T H E DEGREE O F DISSOCIATION AYD T H E IONS OF CADMICM IODIDE I N AQCEOCS SOLUTION
BY JAMES
w.
MCBAIS,
PIERRE J. VAS RYSSELBERGE ASD
w.
A. SQUANCE*
During electrolysis of all stronger solutions of cadmium iodide the cadmium moves away from the cathode instead of toward it.' Hittorf gave the only possible explanation; namely, that more cadmium is moving in complex anions towards the anode than is traveling in the form of cations toward the cathode. The other properties of these solutions are in accordance with this behavior which seems to be coupled with very incomplete dissociation of the molecules into ions. Thus the lowering of the freezing point is deficient and the concentration of ions as given by measurements of E.M.F. and conductivity is much less than that exhibited by corresponding salts of magnesium or calcium. However, the difference, as will appear, is one of degree only, and a careful scrutiny of the data for cadmium salts is therefore of general significance in the search for a valid hypothesis of electrolytic dissociation. N7e present in this paper a discussion of the data, including a new general method for the calculation of the concentrations of the different ionic species present, based upon migration numbers and E.M.F., and independent of the theory of activity coefficients. The results so obtained are used in the discussion of new diffusion data for cadmium iodide. I n Fig. I all the available data for the observed transference of cadmium in solutions of four cadmium salts have been plotted against the logarithm of the concentration.* The curves indicate that the migration number is nearly constant from infinite dilution up to a certain low concentration, 0.01 molar in the case of cadmium iodide and 0.056 and 0.11 molar for cadmium bromide and chloride, respectively. For higher concentrations the curves drop rapidly, and the total movement of cadmium is zero in 0.23 molar cadmium iodide, thereafter becoming negative and seeming to tend toward a limit of -0.23. A negative value for the transference number of cadmium in cadmium bromide has been obtained by Gordon (loc. cit.) with a solution containing 29.4 per cent cadmium bromide. In the case of cadmium chloride, a negative value has been obtained by Hittorf (loc. cit.) (1902, 1903) for a concentration of 7.69 gram mols per liter. The similarity between the curves for the three halides is striking; they are almost parallel, a fact which shows that the three *Died in 1922. l 6 '.Hittorf: Pogg. Ann., 106, 543 (1859); 2. physik. Chem., 39, 613 (1902); 43, 239 (1903); J. W. McBain: 2. Elektrochemie, 11, 2 1 5 (1905);monograph, Proc. Wash. Acad. Sa., (A compilation of the experimental data of the quantitative measurements of electrolytic migration), 9, I (1907); B. Redlich: Z. physik. Chem., 37, 673 (1901); 38, I 2 7 (1901); V. Gordon: 2. physik. Chem., 23, 469 (1897). * See McBain's monograph (loc. cit) and G. Heym: Ann. Physique, 12,4.43 (1919) (the concentrations had to be recalculated); W'. W. Lucasse: J. Am. Chem. Soc., 51, 2597 (1929) (results for CdBrz were not plotted because they coincide with those of the other authors).
