EQUILIBIUIN CADMIUM IODIDESOLUTIONS
Jan., 1938
137
The average values of the constants at 184 and 1000 g. of water. To economize space, initial 194O, namely, 4.72 and 3.92, give the following amounts of substanms are not quoted. Inspecvalue for the heat of the reaction in aqueous solution of them would show that at each temperature the equilibrium was approached from both sides. tion In the experiments at 136O, benzoic acid alone C&IsCONHCH~COOH3- HIO = CaHsCOOH CH2NH2COOH; AH = -7850 cal. was directly determined in the equilibrium solutions, the hippuric acid as well as the glycine fiThe constant a t 136' calculated from the values nally present being calculated from the amounts of a t 184 and 194' is 13.06 as against the directly benzoic acid found and the known initial composi- determined average value of 13.23. tions of the solutions. On this account, less reThe free energies of benzoic acid and of glycine liance is placed on the 136' values. being known, as well as their solubilities, and that of hippuric acid, in water a t 25O, it is possible to TABLE I calculate the approximate value of the free energy Equilibrium amounts in grams Temp., Loss K OC. HrO B.A. H. A. G1. of hippuric acid. This is not done here, in ab184 12.124 0.1172 0.0125 0.3116 0.0001 4.71 sence of heat capacities and activities needed for .0005 4.76 .1164 .Old% .3482 184 10.554 calculation of an accurate value.
+
184 194 194 194 194 136 136
11.185 11.804 10.054 9.929 9.800 11.241 11.042
.1197 .1208 .1226 .1230 .1243 .1316 .1319
,0112 .0153 .0176 .0191 .0190 .0053 .0053
.2522 .3009 .3003 .2997 .3013 ,3030 .3031
.OOOO .0005
4.71 3.94 .o003 3.98 .0003 3.80 . 0000 3.94 13.09 13.36
SUmmmY The equilibrium in aqueous solution between benzoic acid, hippuric acid, glycine and water has been measured a t 136,184 and 194'. BURLINGTON,
[CONTRIBUTIONFROM TEE DEPARTMENT OP &EMISTRY
VERMONT RECEXVED NOVEMBER 30, 1937
OF
DUgE UNIVERSITY]
Equilibria in Cadmium Iodide Solutions' BY ROGERG. BATESAND WARRENC.VOSBURGH The equilibria in solutions of cadmium iodide mium iodide,' equilibrium constants were calhave been investigated by McBah, Van Ryssel- culated for the following reactions berghe and Squame2 and by Riley and Gallafent3 Cdiz Cd++ 21(11 with differing results. This investigation was CdIl CdI+ I(2) undertaken to check the previous results by an CdI+ Cd'+ I(3) electromotive force method that does not have the CdIsCd++ 31(4) objection of liquid junction potentials. The CdI" Cd++ 41(5) electromotive force of the cell
-+ + + + +
Cd(Hg)/CdIe(m) lCdIdm), HgzIdHg
(I)
was measured with varying amounts of either cadmium sulfate or potassium iodide added to the electrolyte, and with a cadmium iodide molality of 0.01 or 0.02. In cells in which the potassium iodide concentration was large, a cuprous iodide electrode was substituted for the mercurous iodide elecQode. From the results, together with the stoichiometrical,activity coefficients for cad(1) Part of a thesis e u b d t t e d by Roger G. Bates in p d a l fulfilment of the requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences of Duke Univerdty, June, 1937. (2) McBain, Van Rysselberghe and Squame, J . Phys. Chcm.. 98. 1006 (1931). (3) Riley and Gallefent, J . Cham. Soc., 622 (1932).
Experimental Methods
The apparatus, experimental methods and the preparation of most of the materials have been described in previous papers.436 A cadmium sulfate solution about 0.8 m w8s prepared from thrice recrystallized cadmium sulfate and standardbed by the evaporation to dryness od weighed samples and beating the residue at 500'. For the preparation. of the cell electrolytes that contained cadmium sulfate, the cakulated quantities of a carefuliy standardized cadmium iodide solution and the above cadmium sulfate solution were wpighed and diluted by weight to the desired malality. The electrolytes that contained potassium i d & were made by dissolving weighed portions of rec-ed m d carefully dried potassium iodideZin 0.01 or 0.02 m cadmium iodide solutions. A 1%copper amal(4) Bates and Vosburgh, THISJOURNAL, 59,1585 (1937). (5) Bates and Yosburgh, ibid., 69, 1188 (1937).
