PETERC. LAMMERS AND JERRY BRAUNSTEIN
2626
method, the range of reactions interpreted and the detailed studies of several reactions examined from the viewpoint of the six stated criteria establish the capability of the method in giving meaningful kinetic data. Acknowledgment. Support of this work by the
National Science Foundation under Grant No. G-21408 is gratefully acknowledged. One of the authors (R. A. S.) wishes to express appreciation for fellowship support t o the Henry Earl Riggs Foundation, the Florence Fenwick Foundation, and the Minnesota Mining and Manufacturing Company.
Hydration and Association Equilibria in Molten Salt Solutions Containing Water. I. The Association of Cadmium Ion with Bromide in the Solvent Lithium Nitrate-Potassium Nitrate-Water1
by Peter C. Lammers and Jerry Braunstein2 Department of Chemistry, University of Maine, Orono, Maine
(Received January 27, 1967)
The electromotive force has been measured of the cells
I (Li,K)N03//(Li,K)NOd
I as a function of temperature and of the concentrations of water, cadmium nitrate, and bromide. Association constants of cadmium ion with bromide were calculated at 119" as 9100, 5600, 4100, 3600, and 2800 (moles/mole of nitrate)-', respectively, at water contents of 0.26, 0.51, 0.76, 1.00, and 1.26 moles of water/mole of nitrate and at 168" as 5800 at 0.10 mole of water/mole of nitrate. The solvent was equimolar lithium nitrate-potassium nitrate. The decrease of association constants with increasing water content indicates the competition of hydration and association equilibria of cadmium ion in aqueous melts.
Introduction Although there has been considerable interest in hydration of ions in dilute aqueous electrolyte solutions, the concentration range between anhydrous and the region in which the hydration sheaths are formed has received but little a t t e n t i ~ n . ~ " In a Previous paper,' we reported association constants ion with &loride in a solvent consisting of of 2 moles of water/mole of ammonium nitrate at 40". The Journal of Physical Chemistry
The association equilibria were interpreted in terms of a quasi-lattice model of molten salts8 with the water considered "bound" to the ions. Such a model is (1) This work was supported by the U. 5. Atomic Energy Commission, NYO 2873-18. Presented as Paper No. 20 of the Division of Physical Chemistry, 152nd National Meeting of the American Chemical Society, New York, N. Y., Sept 11-16, 1966. (2) To whom all inquiries should be addressed at the Reactor Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tenn.
HYDRATION AND ASSOCIATION EQUILIBRIA IN AQUEOUSMOLTEN SALTS
obviously oversimplified, since the "binding" of water to the ions will vary with temperature and concentration. The purpose of the present study is to provide experimental data on association equilibria at different temperatures and over a range of water contents, including anhydrous molten salts, in order to test more realistic models of association in very concentrated aqueous electrolyte solutions. The nitrates are sufficiently soluble in water at moderate temperatures to permit investigations at low water contents. They are relatively low melting and information on association equilibria in several anhydrous molten nitrates is available. In particular, the association of cadmium ion with bromide has been studied extensively in anhydrous nitrate melts.9 The vapor pressure of water in melts containing as much as about 1.25 moles of water/mole of nitrate is low enough, even at temperatures above loo", that a pressurized system is not required.lOsll Hence, it is possible to study the association of Cd2+ with Br- over more than half of the concentration range between the molten salt and the dilute aqueous solutions. In this paper, we describe measurements of the emf of the cell
'
AglAgBr (Li,K)Br Hzo
1
5'
(L1,K)Br iAgBr,Ag
i (reference)ll Cd(NO&
(I)
1
at 119 and 168" with different water contents and at different concentrations of cadmium ion and of bromide ion. From the dependence of the emf on the concentration of cadmium nitrate at fixed values of the concentration of bromide, the activity coefficients of (Li,K)Br and the association constant for the formation of CdBrf are calculated at each water content and at each temperature. The results are compared with the association constants in anhydrous molten salt solutions.