IO00
JAMES W. MCBAIN, PIERRE J.VAN RYSSELBERGE AND
W.A. SQUANCE
salts dissociate in the same manner and form complexes of the same types a t high concentrations.' For cadmium iodide the complex anion is almost certainly Cd13-. Similar negative values for the transference number have been obtained for ZnC122, Zn12a and CuCL4. Movement toward the anode of complex ions containing cobalt has been detected but not measured in mixtures of CoClz with concentrated HC1, MgClz and CaClZ4;complex ions containing iron, copper, move toward the anode in mixtures of FeCh and CuC12 with concen-
a W
m I 3
z W
V
z
W LL W
LL
fn
2c
FIG. I Transference of cadmium in solutions of four cadmium salts. Hittorf, x; Goldlust, 9; Bukschewski, 0 ;Goldhaber, A; Kummel, *;Gordon, 0 ;Heym, 8;Redlioh, 0 ; Lucasse,--o--
trated HC14. The same result has been obtained in mixtures of CuC12 with MgClg, CaCL, LiCL5 Complex anions containing Cu, Fe and UOe have been detected in mixtures of CuSO4, ferric and uranyl salts with alkali bicarbonate in excess.6 Rieger found complex ions in some mixtures; in a solution of potassium ferrous oxalate he found the iron migrating toward the anode.' IF. Bourion and E. Rouyer (Ann. Chim, ( I O ) , 10, 182 (1928); Compt. rend., 184, 598 (1927)) found from ebullioscopic studies of sait pairs that cadmium chloride forms complexes with potsssium, sodium and ammonium chlorides just aa did cadmium iomde with potsssium iodide. See also E. Rouyer: Ann. Chim., ( I O ) , 13, 423 (1930); F. Bourion and 0. Hun: Compt. rend., 191, 97 (1930). 2 W. Hittorf: loc. cit. 8 W, Hittorf: loc. cit. (1859). 4 V. Kohlschutter: Ber. 37, I , 1153 (1904). 5 F. G . Donnan and H. Bassett: J. Chem. Soc., 81, 939 (1902). 6 R. Luther and B. Krsnjsvi: Z. anorg. Chem., 46, 170 (1905). 'E. Rieger: 2.Elektrochemie, 7, 863, 871 (1901).
DISSOCIATION A N D IONS OF CADMIUM IODIDE
IO01
A survey of migration data therefore shows that cadmium iodide is not the only salt of its kind. For almost all the strong electrolytes, the transference number of the slower ion decreases rapidly a t high concentrations; negative values are not generally obtained because the solubilities are rarely large enough. Having admitted complex anions to explain the negative parts of the curves, we have also to admit that such anions are present in more dilute solutions of these salts. For example, in the case of cadmium iodide they are present in sufficient amount appreciably to affect the transport number in all solutions down to 0.01molar. The change of transference number with change in concentration in solutions of strong electrolytes has often been interpreted as signifying unequal changes in the mobilities of the ions.’ This explanation cannot account for negative values, although it is the only one permissible in theories of IOO per cent dissociation. The data just adduced show that cadmium iodide is by no means to be regarded as a unique exception but rather as merely an extreme case. In previous communications we have shown2 that negative transport numbers may be obtained for dilute solutions of any salt involving any divalent ion, provided that a sufficient addition of common anion be made to the solution. This is just like the behavior of cadmium iodide to which a solution of potassium iodide has been added.3 The interpretation of the data for cadmium iodide, therefore, becomes of direct significance for all other solutions. McBain in 1905 (loc. cit.) explained quantitatively the properties of solutions of cadmium iodide then known by w u m i n g very incomplete dissociation and the presence of the complex anion Cd13- and the partially dissociated cation CdI+. The three dissociations occurring were then CdIz = Cd++ 21CdIz = CdI+ I3Cd12 = Cd++ zCdIa-. -4complex ion of the type Cd1,- -, ag originally suggested by Hittorf4, was regarded as improbable, because it is very unlikely that this ion would possess a migration velocity several times greater than the simple Cd++ and Iions. As a matter of fact it is possible that many types of complexes are present together, but by assuming the existence of one or two definite ones, in some cases reasonable explanations can be obtained for most of the properties of the salt. Van Name and Brown3 in 1917 accepted these ions but rejected the calculated concentrations for three reasons. The first was a misunderstand-
+ + +
See, for example, G. Jonas and M. Dole: J. Am. Chem. Soo., 51, 1073 (1929). McBain and P. J. Van Rysselberge: J. Am. Chem. Soc., 50, 3009 (1928);52
* J. W.
2336 (1930). W. Hittorf: Ostwald’s Klassiker, 23, 87; J. W.McBain: loc. cit. (1905). 4 For a reviaion of Hittorf’s calculation of his data see McBah: loc. cit. (1905). 5R. G. Van Name and W. G. Brown: Am. J. h i . , 44,453 (1917).
