + HClO^rr^) , HClO^n^) -v Hg ^ C l O ^ O i ^) +■ ng(cio^)2(iL3), pt The change of state for passage of one faraday through cell (18) may be represented by (1?) |h 2(1 atru.) + HgfClOj^fni ) jHg^ClO^fii^) 4 HClO^m-^ and the electromotive force is given by the electrode potential ^ .. .. t / —»\ * rf-ir^O*-* i _ v _ )fH^2fc(ClOu)2*ull* (f HC1G Hg(C10u)2 E, m^, m2» and m are obtained from data given by popoff, Riddick, Worth, and Ough (9)« V^HClO^ is taken equal to the -30- ^ HCl values of Randall and Young (10). When all these known values are collected together and called E* and equation (10) is ap­ plied in the manner previously indicated, we obtain (21) E* s E t- 0.05Sl5log m2 " *1 1 )T ^C1 2^ E" s £» 4. 0.0^037^/u1 = E° + 3.266xl07a(E° -E*) In Table II are given the results of calculations on those cells in which the ratio is a constant. straight lines obtained. -31- Fig. 2 shows the TABLE II Cell a (Set B) III V VI VII D C G B 13 xlO 200 80 UO 20 IV V VI VII A B F A 120 80 UO 20 Tonic Strength E (Volts) E1 5.0 2.0 1.0 0.5 0.2300 0.0920 0.0U60 0.0230 0.880?0 0.89220 0.9013U 0.91026 1.00627 1.00860 1.01122 1.01301 1.01*961 1.03610 1.03060 1.02672 6.0 0.1560 U.o o.iouo 2.0 1.0 0.0520 0.0260 0.89615 0.90130 0.91032 0.9169U 0.99001 0.99118 0.99338 0.951*99 1.02560 1.02032 1.01398 1.00956 m - m xlO-3 E" (E°-E»). nxlO E —1.< 7.51*1 U.06U 2.312 1.361* E°=i.a -32- 5.297 U.131* 2.U21 1.U52 (Tt Uo'ipvty •-£ $ 7j VI 01 OS Q'h 0T OX 01 001 JOT 001 hOJ Fig. 2 corroborates the results obtained with the cericcerous cell (U)j namely, (1) when the ratio is a con­ stant, equation (21) is a straight line relationship and (2) different ratios of give different straight lines. appears that these straight lines are nearly parallel. It This fact again indicates that the mercuric and mercurous perchlorates are not present as simple Kg**, Hg2 anc* C10£ ions but they are com­ bined in some form which depends on the ratio nn If the interpretation of these regularities are correct, they may be used to tell us what ions are present in solution. For example, we have presumably shown that Ce , Ce H* ions are present in the solutions of cell (U). that HSO^” ions are present. ,SQ^ , and We know also Therefore if a straight line rela­ tion indicates certain ions are present and that their mean con­ centrations are proportional to the stiochiometric concentration, we should be able to set up the change of state in terms of these species and obtain straight line relations. In Table III are given calculations based on the following conditions: Case 1; Change of state for Cell (U): £h 2(1 atm.) + C e ^ S O ^ O ^ ) -^Ce(HSO^)3(m2)+H2SO^(m1) Ionization; Ce(HSC^)^= Ce*,f+* + Ce(HSOu)3= Ce'*"1’*’ + 3HS0U" H2S0a r 2H+ “* su~ -33- (22) E s E° - O.Q591^1og 2?m2 V ke(HSOh h mj 6Um3 X ^?S0}| (H.S0U)U E ’ - E f 0.0^91 5log__27ni?mj ^il?S0l,__________ 6Um ^ Z" - E* f 0.2!i09.y^ = E° 4 3.2£6xl07a(E°- Case 2: Change of state for Cell (1) 5ri0 (l atm.) + H ? Ce(S0, ) (m ) - ^ - i C e 9 (S0. ),0-o )H H SO. (m ) 2 2 U 3 3 2 Li 3 2 2 U 1 Ionization: HoCe(S0 ) = 2tif 4 Ce(S0, ) ‘ 4 3 ^3 Ce^SO^) r 2Ce*"+4‘ 4 350^ H 0Su, 2 U r 2H* + SO, u 1 '2m 5/2 ^ r5/2 (23) E = E° - 0.059151osi27^ '__ ?__ Q m9/2 . 9/2 1 ( H^SQ^ IT H 2 Ce(SOu )3 H.. E . 3.? T?Tt _ T?t 1 0.2711 3ase 3: = E° 4 3.286xl07a(E° Change of state for Cell (U) £h 2C1 atm.)4H2Ce(SO[4)3(m ) -^-HCe(S0j4)2 (m2) 4 H^O ^ n ^ ) Ionization: HoCe(S0i )_ - 2H^ 4 Ce(S0, ) ‘ 2 U 3 U 3 HCe(SCu)2 = H* + Ce(SOu)2~ H2SU^ ■ 2 (2U) E - E° - 0.059l5log 4 SOj^ \ §Ce(S0;,)Pm j *3 -3U- H 2 C e ^S0U^3 (2h) s ’ — e + o . o ^ i ^ i o g - I L . 1. 6 na50U_____________ *3 3 E" - E* + 0 . 1 2 0 5 ^ r E° -f 3-286xl07a(E° - E ’V w 1 Case U : Change of state for Cell (U) |.H (1 ate.) ^ HoCe(S0, )_(m )-5*-HCe(S0, ) (m )-*H SO. (m, 2 2 h 3 3 U 2 2 2 U ] Ionization: HoCe(S0. ) — + HCe(S0, )” 2 U 3 ~ U 3 HCe(SC^) 4 Ce(S0^)2“ h 2S0U z (25) 3r4 * SV E r E° - 0.055151 ( 2 “ if __ 2 m3 ^ H2Ce(SOu)3 E» - E f 0.Q59151O&-1! 2 ^.c2.S0.U_______________ -5 E" = S ’ = E° All of the calculations in Table III are based on the data of Table I. -35- TABLE III Ionic Strength ff 28 27 (equations 1.3757 1.3803 1.3780 1.3818 1.3812 1.3656 Ca: 13 16 17 21 2U 27 (equations 23) 1.565 1.2978 1.2700 0.7756 1.2562 0.5155 1.2365 0.3072 0.1505 1.2217 1.1516 0.0956 Ca: IT 16 17 (equations 1.3979 1.3989 1.3979 1.3951 1.3991 1.3980 Ca! TT 16 17 21 21 28 27 Ca TT 16 17 22) 1.597 0.7910 0.5257 0.3127 0.1985 0.0973 28) 1.528 0.7568 0.5027 0.2995 0.1361 0.0938 E" 1.6802 1.5986 29.01 1.5162 1.8678 1.8607 20.U7 16.23 21 1.0312 1.0616 1.0866 1.1033 1.1077 -36- 209.3 ■123.3 -90.6 -59.8 -Uo.o -15.1 (E° - 1 .3985) 1.5827 1.5037 1.U833 1.U650 1.8511 1.8388 1.2551 1.21*65 1.2255 27 10.11 (E° = 1 .1 3 0 0 ) 0.9585 1.2722 28 (E° - 1 .8180) 53.57 38.51 1.5527 E« » E» - E° 1.3007 1.2838 (eq jations 25) (E° - E xl0J 0.00 0.00 0.00 0.00 0.00 0.00 fi g. 3 O (Cwe 1 (jr-OiF-K)' j 7, 27, (1935) (5) A. S. Brown and D. A. Maclnnes, ibid., 57, 1356 (1935) (6) P. VanRusselberghe, ibid., 65, 12l*9 (19U2) (7) R. T. Birge, Rev. iiod. Phys., 233 (191*1) (6) V. K. Latter, H. T. Gronwall, and L. J* Crieff, J. Phys. Chem., 35, 221*5 (1931) (9) S. Popoff, J. A. Riddick, V. I. Worth, and L. D. Ough, J. Aim. Chem. Soc., 53, 1195 (1931) (10) 1*. Randall and L. E. Young, J. Am. Chem. Soc., 50, 995 (1928) -U3