ROGERG. BATESAND WARRENC. VOSBURCH
1.38
gam was made by the electrolysis of a solution of copper sulfate. I t was filtered through a pin-hole in a filter paper A portion was diluted with an equal weight of mercury and compared with the original in an amalgam concentration cell with a copper sulfate solution as the electrolyte. The identity of the two samples indicated that the amalgam as prepared was saturated.0 Cuprous iodide was prepared by precipitation from solutions of recrystallized potassium iodide and cupric sulfate. In one preparation, 0 1 molar salts were employed a t room temperature. In another, 0.4 molar potassium iodide solution was added to 0.2 molar cupric sulfate solution a t about loo", and sulfur dioxide was passed in to prevent the accumulation of iodine. The two preparations when digested under water a t 85" for t!iree t o five days gave identical cuprous iodide electrodes. The procedure in the construction of a cuprous iodide electrode mas about the same as that followed in the construction of a mercurous iodide electrode. Cells with cuprous iodide electrodes did not agree well when the electrolyte was a cadmium iodide solution, but were quite reproducible in dilute potassium iodide solutions or when considerable potassium iodide had been added to the cadmium iodide solution, The mercurous iodide electrode is questionable with much potassium iodide present, because of the reaction of m c r c u r ~ uiodide ~ with the potaszium iodide.
Results The effect of the addition of cadmium sulfate t o the electrolyte of Cell I is shown in Table 1. Each electromotive force is the average for two cells that agreed within 0.12 niv. or less. The cells were measured at 30" and the electromotive forces at 25" calculated by rneaiis of the relation between electromotive force and temperature found for similar cells without added cadmium sulfate. Since the added cadmium sulfate has little effect on the electromotive force, its effect on the ternperature coefficient is probably small also. The last column in Table I gives the activity, h, of cadmium iodide calculated in the manner described in the previous paper.4 TABLE I CADMIUM-MERCUROUS IODIDE CELLS(TYPEI) CONTAINING CADMIm SULFATE CdIi," m
0.01000 .01006
-
CdSO,.
I>i c
711
Y
. .
0 5123 5123
1cd ) V
a? X 10'
0.5083 2.183 5083 2.183 .OlOO8 ,02016 5131 ,5091 2 052 ,5 165 5124 1.587 .01014 ,05071 ,1025 5208 5166 1 144 .01035 . . 4969 4932 7.057 .02015 7.006 ,02019 .01010 ,4970 4933 ,02033 ,02023 4975 4938 6.737 5 675 ,02036 .05091 ,4997 4960 ,5035 ,4997 4.257 ,02058 ,1029 This molality is designated in the discussion as M . 0 010%
(6) Richards and Garred-Themaq. Camugre: Insl No. 118. p. SO tl9Q9>,
Wash, Pub.,
1701.
60
The effect of the addition of potassium iodide to the electrolyte of Cell I is shown in Table 11. For cells in which the potassium iodide concentration was large, a cuprous iodide electrode was substituted for the mercurous iodide electrode. The relation between the mercurous iodide and cuprous iodide electrodes was determined by the Cell Cu(Hg)/CuI, KI(nz)/KI(m), Hg&/Hg
(11)
The best six cells (two of them with an electrolyte 0.02 molar with respect to both cadmium and potassium iodides) gave E25 = 0.13308 v. with an average deviation of * 0.09 mv.' The value 0.1331 v. was therefore adopted, allowing the calculation of the electromotive force of Cell I from the corresponding cell with a cuprous iodide electrode. Such calculated values axe given in the fifth column of Table I1 along with a number of similar electromotive forces that were observed directly . TABLE I1 CADMIUM-MERCUROUS IODIDECELLS (TYPE I) AND CADMIUM-CUPROUS IODIDE CELLS CONTAINING POTASCdIz," m
KI, ni
SlUM IODIDE En6 Ea
(HgzIn), v
Ens (obsd
(CUI), and calcd ) , b Y.
v
a2 X 107
0.01032 ... 0.5073 . . 0.5073 2.353 91023 ... ,5076 . .5076 2.299 ,01032 0.00740 .. 0 3715 .5046 2.913 01023 ,00824 ,5025 .. .5025 3.430 ,01032 .01615 .. .3669 .5000 4 201 ,01023 .02079 .. .3653 .4984 4.721 01023 ,03228 .4975 .. .4975 5.062 01032 .05293 .. .3641 .4972 5.182 ,01023 06253 .. .3w .4974 5 101 02020 . . .. .. .493lC 7.110 02020 .OM88 .4916 .. .4916 7 954 02020 .01065 .. ,3576 .4907 8.570 ,02020 .01219 .4903 .. ,4903 8 872 .0202U ,01850 .. .3561 ,4892 9.672 02020 .04842 .. .3553 .4884 10.27
.