1002
JAMESW. YCBAIN, PIERRE J.VAN RYSSELBERGE AND W. A. SQUANCE
ing, whereby, through confusing equivalent and molar conductivity, they thought that the calculated conductivity was only half that observed. The second was because they assumed that simple molecules must freely combine with iodine, whereas they felt that they need not make such an assumption if they assumed double molecules of cadmium iodide. The third reason was that they inferred from E.M.F. data, using an iodine electrode extrapolated to solutions containing no iodine, that the concentration of the I- ion in such solutions was higher than that calculated by McBain. Actually, for the same reason as indicated above, McBain’s value is somewhat higher than theirs. His was for a decimolar solution 0.126 X 0.2 = 0 . 0 2 5 2 N Ias compared with their value 0.021 plr I-. The present paper is divided into two parts. I n the first are recorded electromotive force measurements carried out by one of us (W. A. S.) at the University of Bristol in 1 9 2 2 . They are used, together with other electromotive force data obtained by Getman’ and with migration data, in the calculation of the concentrations of the various ionic species present in aqueous solutions of cadmium iodide. In the second part, diffusion data obtained by Dr. Tsun Hsien Liu at Stanford in 1930 are presented and discussed in the light of the information obtained in Part I as to the composition of aqueous solutions of cadmium iodide. PART I Experimental Measurements were made of the E.M.F. of the following cells together with two in which K I was added to the CdL: KC1 satd.
Hg
1
Hg
KCl, HgzClz N solid
KC1 satd.
HgJ?, KI solid 0 .I and 0.05
KCl, HgzCIz N solid
0.I
0.I
M
Hg?I?, CdIz solid 0.1M
KC1 satd.
1
KC1, HgzClz N solid
0 .I
Merck’s pure cadmium was fused to a stout copper wire without solder and the copper, including about I cm. of the cadmium beyond the joint, was sealed into a glass tube with shellac, sealing wax or piccin. Other materials were Kahlbaum’s purest chemicals. The Weston cadmium cell was standardized by the National Physical Laboratory. Decinormal calomel electrodes were made and used in duplicate. It was assumed that the satuF. H.Getrnan: J. Phys. Chern., 32, 941 (1928).
I 003
DISSOCIATION AND IONS O F CADMIUM IODIDE
rated KC1 had eliminated diffusion potential. All vessels and instruments used were calibrated. A large Kohler precision potentiometer was employed together with a delicate Leeds and Northrup ballistic galvanometer. After each series of measurements on a solution of one concentration, the cell was taken apart and the cadmium electrode washed and then rubbed with a fresh piece of emery cloth to ensure removal of any oxide or other contamination. It was found impractible to use a dilute solution of ammonia to remove the oxide film, as suggested by Richards, except when piccin was used instead of shellac for insulating material, because on standing the ammonia attacked the shellac. The cadmium electrodes were tested immediately before use, and a potential difference of j=0.0002 volt was considered sufficiently small to proceed with the actual measurement of the electromotive force of the combination cell employing one of these electrodes. The electromotive forces given in Table I are the means of a series of observations and in several cases represent the average of two or more entirely independent series made upon solutions of the same concentration. The negative sign indicates that the named electrode was negative as compared with the mercury of the calomel electrode. The concentrations are expressed as mols per liter, and the values for the electromotive force are considered accurate at room temperature to within i o . 0 0 ~volt.
TABLE I consisting of Solutions of Cadmium Iodide and Potassium Iodide, alone and together, measured against X/IO Calomel Electrodes through Saturated Solutions of KC1
E.M.F. of Cells at
20’
Electrode
Concentration of salt Mols per liter
E. M. F. Volts
Cd/CdIz
0.001 0.01
-0.8133 -0.8061
0.05
-0
0 .I
0.2
-0,7958 - 0.7896
0.3
-0.7808
0.4
-0.7718 -0.2927
11
1)
0.0; ,I
0.I
Hg/HgnIn, CdIz Hg/HgzIs, KzCdIa Cd/KnCdI*
0. I 0.025
0.025
8028
-0,3094 -0.2799 -0.2916
-0.8238
A . Mobilities of the Simple and Complex Ions. We shall suppose that the mobilities of the simple ions Cd++and I- vary with concentration but remain proportional to their values a t infinite dilution. For CdL the transference numbers of Cd* and I- a t infinite dilution are, respectively, 0.45 and 0.55. Our assumption on the mobilities means that, at any concentration, the ratio of the mobilities of the Cdff and Iions is equal to 0.45/0.5 5 .