Experimental Section The emf of the cell I was measured using a modification of the apparatus and method used previously for measurement,s of the emf of cells similar to I, but at a lower temperature and with the solvent NH4NOa2H20. A diagram of the modified apparatus is shown in Figure 1. The cell is a glass vessel immersed in a constant-temperature ( =f=O.l") bath containing silicone oil. The cell is provided with ports for the insertion of a reference half-cell, electrode leads, a motor-driven stirrer, solute additions, and a gas inlet. To minimize changes of composition due to the evaporation of water, a stream of equilibrated nitrogen was passed
2627
HEATERS%
(Li,K)NOa Ag,AgBr (Li,K)NOa (Li,K)Br AgBr,Ag. (Li,K)Br Cd(NO&
Hz0
,
KO
over the solution in the cell during the measurements. The nitrogen was equilibrated by passing it through a flask of solution having the same composition and temperatures as the solvent in the cell. The connecting tubes were heated electrically to prevent condensation of water. The reference half-cell consists of a Pyrex ultrafine fritted glass Buchner funnel containing the same solvent as the indicator half-cell. The electrodes are silver mires which were coated with silver bromide by first flaming the end of a clean silver wire (about 26 gauge) and then immersing it in a dilute solutiori of potassium bromide and adding silver nitrate." In some of the measurements, platinum foils (3) R. H. Stokes and R. A. Robinson, J. Am. Chem. Soc., 70, 1870 (1948). (4) M. L. Miller and C. L. Sheridan, J.Phys. Chem., 60, 184 (1956). (5) A. N.Campbell, E. M. Kartzmark, and D. F. Williams, Can. J . Chem., 40, 890(1962). (6) A. G.Keenan, J. Phys. Chem., 61,780 (1957). (7) (a) J. M. C. Hess, J. Braunstein, and H. Braunstein, J. Inorg. Nucl. Chem., 26, 811 (1964); (b) J. M. C. Hess, Ph.D. Dissertation, University of Maine, 1961 (University Microfilms, Ann Arbor, Mich., No. 61-5210). (8) M. Blander, J . Phys. Chem., 63, 1262 (1959). (9) J. Braunstein and A. S. Minano, Inorg. Chem., 5, 942 (1966); 3, 218 (1964). (10) T. B. Tripp and J. Braunstein, unpublished data. (11) A. N. Campbell, J. B. Fishman, G. Rutherford, T. P. Schaefer, and L. Ross, Can. J. Chem., 34, 151 (1956).
Volume ?'I, Number 8 Julg 1967
PETER C. LAMMERS AND JERRY BRAUNSTEIN
2628
Table I: Change of Emf of Cell I and the Activity Coefficient Function the Stoichiometric Mole Ratios of Cd(NOa)z, (Li,K)Br, and H20
[(l/rcLi.K,er)
- 11 us.
LiNOa-KNOa; 0.26HeO/NOa T = 119.1O
RB= ~ 0,1255 X 10-3
R B= ~ 0.0819 X 0.03324 0.110 0.712 0.08534 0.1504 1.283 0.2536 2.184 0.3855 4.372 0.5799 5.424 R B= ~ 0.6617 X 0.0395 0.156 4.90 0.0945 0.419 11.84 0.826 20.41 0.1767 0.2422 1.232 27.19 0,3655 1.960 36.76 0.4443 2.504 42.47 3.848 53.48 0.6073 5.612 63.99 0.8746 RB= ~ 2.273 X lo-' 2.33 0.0393 0.071 5.59 0.0931 0.179 9.16 0.1551 0.310 13.64 0.2282 0.496 2.5.17 0.4202 1.103 36.55 0.6115 1.942 51.22 0.8884 3.536 3.54 18.22 27.97 39.23 56.95 61.54
11.25 22.17 30.75 41.52 52.81 59.36
0.05108 0.1157 0.1836 0.2984 0.4565 0.5809 R B= ~ 0.6927 X 9.96 0.0728 20.46 0.1613 30.45 0.2424 41.60 0.3835 53 96 0.5631 64.23 0.7723