' S e e footnote t o Table I. * The observed values are 0.1331 those for &a(HggI,); the calculated are &(CUI) Calculated for this molality from the data ref. 4. v
+
Discussion It is possible to check the compositions given by McBain, Van Rysselberghe and Squame2 by the calculation of the stoichiometrical activity coefficients for cadmium iodide from their cadmium ion, iodide ion and total cadmium iodide concentrations and the activity coefficients of Rielland.* I?)
With electrolytes of 0.1 n and saturated cadmium iodide soluWith 0.02 m
tions the electromotive force of Cell 11 was 0.1322 v.
cadmium iodide solution the results varied. ( 8 ) Kielland, Tarn JOURNAL, 69, 1675 (1937).
139
EQUILIBRIA LN CADMIUM IODIDE SOLWTU~NS
Jan., 1938
The results of this calculation may be compared with the activity coefficients of Bates and Vosburgh.*
A similar calculation was made from the activities in dilute cadmium iodide solutions not containing cadmium s ~ l f a t e . For ~ molalities of 0.001025, 0.002043, 0.005, 0.010 and 0.1023, the CdIz, c 0.005 0.01 0.02 0.05 0.10 0.20 X los were, respectively, 1.4, 1.7,2.9, y, calcd. 0.52 0.36 0.23 0.12 0.075 0.044 values of K1’ y, obsd. B. 4.2 and 4.4. J t is to be concluded that Equation and V. 0.49 0.38 0.28 0.17 0.11 0.069 1 does not represent the only equilibrium in a The calculated coefficients agree fairly well with cadmium iodide solution. Furthermore, the asthe observed in the more dilute solutions, but fall sumption that the only other molecular or ionic rather far below the observed in the more concen- species present is a complex anion leads to the prediction of decreasing values for K1’, when caltrated solutions. culated as above for the pure cadmium iodide In 0.01 m cadmium iodide solutions it is probsolutions. able that the quantity of complex anions conA calculation was made from the results in taining cadmium is small enough to neglect for a Table I of the equilibrium constant K3’ of the first approximation. This is in agreement with reaction the results of Riley and Gallafenta and was asCdI+ + IC d + + 21(34 sumed also by McBain, Van Rysselberghe and with the assumption of the absence of molecular Addition of cadmium sulfate increases the electromotive force of Cell I, indicating a cadmium iodide, Cd12, by means of the equation smaller cadmium iodide activity. Since this [CdI+][I-]fi_, Ks = (Cd++)(J-)* (7) must be mainly the result of a decrease in the ioIn this equation fl-l is the activity coefficient for dide ion concentration, it follows that the complex potassium chloridelo at the ionic strength of the anion concentration in the presence of cadmium solution in question. The right-hand term is the sulfate is less than in the pure cadmium iodide activity from Table I, as before. The molality solutions. of the ion CdJ+ was assumed to be given by the A preliminary calculation was made of the relation equilibrium constant of the reaction [CdI+] = 2M - [I-] (8) CdIz J _ Cd++ 21(1) in which M is the total molality of cadmium iodide on the assumption that this equilibrium accounts and I- was again calculated by an approximation for all of the difference between the activity of method from Equation 6. cadmium iodide and that of a typical bi-univaleiit CdSOl (m) 0 01 0.02 0.05 0.10 salt. The equilibrium constant, K,, was cal- K ~ x’ 103, M = 0.01 3.4 3.7 4.2 4.5 culated from the equation K,’ x 103, M = 0.02 3 I 3 3 3.9 4.2
+
+
lCdIz]Ki = (Cdt+)(I-)a
(5)
in which brackets indicate molality and parenthcses activity. The right-hand term of the aquation is the activity, aa, as given in Table I. ’The molality of un-ionized cadmium iodide, ICdI2.1, in the solutions containing added cadmium sulfate was calculated by subtraction of half the iodide ion molality from the total cadmium iodide molality, AI, as given in Table I. The iodide ion molality was calculated by a11 approxima tion method with the use of the equation (Cd++)(I-)* = [ C d + + l [ I - l 2j:-l
(6)
in which fi-l is the mean activity coefficient of barium chlorides a t the ionic strength of the cadmium iodide solution. CdSO4, m
&’ X lo’, M
= 0.01
0.01 3.4
0.02 3.0
0.05 2.0
(9) Tippetts and Newton, THISJOURNAL, 66, 1675 (1934).