1004
J A M E S W.MCBAIN, PIERRE J.VAN RYSSELBERGE AND W. A. SQUANCE
The mobility of the ion CdIa- was calculated by McBain (loc. cit. 1905) who used two different methods. The first one is based upon migration data for pure CdIz in concentrated solutions; the second is baaed upon a recalculation of Hittorf's experimental data for migration in the mixture 2KI CdIz. If we assume that in very concentrated solutions we have only Cd++ and CdIa- ions, a hypothesis corroborated by E.M.F. data, the transference number of CdIa-, or better the ratio of its mobility to the sum of the mobilities of Cd++ and Cd18-, is given by I.23/3 = 0.41. This value 0.41 means that the complex ions CdIa- carry 41 per cent of the total current carried by the ions resulting from the dissociation
+
+
3Cd12 = Cd++ zCdIsor that the mobilities of Cd++ and CdIa- are in the ratio of 0.59 to 0.41. McBain had to assume that the CdIf ion had the same mobility aa the Cd++ion, because no data were available for the calculation of its exact value. In part B, we shall show that this mobility can be deduced from E.M.F. data. The calculation gives the ratio between the mobilities of CdI+ and Iequal to 0.1610.55.
B . E v a l d i o n of the Data jor E.M.F. In the first type of cell used in Table I the E.M.F. depends solely upon the concentration of Cd++ ions, and for any two concentrations the difference in E.M.F. observed is El - Ez = 0.029 log (Cd")z (Cd'+)i where changes in activity coefficient are neglected. Getman' has recently measured cells of the type Cd I CdI2, AgI I Ag, and for any two concentrations the difference in E.M.F. observed is ~
Hence
Thus the two series of data, considered together, furnish the ratios of Cd++ ions aa well aa I- ions in the two solutions. To obtain absolute amounts, we have assumed that the concentrations of Cd++ ion and I- ion in 0.005 molar CdIs are given by conductivity. It waa shown in McBain's paper (loc. cit. 1905) that for low concentrations the data for freezing point and conductivity are in close agreement, and similar freezing point data were since obtained by Van Name and Brown floc. cit.). Hence we take the concentrations in 0.005 molar CdIz aa 0.00315 molar Cd++ and 0.0063 I-, the degree of dissociation being 63 per cent.
IF.EI. Getman: J. Phys. Chem., 32, 941 (1928).
DISSOCIATION AND IONS OF CADMIUM IODIDE
I005
In Table I1 the calculation of the concentrations of the cadmium and iodine ions relative to their concentrations in a 0.005 molar CdIz solution are given, using smoothed values for both Squame’s and Getman’s curves for E.M.F. and converting Getman’s concentrations into mols per liter by means of the densities given in International Critical Tables.
TABLE I1 Concentrations in Mols per Liter of Iodine and Cadmium Ions deduced from E.M.F. Data of Squame and Getman and the Degrees of Dissociation of the Two Ions. Total - e2 - E1 (I-) (Cd++) $(I-) (Cd++) cadmium
volts
0.2
0.6078 0.5933 0.5701 0.5605 0.551~ 0.5380
0.5
0.5285
0.005 0.01 0.02
0.05 0.1
volts 0.8082
0.8061 0.8050 0.8028 0.7958 0.7896
0.765
0.0063
0.00315
0.0037 0.0148 0.0040 0.0048 0.0228 0.0084 0.0252* 0.0285 0.0138 0.0181 0.0973 0.0103
(.CdI1)
(CdI2)
0.630 0.515
0.630 0.370
0.370
0.200
0.096 0.126’ 0.084 0.071 0.069 0.018 0.194 0.228
* The same fraction waa obtained from the freezing point data by McBain in 1905, but
ignoring any CdI+ present (loc. cit., compare page
1001 above).