lo-'
x
10-3
R B= ~ 3.668
RB= ~ 0.1218 x 10-3 6.21 11.91 18.16 32.84 49.01 58.71 71.26
0.05919 0.200 0.08453 0.421 0.1384 0.706 0.3192 1.636 0.6322 3.268 0.8986 4.658 1.4004 7.195 R B= ~ 0.6572 X lo-' 0.235 7.16 0.0507 0.1611 0.675 17.47 0.2753 1.230 27.15 0.3776 1.775 34.55 0.5815 2.507 42.86 4.247 56.06 0.9332 6.526 68.31 1.2989 RB= ~ 1.745 X 0.0399 0.078 2.57 0.1417 0.277 8.28 0.2657 0.592 15.75 0.975 23.06 0.4023 2.217 39.58 0.6149 2.629 43.67 0.8102 1.288 4.507 57.80
The Journal of Phyaical C h m k t r y
0.342 0.830 1.457 2.315 3.917 5.660
I
1.22 2.67 6.32 11.32 17.25 25.57 39.99
RB= ~ 0.3335 X 10-3 0.394 0.924 1.479 2.407 3.754 4.768
0.0296 0.0695 0.1417 0.3055 0.4204 0.6036 0.8329
R B= ~ 0.09348 X
R B= ~ 0.2815 X lo-' 0.176 0.0474 0.597 0.1477 0.2476 1.062 0.3584 1.641 2.561 0.5402 1.260 6.220 8.860 1.7067 R B= ~ 1.107 X lo-' 0.05858 0.137 4.35 0.1165 0.312 9.20 0.3253 0.944 22.50 2.078 38.06 0.6119 0.8384 3.210 48.65 5.662 64.20 1.381
R B= ~ 1.762 X lo-* 0.03202 0.09851 0.1696 0.2543 0.4946 0.7226 1,0145 1.8200
0.0294 0.207 0.0797 0.511 0.1601 1.059 0.2616 1.656 0.4078 3.006 0.6190 6.727 R B= ~ 1.375 x 10-3 4.25 0.0365 0.133 8.96 0.0440 0.303 28.55 0.3365 1.323 39.49 0.5021 2.209 49.77 0.6778 3.347
0.037 0.082 0.205 0.397 0.664 1.729 2.256
5.49 15.86 24.51 32.90 43.03 66.97 76.03
2.03 5.30 9.12 13.71 27.26 37.26 49.41 69.85
6.38 13.99 24.46 33.08 47.01 69.30
0.062 0.169 0.309 0.499 1.236 2.004 3.300 6.864
4.05 7.59 17.41 28.38 50.11 57.41 67.40
0.02087 0.127 0.04703 0.251 0.1258 0.671 0.2155 1.309 0.5777 3.285 0.7496 4.438 1 ,0567 6.302 RB= ~ 1.398 X 10-8 2.89 0.03306 0.089 5.89 0.07179 0.190 11.99 0.1519 0.425 28.55 0.3944 1.323 44.70 0.6642 2.741 55.56 0.9217 4.156 62.59 1.125 5.345 RB= ~ 3.183 x 10-3 2.95 0.0744 0.091 4.30 0.1252 0.135 9.87 0.3231 0.338 18.10 0.4672 0.706 32.40 0.9312 0.591 46.96 1.1716 3.119 63.44 1.7334 75.90 2.469 82.12 3.117
HYDRATION AND ASSOCIATION EQUILIBRIA IN AQUEOUSMOLTEN SALTS
2629
LiNOa-KNOa; 0.76HzO/NOa T = 119.1"
R B= ~ 1.191 x 10-3
R B= ~ 0.3545 X lo-' 2.44 8.19 12.64 24.64 31.67 41.74 53.71
0.0203 0.0920 0.1444 0.3276 0.5037 0,7452 1.1810 RB= ~ 0.1969 X 4.12 0.0598 7.50 0.0865 9.25 0.1019 12.72 0.1440
0.074 0.261 0.452 1.044 1.547 2.429 3.882
9.20 18.00 28.94 38.93 47.35 55.55
0.129 0.248 0.324 0.456
7.58 18.25 27.85 36.80 45.60 51.76 60.90
0.0267 0.0490 0.0685 0.0887 0.1033 0.1473 0.1661 R B= ~ 1.001 X 8.75 0.1298 16.48 0.2553 0.3772 22.95
0.064 0.157 0.212 0.250 0.316 0.394 0.435
0.05936 0.1333 0.2459 0.3318 0.5498 0.7433 1.1266 1.5563
0.1128 0.250 0.2803 0.714 0.4750 1.175 0.6939 1.964 0.9907 2.843 1.248 3.609 1,706 4.947 RB= ~ 1.771 x 10-3 4.91 0.0851 0.156 10.48 0.2012 0.362 17.48 0.3387 0.675 35.25 0.8144 1.831 43.75 1.0995 2.639 51.00 1.3940 3.348 1.1045 X 0.1144 0.2449 0.4544 0.6201 0.9510 1.589 RB= ~ 3.1869 X 8.05 0.2141 20.89 0.5288 32.69 0.8399 43.73 1,1340 54.83 1 .4988
3.26 8.53 16.30 23.90 36.42 47.46 53.94
0.00271 0.101 0.0859 0.285 0.1867 0.570 0.3106 0.938 0.5717 1.740 0.8908 2.719 1.1169 3.450 R B ~ 0.1234 X 10-3 3.89 0.0324 0.122 11.05 0.1055 0.386 18.91 0.2026 0.748 26.50 0.3128 1.186 36.52 0.5077 1.872 48.05 0.7974 3.131 66.46 1.3078 6.117 R B= ~ 0.0436 X 4.43 0.02816 0.140 11.14 0.09258 0.389 18.67 0.1881 0.735 25.99 0.2919 1.154 35.36 0.4939 1.840
