1538
A. ALVAREZ-FUNEZ, J. BRAUNSTEIN AND M. BLANDER
junction potential of the cell might not be negligiblesb and where the increased solubility of silver halides in excess halide would necessitate a knowledge of the association constants of AgX and X-. The specific Helmholtz free energies of formation AA of CdX+ and CdXz (where X is bromide or iodide) were evaluated using the equations of the quasi-lattice modelgJO(asymmetric approximation) with the coordination number Z = 6. Since the equations of the model were derived for ions of the same charge, they might not be expected to apply to a mixture of singly charged and multiply charged ions. It is seen from the values of AA in Table I1 that the variation with temperature although very small is somewhat larger than in the case of singly charged ions.ll The decrease of AA with increasing temperature is in the same direction as was observed for the association of silver ions with sulfate (9) M. Blander, J . C h m . P h y s . , 84, 342 (1961). (10) M. Blander and J. Braunstein, Ann. N . Y. Acad. Sci., 79, 838 (1960). (11) D . 0.Hill, J. Braunstein, M . Blander, J . P h y s . C h c m . , 64, 1038 (1960).
Vol. 84
ions in molten KNOa.12 The “specific entropy of may be characteristic of a a~sociation”~ change in the- internal. degrees of freedom of the ions involved in the association, although the effect in this case is almost within the experimental uncertainty. The relatively small variation of Ad with temperature indicates that the quasi-lattice model may be useful for predicting the temperature coefficients of the association constants of singly charged ions with multiply charged ions as well as with other singly charged ions. Acknowledgments.-One of us (J. B.) is grateful to Dr. Milton Blander of the Oak Ridge National Laboratory for many valuable discussions and to Dr. John Hess of the University of Maine and Professor T. F. Young for their comments on the manuscript. He would like to express appreciation for support of part of this work by the Coe Research Fund of the University of Maine and by a grant from the U. S. Atomic Energy Cornmission, AT(30-1)-2873, to the University of Maine.
(- (g))
(12) W. J. Watt and M. Blander, ibid., 64, 729 (1960).
[CONTRIBUTION FROM THE REACTOR CHEMISTRY DIVISION, O A K RIDGENATIONAL LABORATORY,$ OAK RIDGE, TENNESSEE, OF CHEMISTRY, UNIVERSITY OF MAINE,ORONO, MAINE] AND THE DEPARTMENT
Thermodynamic Association Constants of Silver Ions with Bromide or Iodide Ions in Molten Potassium Nitrate and their Comparison with the Quasi-lattice Theory BY A. ALVAREZ-FUNES,’ J. BRATJNSTEIN~ AND M. BLANDER RECEIVED AUGUST21, 1961 Electromotive force measurements in dilute solutions of Ag+ and Br- in molten K N O s at 403, 438, 452, 474 and 500’ and Ag+ and I- in molten KNO, at 402’ were used to evaluate the association constants K1,K Zand K H for the formation of AgX, AgX2- and AgsX+, respectively, where X = Br or I. The comparison of the values of Ki in the bromide containing system with the theoretical calculations based on the quasi-lattice model demonstrated that the temperature coefficients of the K Iare correctly predicted by the theory for any reasonable choice of the coordination number using values of the “specific bond free energies” AAi, which are independent of temperature. For Z = 5 average values of dl,AA2 and hA11 are 7.14, 7.0 and 6.7kcal./mole, respectively. The values of the “specific bond free energies” for the formation of the ion pairs Ag+-Cl-, Ag+-Br- and Ag+-I- in KNOI for Z = 5 are 5&, 7.1, and 9.38 kcal./mole, respectively, and are consistent with the relative but not absolute values of the predictions of Flood, Fgrland and Grjotheim.
Introduction Measurements of the activity coefficients of AgN03 in molten KNOI in dilute solutions of Ag+ and Br- ions a t five temperatures ranging from 403 to 500’ and of Ag+ and I- at 402’ are described in this paper. In previous papers the comparison with calculations based on the quasi-lattice of similar measurements in dilute solutions of Ag+ and C1- in pure KNOa,’.*pure NaNOg and in equimolar NaN03-KNOa10mixtures demon(1) Fellow of the Consejo Nacional de Investlgaciones Cientificas y Tecnicas of Argentina. (2) On sabbatical leave from the University of Maine with the Reactor Chemistry Division of Oak Ridge National Laboratory Sept. 1960-August 1961. (3) Operated for the United States Atomic Energy Commission h y Union Carbide Corporation. (4) M. Blander, J . P h y s . Chcm., 68, 1262 (1959). ( 5 ) M. Blander and J. Braunstein, Ann. N . Y. Acad. Sci., 79, 838 (1960). (6) M. Blander, J . Chem. Phys., 84, 342 (1961). ( 7 ) M. Blander, F. F. Blankenship and R. F. Newton, J . P h y s . Chem., 68, 1259 (1959). (8) J. Braunstein and M. Blander, ibid., 64, 10 (1960). (9) D. G. Hill, J. Braunstein and M. Blander, ibid., 64, 1038 (1960).