C . Migration Data applied to the Calculation of the Concentrations of Complex Ions. 1. Calculation of the mobility of the CdI+ ion. Let us suppose (see Fig. I) that for a concentration of 0.01 mol/l. the concentration of the CdIs- complex is 0. Then the apparent transference number of the Cd++ ion is given by the general expression1
where the m’s represent the respective mobilities referred to any common unit. For the concentration 0.01mol/l. we have z(Cd++)’* 0.55
Ncd = z(Cd++)-0
45
0.55
+ z(CdI+) 0 . 5 5
+ (CdI+) m Cdl + (I-) 0.55
= 0.45
E.M.F. data gave: (Cd++) = 0.0037 (I-) = 0.0103
AS (CdIs-) =
0,
(CdI+) = (I-) - z(Cd++) = 1
MLs M. E. Laing: J. Phys. Chem., 28, 673 (1924).
0.002g
1006
JAMES W. MCBbIN, PIERRE J.VAN RYSSELBERGE AND W. A. SQUANCE
Hence the equation when solved for mCdI gives: mcdI+ = 0.16, expressed in the same units as give mI- = 0.55. That is, the equivalent conductivity of CdI+ is 0.16/0.55. or 29 yc of that of the I- ion.
1. Calculalion of (CdI3-) as a function of (Cd++), (I-) and N,. I n the same way,
+
Replacing (CdI+) by (I-) (CdI3+) - z(Cd++) and solving for (CdI3-) we obtain: (0.26 - 0.58 N c ~ )(Cd++) (0.32 - 0.71 N c ~ (I-) ) (CdIz-) = 0.4727 N C d f 0.3054 It is easily seen that, when N C d = 0.45 (corresponding to the migration number for extreme dilution), (Cdk-) = 0 . Again, the equation is reduced to an identity when N C d is put equal to -0.23, (I-) equal to o and (CdI3-) equal to 2 (Cd++). Knowing the values of NCd, (Cd++) and I(-), it is then possible to calculate (CdIa-) for different concentrations. (CdI+) is deduced from (CdI+) = (I-) (CdIs-) - 2(Cd++).
+
+
Table I11 gives the values of (Cd++), (I-), (CdIa-) and (CdIf) corresponding to total concentrations of CdIz ranging from 0.005 mol/l. to 0.5. The values obtained for this latter concentration must only be considered as approximations, one of the values for the E.M.F. having been determined by extrapolation. TABLEI11 Concentrations in Mols per Liter of each of the Ions present in Aqueous Solutions of Cadmium Iodide Total cadmium
(I-)
(Cd++)
(CdI3-1
0 . oo j
0,0063
0.01
0,0103
o .0000 o.oooo
0.02
0.003 I 5 0.0037 0.0040 0.0048 0.0084 0.0138 0.0973
0.05
0.0148 0.0228
0.1
0.0252
0 . 2
0.0285 0.0181
0.5
0.0011
0.0064 0.0153 0.0350 0.1769
(CdI+l o , 0000
0.0029 0.0079 0.0196 0.0237 0.0359 0.0004
Total ,CdL dissociated 0.003 I j
0.0066 0.0130 0.0308
0.00474 0.0847 0.2746
In Table IV we give for comparison the conductivity ratios and the activity coefficients as calculated by Getman (loc. cit.) and the ratios ~/zC[(Cdt+) (I-)/2)], where C is the total concentration of CdIz, and also the ratios I/C [(I-) (CdI3-)].