R B= ~ 0.6959 x 10-3
RBr
0.295 0.627 0.969
R B= ~ 0.1318 X 10-3 6.06 12.04 20.06 25.06 34.50 42.56 54.45 62.42
R B= ~ 0.1371 X 10-3 0.312 0.702 1.350 2.250 3.046 4.156
R B= ~ 0.4642 X
R B= ~ 0.2380 X lo-' 2.11 4.95 6.50 7.58 9.30 11.25 12.24
0.1363 0.2695 0.4773 0.7555 0.9858 1.320
0.196 0.427 0.808 1.096 1.774 2.513 3.990 5.313
7.58 15.50 27.05 36.14 46.10 64.33
0.251 0.580 1.222 1.906 2.900 5.672
11.00 22.57 40.03 54.93 60.09
0.1430 0.3185 0.6615 1.1360 1.3207
0.384 0.947 2.260 4.061 4.893
0.268 0.853 1.625 2.639 4.046
LiNOs-KNOs; l.OOHzO/NOa T = 119.1°
Rer = 0.0961 X 10-8 6.55 11.86 21.55 30.90 43.10 53.60
0.0466 0.1042 0.2291 0.3705 0.6385 0.9577
RBr
0.213 0.420 0.890 1.490 2.569 3.867
4.80 9.57 18.44 27.63 35 20 43.84 49.45 I
= 1.181 x 10-3
0.0887 0.1731 0.3395 0.5341 0.7615 1.048 1.273
0.152 0.326 0.723 1.260 1.827 2.649 3.305
1.62 3.98 9.24 14.76 24.50 30.96 37.30 47.22
Rer = 0.1654 X 0.01560 0.04659 0.1187 0.2054 0.3537 0.4937 0.6803 0.8908
0.049 0.125 0.314 0.546 1.062 1.494 2.052 3.031
Volume 71, Number 8 July 1967
PETERC. LAMMERS AND JERRY BRAUNSTEIN
2630
LiN03-KNOs; l.OOHzO/NOa; Z!' = 119.1' R B= ~ 0.0798X 0.0267 0.120 3.83 0.415 11.76 0.0871 0.646 16.88 0.1483 0.2739 1.229 25.59 1.885 35.90 0.5103 2.753 44.80 0.7838 RB? = 0.1381X lov3 0.057 1.89 0.0261 0.156 4.90 0.0683 0.318 9.34 0.1388 0.638 16.71 0.2587 Rer = 2.305 X 3.08 0.0851 5.99 0.1777 7.89 0.2428 0.3221 11.14 19.54 0.5083 34.89 0.9107 47.71 1.298 R B= ~ 0.6176X 0.0669 5.76 14.00 0.1794 0.3272 22.65 31.05 0.4990 0.9912 49.39 64.75 1.7142 75.21 2.2964
0.095 0.193 0.262 0.389 0.780 1.801 3.089 0.185 0.512 0.952 1.501 3.172 5.763 8.210
Rgr = 0.1554X lo-'
3.78 7.86 15.05 25.75 35.37 40.34 44.75
0.0634 0.1426 0.3077 0.5053 0.7512 0.9725 1.1623
0.119 0.261 0.558 1.138 1.821 2.290 2.747
R~~ = 1.642x 10-3 0.0478 0.078 2.54 0.110 3.53 0.1021 0.261 8.29 0.1665 0.525 14.29 0.2705 0.857 20.96 0,4374 1.267 27.69 0.5962 1.524 32.03 0.7229 2.447 41.91 1.0320 RB= ~ 0.3015X 10-3 1.70 0.0231 0.051 5.50 0,0494 0.176 10.77 0.1473 0.375 17.00 0,2283 0,652 21.00 0.3329 0.859 30.60 0.5555 1.468 38.60 0.7779 2.125
The Journal of Physkal Chemistry
RB= ~ 0.1203 X lov3 12.59 0.1356 0.450 20.10 0.2216 0.810 27.69 0.3332 1.264 36.76 0.5013 1.960 47.14 0.7713 3.021
Rgr = 0.1014X 10-3 8.94 0.0944 0.301 20.02 0.2477 0.806 28.43 0.4068 1.315 37.84 0.6687 2.036 48.54 0.9929 3.190 62.34 1.324 5.298 RB= ~ 0.4848X 10-3 3.36 0.0357 0.105 9.16 0.1066 0.310 16.34 0.2238 0.620 27.40 0.3833 1.245 2.447 41.92 0.7437
RB= ~ I.722 x 10-3 0.0883 0.087 0.2124 0.321 0.4497 0.879 0.6727 1.633 0.9010 2.164
2.82 9.43 21.37 32.79 39.02
RB= ~ 0.3059X 0.0818 0.2017 0.4281 n.6286 1.2010
8.21 16.38 28.57 38.89 57.16
0.274 0.622 1.324 2.152 4.405
R B ~ 0.5042X 10-3 8.80 0.1286 0.297 14.44 0.2484 0.532 27.08 0.5284 1.224 33.74 0.7109 1.707 2.612 43.50 1.0499