strated that the temperature coefficient of the association constant K1 for the formation of the ion pair Ag+-Cl- is correctly predicted by the expression derived from the theoretical calculations KI =
z (exp ( -AAI/RT)
- 1)
(1)
where 2 is a coordination number and A A 1 is the “specific bond free energy” and was constant.” A.41 was about 1 kcal. more negative in the solvent KNO3 than in NaN03 and the value of AA1 in the equimolar NaNOgKNOa mixture appeared to be the average of the values of A.41 in the pure nitrates. The purpose of this paper is to demonstrate that equation 1 gives a correct prediction of the temperature coefficient of K1 in the bromide containing system. We shall show further that the generalized calculations6 based on the quasi-lattice model, within experimental error, lead to a correct prediction of the temperature coefficients for the as(10) D. G. Hill and M. Blander, ibid., to be published. (11) In systems in which the change of the entropy of the internal degrees of freedom of the ions involved in the association process i 4 small dAAi/dT Y 0 and A A i ‘v AEi.
THERMODYNAMIC LkSOCIATION CONSTANTS OF SILVER IONS
May 5, 1962
1539
80
40
0
J
E -40
lL
3 - 80 -120
-160 5 ~ 1 6 ~
2
5
2
RAPNO,
+
Fig. 1.-E.m.f. of the concentration cell Ag IAgNOa(R~NO~)llAgNOI(R~-No,) IAg
KNOi
KNOI
Plotted against the mole ratio of silver nitrate in the right hand half cell in the absence of bromide or iodide ions.
sociation constants KZ and Klz for the formation respectively of AgBr2- and Ag2Br+ from the ion pair Ag+-Br- if the “specific bond free energies” L 4 i are assumed to be independent of temperature. Lastly we will illustrate the differences in the values of KI and the values of AA1 for the association of Ag+ with C1-, Br- and I- in molten KN03. Experimental
0
.I
2
3
4 R~~ x 403
5
6
7
Fig. %.-Negative logarithm of the activity coefficient of silver nitrate in molten potassium nitrate as a function of the mole ratio of potassium iodide a t several fixed mole ratios of silver nitrate.
a t the given temperature and concentration of AgNOa. The rejected set of measurements at 438’ was rejected because it was inconsistent with data a t other temperatures. Because of the low soluReagent grade KBr and KI from Baker and Adamson were heated in a dry atmosphere to remove water and used bility of AgI, the measurements in the iodide conas solute. Otherwise, the materials, apparatus and pro- taining systems were of necessity made at very cedure were essentially the same as previously described.’s*J0 low concentrations of Ag+ and I- or at concentrations of K I in sufficient excess to keep AgI in soluResults tion. Figure 1 is a plot of e.m.f. V S . log RA,NO~, Electromotive force measurements were made of where I i A g N O I i s the mole ratio of AgN03, at 402’ the concentration cell as obtained in the concentration cell
where X is Br- or I-. As described previously the activity coefficients of AgN03 may be calculated from the relation AE =
2.303 RT 7 log YagNOi
where AE is the change of e.m.f. upon the addition of KBr or K I to the right hand electrode compartment a t a constant concentration of AgNOa and at concentrations of Ag+ and Br- or I- ions too low to precipitate AgBr or AgI. In Table I are given values of AE obtained in this system at several concentrations of AgN03 and KBr a t 403, 438,452,474 and 500°. The reproducibility of the measurements was not as good as in the chloride containing systems. Many duplicate series of measurements were made to check the reliability and reproducibility. Four somewhat low sets of measurements were rejected out of the total of 31 sets measured. Only one set of measurements (438’) was rejected without making at least three sets of measurements
for low concentrations of AgNOa. The points fall on the line of the Nernst equation slope down to concentrations below lo+. This indicates that the electrode may be used to measure activities of AgNOs a t these low concentrations. The e.m.f. changes upon the addition of iodide a t fixed concentrations of AgNOa are given in Table I a t the low concentrations of KI. The activity coefficients of AgNOa are plotted in Fig. 2 at the higher concentrations of KI. Evaluation of K I , K12 and &.-The method of evaluating K1, KI and Kts has been described previously.12 In the bromide system large scale plots of -log 7 ~ (or~of AE) ~ were 0 made ~ as a function of the mole ratio of KBr(&Br) a t several fixed concentrations of AgNOa(&,No,). The limiting slopes of these plots were obtained graphically at RRBr == 0 and are plotted as a function of I i A g N O I a t five temperatures in Fig. 3a. The intercepts of the plots in Fig. 3a a t R A ~ N= O ~0 are equal (12) J. Braunstein, M. Blander and R. M. Lindgren, Soc., 84, 1529 (1962)
J. A m .
Chem.