+
+
1007
DISSOCIATION AND IONS OF CADMIUM IODIDE
TABLE IV Comparison of the Ionic Concentrations deduced from Migration Data and and E.M.F. with Arrhenius’ Degrees of Dissociation and with Activity Coefficients Total cadmium
Activity coefficients
r/zC[(Cd++)+(1-/2)]
1/2C[(I-) +(CdId]
0.005
0.56
0.63
0.63
0.01
0.40
0.44
0 . j1
0.02
0.26
0.28
0.40
0.Oj
0.14
0.16
0.29
0.I
0.09 0.06 0.03
0.IO
0.20
0.07
0.16 (0.19)
0.2 0.5
(0.11)
Conductivity ratios (25‘c)
0.63 0.53 0.43 0.30 0.23 0.19 0.16
It is interesting to notice that the conductivity ratios and the values of I/C [(I-), (Cd13-)] are in close agreement, and also that the activities
+
calculated by Getman are of the same order of magnitude as the values of I / & [(Cd++) (1-)/2]. This seems to prove that, for CdL, the conductivity ratios fairly closely represent the percentage of ions present in the solution in Arrhenius’ sense. The activity coefficients deduced from E.M.F. measurements correspond to the total percentage of the simple ions measured by the electrodes used, in this case Cd++ and I-, and ignoring the complexes CdI+ and Cd18-.
+
PART I1 Table V contains diffusion coefficients measured for various concentrations of cadmium iodide, a t z~OC.,by the method of McBain and Liu.*
TABLE V Concentration m/i.
DiEusion coefficients
Concentration, m/r.
Diffusion coefficients
0.005
0.956 0.964 0.965 0.951 0.859
0.05 0.05 0 . 15
0.788 0.790 0,732
0.5
0.690
0.005 0.005
0.005 0.01
The diffusion coefficient corresponding to infinite dilution, Le., t o complete dissociation into Cd++ and I- ions, is given by Haskell’s equation for infinite dilution, which is an extension of the Nernst formula to the case of unsymmetrical salts: mCd++ . m ID, = R T mCd++ mI-
+
J. W.McBain and T. H. Liu: J. Am. Chem. Soc., 53, 59 (1931).
I008
JAMES W. MCBAIN, PIERRE J.V.4" RYSSELBERGE AND W. A. SQUANCE
At 25OC. the limiting mobility of I- is 75.4. From the ratios of mobilities used in Part I we deduce mcd++ = 61.6, mCd13- = 42.8, mCdI+
= 22.0
At a finite concentration a t which the only ions present are the simple Cdff and I- ions, the degree of dissociation beinga, the part of the diffusion coefficient due to those ions is given by:
D=D,Xa We have, a t 2 5°C. :
D, = 0.023 X 6 1 . 6 X 75.4 137.0
(I+:)
= 1.170
McBain and Liu proposed the following general equation for the diffusion coefficient of any electrolyte a t any concentration :-
in which C is the fraction of the total concentration which is in the form of ions or molecules of mobility m. The summation is extended to all the ions, simple and complex, and to the neutral molecules. i is van%Hoff's coefficient. At any concentration of cadmium iodide where, beside neutral molecules, simple Cd++ and I- ions only are present, this equation gives for 2 5 O C .
D =
0.023 i
2a -+-+-mCd++
I --a
2 4
mI-
rnCdIl
i is deduced from freezing point measurements.' studied by us (0.005 molar) i =
I
+
2
At the lowest concentration
X 0.63 = 2.26
I n the first part of this paper we assumed as a first approximation, since the conductivity ratio is 0.63 a t that concentration, that the degree of dissociation is equal to 0.63. Now we shall consider the degree of dissociation a t 0.005 molar and the mobility of the CdIz molecule as two unknowns. We are going to determine their values by requiring that Haskell's formula and the McBain-Liu formula give at the concentration 0.005 molar the experimental value 0.959,recorded in Table V. At z5'C. and 0.005 molar, DCd+++ I- = 1.17 X a. The difference between 0.959 and 1.17 X a is then due to the diffusion of the neutral molecules. The mobility of the Cd12 molecule must then be given by: mCdlt
1
0.959 = (I )-.
-
1.17n
RT
- 0.959
-
1 . 1 7 ~
0.023 ( I -).