R B ~ 0.6980X lo-' 8.56 0.0928 0.288 15.03 0.2055 0.559 22.21 0.3367 0.927 30.05 0.5029 1.421 42.91 0.8548 2.549 57.84 1.188 3.758 58.98 1.286 4.703 LiN03-KNOa; 1.26HzO/N08;2' Rgr = 0.5829X 2.74 0.04680 5.53 0.1138 11.33 0,1999 16.33 0.3053 24.96 0.4935 31.32 0.6902 39.71 1.009 50.19 1.448 R B= ~ 0.3056X 3.49 0.04639 14.54 0.2516 21.83 0.3865 28.52 0.5221 33.03 0.6785 40.30 0.8965 49.72 1.2472 57.19 1.6248 R B ~ 1.0908X 0.84 0.0221 0.0991 3.59 8.36 0.2253 16.12 0.4678 23.13 0,6122 27.19 0.8787 30.94 1.0491
= 119.1' Rgr
0.084 0.177 0.397 0.619 1.089 1.521 2.229 3.400
5.16 10.00 15.50 27.32 39.81 46.33 53.70
0.109 0.536 0.905 1.321 1.651 2.286 3.340 4.410
6.45 19.54 28.38 31.43 34.93 41.02 48.23
Rgr
0.023 0.112 0.280 0.609 0.979 1.232 1.493
=i
0.1292X lo-' 0.0677 0.165 0.343 0.1467 0.580 0.2504 1.240 0.5103 2.238 0.8789 1.156 2.926 1.475 3.880
= 0.2657 X
0.08003 0.2840 0.4327 0.5237 0.6029 0.7781 1 .0225
0.210 0.780 1.311 1.529 1 ,804 2.357 4.153
HYDRATION AND ASSOCIATION EQUILIBRIA IN AQUEOUS MOLTENSALTS
2631
Table I (Continued) AE, mv
RCd
x
10'
(I/'YBr)
-
1
AE, mv
RCd X 10'
(1/YBr)
-1
AE, mv
RCd
x
10'
(I/YBr)
-
1
LiN03-KN03; 0. 10HzO/N03
T 0.0178 0.0472 0.2745 0.3958 0.5968
0.060 0.156 1.035 1 ,694 3.029
RB? = 0.7200 X lo-' 2.82 8.10 21.03 29.39 43.29
0.03059 0.08187 0.1699 0.2364 0.4763
168"
R B= ~ 2.624 X
RB? = 0.8999 X lo-* 2.20 5.50 27.00 37.65 52.95
=
0.077 0.238 0.739 1.167 2.125
R B= ~ 0.1581 X 6.50 13.75 20.65 30.48 39.48 51.50
0.032 0.0184 0.0393 0.058 0.1256 0.168 0.2241 0.305 0.2931 0.438 0.4228 0.714 0.7970 1.152 0.8282 2.121 0.9935 2.935 R B= ~ 1.401 X lo-' 1.14 0.02026 0.030 5.44 0.06807 0.153 9.16 0.1428 0.273 15.61 0.2326 0.507 22.24 0.3333 0.796 33.96 0.5134 1 ,444 44.16 0.7036 2.198 56.74 0.9873 3.450
1.16 2.14 5.89 10.11 13.81 20.47 29.14 43.25 52.05
coated electrolytically with silver and silver bromide were used as electrodes' with no difference in the results. The chemicals were Mallinckrodt reagent grade and were used without further purification other than oven drying. The cell was assembled with the solvent of the same composition, equimolar LiN03-KN03 containing between 0.1 and 1.26 moles of water/mole of nitrate, in the reference half-cell and in the indicator halfcell. Approximately 1 mole of LiN03-KN03 was used in the cell. The liquid junction potential in such a cell is virtually zero since the ccncentrations of bromide and of cadmium in the solutions are less than mole fraction and the current is carried virtually entirely by the solvent ions. Before adding cadmium nitrate to the cell, additions of KBr were made either as crystalline KBr or, with a syringe microburet, as an almost saturated aqueous solution of KBr. The minute amount of water added with the KBr was found to have no effect on the emf of the cell. The use of KBr instead of (Li,K)Br for solute additions had no measurable effect on the emf or solvent composition. The emf was measured as a function of the concentration of bromide in the indicator half-cell and was found to follow the Nernst equation with respect to the stoichiometric concentration of bromide, as in previous s t u d i e ~ . ~Additions ,~ of cadmium nitrate then were made to the indicator half-cell and the emf was measured, at a fixed bromide concentration, after each