0.10
1.3
Neither K1’ nor Ka’is of satisfactory constancy, but Ks’varies less than KI’. This was taken to mean that both ions are present and a larger por tioti of the total cadmium is in the form of the ion CdI+ than in the form of molecular cadmium iodide. Therefore, K 1and K Bwere calculated OH the assumption of the presence in the solution of both the ion CdI+ and the compound cadmium iodide. A plot of Ks’ against the molality of cadmium sulfate suggested that a maximum was being approached as the molality increased. If the increase in K3‘ was the result of a decrease in the quantity of molecular cadmium iodide present, as more and more cadmium sulfate was added, the maximum value of Kat should be the true value of K s . Accordingly, some values higher than 4.5 (10) Hnmed, ibid., 61, 416 (1929).
ROGERC;. BATESAND WARRENC.VQSBURGH
I4)
were a s w e d for Kg and corresponding X values for K1 calm from the data in Table J. The value of K:,that led to constant values for K1 was taken as the correct value. I t was assumed for the first approximation that the iodine in each solution was entirely in the form of the ion CdI+. The molality of the cadmium ion, [Cd-r+], was accordingly m‘-M in which m‘ was the molality of cadmium sulfate as given in Table I. Substitution of m’-M €or [Cd++] in Equation 6 gave a first value for [I-]. The graphical solution of the simultaneous equations m‘
-+-
-VI - [CdI j - [Cd+-j = iCdIS1 2M - [CdI”] - 11-1 c 2[CdIz1 1CdI-][I-]fi-, Ka = (Cd+’)(I-)’
1’01. 60
‘The data in Table IJ taken alone do not serve to distinguish between the two possible anions. They may be interpreted equally satisfactorily with either assumption, as shown in Table IV. The instability constant, K4, for the ion CdT3was calculated by means of the equation
1 [I-lY;-l (11) The molalities were calculated by means of the [CdII--]K4= [Cd +
+
equations
- 2[CdI?] + VZ’’-
2M
iZf
f C d I + ] - 3[CdI;1-] = 11-1
- [CdIt] - [CdI+] - [CdI,-I
(12) = [Cd-+j
(13)
(9)
and Equations 5, 6 and 7, with the use of the values of as, in Table 11. In Equation 12, m n is (7) the molality of porsSsium iodide. The assumpgave values of ICdlT] and IC~I.L] and a corrected tion is thus made that the ion CdI3- was the only value of [Cd++fwhich, substituted in Equation 6 complex ion present. The equations were solved with an appropriate change of activity coeffcient by a graphical method, and an approximation to correspond with the new ionic strength, enabled method was used for the calculation of the ionic a second, more accurate, value of [I-] to be ob- strength. A similar cakulation was made of the tained. The simultaneous equations were solved constant KSof the equation again with this new value of [I-] and the process [CdIi’lKs = [Cd+ + I [1-]4f;-, repeated until two successive approximations gave like values for the quantities involved. Then K , with the assumption that CdI4’ was the only complex anion present. The quantity of complex was calculated by Equation 3. In this manner, K1 and Ks were found to be 1.2 anion in the solutions containing only a little poX lo-* and 0.0053, respectively. Riley and Galla- tassium iodide was so small that errors of calculafent3 found 4.0 X and 0.0038. The values tion were large, and the results for these solutions found for K 1when KS is taken equal to 0.0052 are are not included in Table IV. shown in Table IZI TABLE IV rABLE
(10)
INSTABILITYCONSTANTS Kr AND Ks
111
TALTESOF K , WHEN K3 = O.OOb2 c d l r I l a ( ~ ~ ~ n) n i 0.01 o 01 0 01 0.02 no:! n o z o 02 c s s n 4 , m ( m ‘ i o 01 0.02 CJ 05 n 10 n.01 0 O L o O i o i n Ki X 10%
1.10 1.17 1 24
J 04
1.79
1.3.5
1 4h
1 74
When potassium iodide is added to 0.01 M cadmium iodide solution, the formation of a complex anion can be expected. McBain, Van Rysselberghe and Squaiice2 have assumed that the ion CdIa- is present in cadmium iodide solutions. Riley and Gallafent* roiicluded that both CdIa and CdIIp are present, the latter, however, in much smaller coricentration than the former. On the other hand, Cornec and Urbain” by a cryoscopic method, Jab** by a spectrophotometric method and Bourion and Rouyerla and Rouyer14 by a boiling point method obtained no evidence for the existence of the ion Cd13- in solution, Ending only the ion CdIs%. (11) Corncc and Urbain, Brtl. JOG ehirn. 88, 137 (IHI’J) (12) Job, Ann. cktm ,9, 185 11922328) (13) Bourion and Rouver, rbi (111 Rouxer ? b i d 13, 177 ‘I
Cdh,m X 10’ 10 23 10.23 10 X4 10.23 20.20 20.20 20.20 KI, m
x
k” x
10’
K,
10-
x
10.