TABLE I HALFCELLS CONTAINING SOLUTIONS KNOBUPONTHE ADDITION OF KBr OR K I T = 403'
E.hf.F. CHANGE OF
AgNOa IN
= 0 3 1 8 x 10-1 R I ~ AE RAsh03
X lo3
(mv.)
0.071 .141 .289 ,500 .745 1.057 1.630 1.916 2.390 2.621
3.6 6.8 14.0 23.5 34.1 47.1 68.0 77.7 92.1 98.7
T
=
8.5 23.3" 31.3 39.2
0.194 0,656
RAgNOs = 0.630 X 10-2 RKB~ AE X IO3 (mv.)
0.180 .422 .786 1.173 1.554 2.006 2.610 2.980
452'
-
0.596 1.065 1.450 1.936 2.595 3.051
6.6 14.9 27.1 39.4 51.2 64.1 79.6 88.9
R.4aXOs
R K H ?X
23.9 40.7 53.5 68.2 86.2 97.6 RA.503
=
0.643 X 10-3 AE X 103 (mv.)
RKB~
15.5 27.3 43.0 54.5 65.3 74.9 85.4
RAzN03 = 1.084 X 10-8 AE X 101 (mv.)
16.0 30.7 41.8 56.6 66.6 78.9 90.4 109.8
RAgh.03 = 0.634 x 10-3 RKB? AE x 108 (mv.)
0.523 0.961 1.382 1.917 2.465 2.912
18.6 33.2 46.2 62.2 77.1 89.3
2.554 3.097 3.511 RAqNO3
77.1 90.1 98.9
2.520 2.904
=
RAENOJ= 1.420 X 10-2 RKB? AE X 10' (mv.)
1.086 x 10-2 KKR~ AE X 10' (mv.)
0.389 1.110 1.541 1.919 2.263 2.689 3.080
11.2 30.9 42.1 51.7 59.6 70.3 79.5
0.341 0.830 1.468 1.805 2.085
T
9.6 23.3 40.5 50.2 57.4
0.474 1.114 1.459
12.2 29.3 39.4
0.412 0.833 1.455 1.765 2.179
0.430 0.796 1.162 1.466 1.935
14.4 25.7 36.3 45.0 57.6
RAgI.03 = 0.655 X 10-8 RKBP AE X 101 (mv.)
0.470 0.798 1.352 1.791 2.380
15.1 25.3 41.3 53.3 68.6
14.3 23.8 35.5 46.9 59.5 69.9
2.899
81.1
RAgNO8 = 1.418 X 10-8 AE RKB~ X 103 (rnv.)
0.404 0.867 1.284 1.710 2.158 2.829
10.0 20.9 30.9 42.1 53.9 69.7
T = 500" RAzNO) = 0.330 x 10-3 RKB? AE X 103 (mv.)
0.467 0.912 1.434 1.948 2.441 2.831
15.5 29.3 44.3 58.2 69.8 79.0
RAgN03 = 0.329 X 10-1 RKB~ AE X 10, (mv.)
0.417 0.878 1.367 2.046 2.512
14.1 29.5 44.2 62.4 73.4
R.4gN03 = 0.331 x 10-1 RKB? AE X 103 (mv.)
RAcS03 = 0.632 X 10-3 RKn? AE X 103 (mv.)
0.550 1.059 1.555 1.961 2.581 2.897 3.285 3.656
0.401 0.842 1.199 1.525 1.919 2.424 2.817 3.286
17.8 33.1 46.9 57.0 71.7 78.6 86.9 94.3
RAxNO8 = 1.086 x 10-1 AE X 10' (mv.)
RKB~
0.352 0 954 1 549 2 035 2 492 2 939 3 268
8 24 38 49 59 68 75
8 2 3 3 2 8 3
12.1 24.0 34.3 42.9 52.7 64.3 72.9 82.8
RADNOS = 1.417 X 10-2 RKBP AE
X 10%
R.4~N08= 0.331 X 10-8 AE (mv.)