Compare J. W. McBain: Z. Elektroohemie, 11, 215 (1905).
DISSOCIATION AND IONS OF CADMIUM IODIDE
1009
We then have the two simultaneous equations :
I
2.26
0959 =
2CY
X
0.023
I--a
2CY
or
These two equations represent hyperbolae. Drawing the two curves, one finds for their intersection point: mCdI, =
22.3
CY = 0.675
The actual degree of dissociation a t the concentration 0.005 molar is thus, as expected, a little higher than the conductivity ratio 0.63. All our calculations in Part I could be modified accordingly. We will not do so, because the new value obtained for the degree of dissociation a t the concentration 0.005 molar is probably not yet the final one. We only attempt to calculate as well as possible the orders of magnitude of the concentrations of the various ionic species. Taking the concentrations given in Table IV (except for the 0.005 molar solution for which the new value of the degree of dissociation is used) the diffusion coefficients listed in Table IV are obtained from the McBain-Liu formula.
TABLE VI D
D
Concentration, mol8 per liter
van’t Hoff’s
0,005
2.26
0.959
0.959
0.01
2.08
0.883
0.859 0.831
1
.88
0.02
I
0.05
1.52
0.I
I.2j
0.2
0.96*
calculated
0.844
measured or interpolated
* By extrapolation.
The results show that a t low concentrations the agreement is to be regarded as fairly satisfactory. It should be pointed out that the calculated values are exceedingly sensitive to a slight change in the mobility of one of the constituents. If, for instance, we deduce the mobility of the CdIz molecule from Haskell’s formula and from the value 0.63.for the degree of dissociation of 0.005 molar CdI2, we find 26.1 This value when used in the McBain-Liu formula for the concentration 0.005 molar gives 1.02for the diffusion coefficient instead of 0.959.
IOIO
JAXES W.NCBAIX, PIERRE J.VAN RYSSELBERGE AZSD W.A . SQCANCE
It is probable that if all the concentrations given in Table IV were corrected by taking 0.6; j instead of 0.63 for the degree of dissociation of 0.005 molar CdI2, a better agreement between calculated and measured values of the diffusion coefficient than that shown in Table S'I would be obtained; this because of the fact that the term corresponding to the molecules CdIz in the McBain-Liu formula would be decreased. However, the chief reason for the very significant difference between observed and calculated values for higher concentrations is that the observed values were obtained by diffusion into pure water instead of into slightly less concentrated ca,dmium iodide. The experimental data are therefore integral values, whereas those calculated refer only to the concentration indicated. McBain and Liu have shown for other cases that integral values diverge in this manner. On the whole the preceding calculations show that the concentrations of the various ionic species calculated in Part I give reasonably good values of the diffusion coefficients. summary
Measurements have been made of the E.R.I.F. of cells containing (I) cadmium iodide in concentrations from 0.001to 0.4 molar. These measurements have been combined with those for other cells measured by Getman to deduce the concentrations of the simple ions. (2) ITsing the general formulation of migration of Laing and McBain, the concentrat,ions and mobilities of the complex cations and anions have been evaluated. (3) I t is found that the sum of the concentrations of the simple ions follows closely or is equal to the activity coefficients and that, further, for the weak electrolyte, cadmium iodide, the total dissociation is substantially in agreement with (and slightly more than) the conductivity ratio of Arrhenius. (4) Diffusion coefficients have been measured for solutions of cadmium iodide for concentrations from o.ooj to 0.5 molar. From these measurements and from the combination of the Haskell and McBain-Liu diffusion formulae the mobility of the cadmium iodide molecule and a more accurate value of the degree of dissociation of 0.005 molar cadmium iodide have been deduced. The concentrations of the various molecular species present in solutions of cadmium iodide have been used to calculate the diffusion coefficients. Fairly good agreement with the experimental values has been obtained. (j) The behavior of cadmium iodide with respect to the dissociation and formation of complexes differs only in degree from that of all other salts containing divalent ions. Department of Chemistry, Stanford L'nizmersity, Calif.