20 70 72 28 52 43 62 53 1 2 . 1 9 18.50 48.42 1 2 1 0 J I> 1 0 2.3 2.1 1.0 4 (I h 7 7 7 7 7 1.6 10.4 7.7
In the last column of Table IV it is shown &hat K gis somewhat more nearly constant than Kp,but it is probable that the dBerence is not significant. The accuracy of the data and calculations is prabably not sufficient for making a decision betweell the two comp€ex ions, or for showing whether or riot bath ions may be assumed present. The most probable values of the constants, K1 = 1 X 10-j and K5 = 8 X lo--’, agree with the corresponding constants of Riley and Gallafent, 1 X 1Ud6 and 7.0 X respectively, in spite of the fact that their constants were determined on the assumption of the simultaneous presence of the two complex ions. The value for K5 is in fairly good agreement with the constant 4.3 X found by Knobloch.1 b (151 Krmbioch,
Le&>, 76,
110 ~ l & W l .
Jan., 1938
EQUILIBRIA IN CADMIUM IODIDESOLUTIONS
141
It was of interest to extrapolate the electroWhile the evidence from freezing and boiling points and absorption spectra favors the assump- motive force data presented in a previous paper4 tion of the presence of the ion CdI4- in cadmium with the aid of the data in this paper on the comiodide solutions and the absence of CdIa-, this position of cadmium iodide solutions. The assumption does not seem to be compatible with method of Hitchcockl* was used, the equation transport data. The transport experiments of being Hittorfl6 and Redlich and B~kschnewskil~ EO" E R log [Cd++][I-]' - 3k (1.012~ ' 1 1 ) showed2 that in a cadmium iodide solution con- in which k = 2.303 RT/BF and p is the ionic taining about 0.23 mole per liter the cadmium strength. The concentrations of cadmium and does not migrate in either direction, and that in iodide ions were those calculated for Table V. more concentrated solutions it migrates to the The results are shown in Fig. 1, in which the curve anode. Calculation of the composition of various is drawn to give Eo = 0.3113 v., the value calcucadmium iodide solutions with the use of the above lated' by the addition of the two normal electrode values of K1, K)and Ks gives calculated quantities potentials. of the complex anion CdL' that are too small in 0.310 comparison with the quantities of the cations Cd++ and CdI+ to account for the transport re- 6 0.308 sults in solutions of the order of 0.2 M or more. 0.306 On the other hand, assumption of the ion Cdb0 0.01 0.02 0.03 0.04 Ka and K4 and calculation from the constants K1, Ionic strength. gives results in better agreement with the transFig. 1 .-Extrapolation of electromotive force data for port data. Table V shows the results of such a Cell I to zero ionic strength. The curve is drawn to calculation, the concentrations of the various ions pass through B@' = 0.3118v. at zero ionic strength. being given in terms of the percentage of the total Stllllmq molality in the first column. The effect of the addition of cadmium sulfate TABLEV and of potassium iodide to the electrolyte of the COHPOSITION OF CADMIUMIODIDE SOLUTIQNS ON T ~ I E Hg&/Hg was deASSUMPTION THAT CdIs- IS THE ONLY COMPLEX ANION cell Cd(Hg)/CdI~(rn)/CdI~(rn), PBIESENT termined. CdIa, I-, Cd++, CdI+, CdIz, CdIa-, The results have been interpreted on the asm % % % % % sumption of the simultaneous presence of un77.1 21 1.5 .. 0.001025 179 3.7 .. 160 66.0 30 .002043 ionized cadmium iodide, the ion CdI+, and a com49.0 41 9.7 .. 132 .00500 plex anion, in addition to the simple ions, and cor34.0 46 18 3 .01000 111 responding equilibrium constants have been cal29 5 84.4 23.2 43 .02000 culated. The results of this investigation alone 14.6 37 39 10 55.5 ,0500 do not serve to distinguish between the two com10.7 32 42 15 38.0 .loo0 7.8 27 44 22 .2500 20.7 plex anions CdIa' and CdL'. 6.9 23 46 24 12.5 .500 DURHAM, N. C. RECEIVED JULY 28, 1937
+
h.
(16) Hittorf, Anx. Physilr, 106, 643 (1869). (17) Redlich and Bukschnewski. 2. physik. Chcm., 57,700 (1901).
(18) Hitchcock,
THIS JOURNAL, 10, 2076 (1928).