RKBI X 103
0.352 0.826 1.099 1.644 2.024 2.461 2.924 3.347
11.0 27.0 35.6 51.8 61.9 72.7 83.2 92.4
0.360 0.821 1.386 1.878
10.5 23.6 38.4 50.9
R4pN03 = 1.416 X 10-3 X RK 108 B~ (mv.) AE
(mv.)
0.356 0.812 1.123 1.442 1.836 2.218 2.675 3.361
8.7 19.6 26.6 33.8 42.7 51.0 61.0 75.7
0.794 1.472 1.930 2.335 2.735 3,030
19.7 35.3 45.3 54.6 62.9 69.3
T = 402" R.4zX03 = 6.84 X 10-6 RKI AE X IO5 (mv.)
0 0.48 1.0 2.0 3.6 7.3
0 1.4 3.0 7.1 11.6 20.4
= 474'
RAgNoa = 0.656 X 10-8 RKB~ AE X 102 (mv.)
72.5 81.5
0.581 0.937 1.404 1.851 2.318 2.711
RAgx03 =
RAgNoa 0.374 X lo-' RKB? AE X 101 (mv.)
14.5 28.8 47.9 56.9 68.0
27.0 43.7 74.0
1.423 x 10-3 RKB~ AE X 103 (mv.)
RKB,
0.555 1.072 1.486 2.015 2.400 2.900 3.380 4.126
5.9 20.2
= 0.319 x lo-' IO3 A E (mv.)
0.689 1.167 2.149
0.445 0.780 1.271 1.650 2.026 2.372 2.791
1.5 3.7 5.1 8.3 10.7 14.1 16.2 19.5
RA.NO~= 1.085 X 10-3 R K BX ~ 103 A E (mv.)
1.5 12.8 21.7 33.4 52.5 62. 7 70.4
T = 0.319 x Io-' R K B ~X l o 3 A E (mv.) RAgNO3
0.040 '104 .149 ,242 ,319 419 ,481 ,576
438"
RA.NO~= 0.315 X lo-' A E (rnv.) RKB, X 103
0.032 .317 .540 .864 1.429 1.767 2.044
RACNO =~ 1,091 x lo-' RKB~ AE X 108 (mv.)
RACXO =~ 0.635 x 10-3 RKB~ AE X 103 (mv.)
0.199 ,426" 741 912
OF
RAgNO3 3.82 X 10-6 RKI AE X 105 (mv.)
0 0.85 1.81 2.69 4.14
0 2.9 6.9 10.0 15.1
= 10-5 AE (mv.)
RAzN03
2.01 RKI X 10:
0 0.32 0.80 2.21 3.59 5 25 7.01 9.48
x
0 2.0 4.5 i.0
0
0.43 1.08 4.10 10.91
1.5 5.9 13.8 34.0
12.0 17.0 23.0 31.0
RAgN03 3.84 X 10-6 RKI AE X 10' (mv.)
0.60 1.43 2.85 5.12
RAgX03 = 3.12 X 10-6 AE RKI X 105 (mv.)
0 2.0 5.8 11.1 18.0
RAgNOa = 3.99 x lo-' RKI AE X 106 (mv.)
0 2.43 7.67 27.9
0 8.6 28.0 100
THERMODYNAMIC ASSOCIATIONCONSTANTS
May .i, 1962 6.17 12.9
10.3 14.0
24.0 46.5
X 105
(mv.)
0
0 0.53 1.84 2.74 3.56
8.4 16.8 26.1 50.6
7.55
RKI
x
X 108
(mv.)
0 0.81 1.39 2.70 3.79 4.39 5.41
0 1.7 6.1 9.2 11.6
1511
.
i
a
10-5
AE
(mv.)
0 2.5 4.0 9.0 12.3 12.8 16.0
I60
I
RA.NOI = 8.36 X 10-5
RKI X 105
IONS
380 -
R A Z N O=~
R A I N O=~ 6.68 X 10-6 RKI AE
RAgNOa = 4.48 X 10-6 RKI AE
x 108 0 2.33 4.36 6.75 11.88
420
32.4 48.9
OF S I L V E R
I40
A E (mv.)
0 0 0.92 4.0 1.18 4.4 1.91 7.8 2.37 8.0 2.72 8.9 = Data point not used in calculations.
2
-E
to (-K1/2.303) and the limiting slopes are equal to [(K12- 2K1K12)/2.303] since
I
I 0.5
0
and RAgN03=O
Values of K1 and Klz obtained in this manner are listed in Table 11. Kz was evaluated by a least squares fit of the experimental data (at fixed concentrations of AgN03) to the equation
- log Y A ~ N O=~ A R K B4~ BR2~