0.0328 0.0782 0.1264 0.2062 0.3169 0.4544
0.187 0.436 0.722 1.131 1.827 2.878
R B ~ 0.3435 X 5.71 9.59 19.23 28.42 38.66 48.54 60.62
0.01722 0.07719 0.1633 0.2561 0.3869 0.5780 0.7777
0.161 0.285 0.660 1.110 1.767 2.589 3.932
cadmium addition. The measured emf was stable within 1 0 . 1 mv for periods of several hours. In some of the measurements at 168", a slow drift of emf was observed and the precision of these measurements is 1 0 . 3 mv.
Results The results of the measurements are listed in Table I. The concentrations are given as the stoichiometric mole RBr
= n(Li,IoBr/n(Li.R)No,,
Red =
%dCwo3,/
and RH = nxr,o/n(Li,K)Noa. The n are the numbers of moles of Cd(N03)2, (Li,K)Br, water, and
?E(Li,K)NOa,
(Li,K)NOa. The emf of the cell I is given by the equation
if the indicator and reference half-cells contain solvent of the same composition and the concentration of the solutes is below mole f r a c t i ~ n . ~ ,The ' ~ activities of (Li,K)Br in the indicator and reference halfcells are a ( L i , K ) B r and u ' ( L ~ , K ) B ~ . The other symbols have their usual significance. Equation 1 may be written
~
~
~~~~
~~
(12) J. Braunstein, A. R. Alvarez-Funes, and H. Braunstein, J . Phye. Chem., 70, 2734 (1966).
Volume 71, Number 8 July 1967
PETERC. LAMMERS AND JERRY BRAUNSTEIN
2632
where Y ( L ~ , K ) Bis~ the activity coefficient of (Li,K)Br. Since the emf of the cell at each water content in the abserice of cRdmium nitrate is observed to follow the Nernst equation in the concentration of bromide, Y ( L ~ , K ) Bis ~ constant in the absence of Cd(NOa)2 and may be taken as unity if the reference state is infinite dilution of bromide in equimolar LiNOrKN03 H 2 0 at each water content. When Cd(NO& is added to the indicator half-cell, the emf changes as shown in Table I. The activity coefficient of (Li,K)Br in the presence of Cd(N03)2may be calculated from the difference, aE, between the emf of cell I in the presence and in the absence of Cd(NOa)27
+
The activity coefficients also are given in Table I as the function [ ( ~ / Y ( L ~ , K ) B ~ ) 11 which is convenient for the graphical evaluation of the association constants. Thermodynamic equilibrium constants for the association reaction
-
Cd*+
+ Br-
= CdBr+
(4)
Table 11: Association Constants of CdBr+ in the Solvents ( Li,K)NOa-&O Molality of (Li,K)NOa, moles of (Li,K)NOa/ kg of HsO
T, OC
RHsO
119
1.26 1 .oo 0.76 0.51 0.26 0 0.10 0
168
44
55 73 109 214 03
550 CD
K,
Km,
moles of (Li,K)NOa/ mole
kg of
2800 3600 4100 5600 9100 19000 5800 8200
solvent/ mole
300 370 400
530 820 1600 500 700
salts has been used to estimate the association constants in the anhydrous molten salt at the temperatures of the aqueous melts. At 168", Klsa = 8200; at 119", KIIO= 19,000.819 The association constants are seen to decrease with increasing water content. In an anhydrous molten salt solvent the association reaction (eq 4) may be interpreted as the replacement of a solvent anion from the coordination sphere of a solute cation by n solute anion
in each of the solvents, Le., at each water content, were calculated by graphical analysis of the activity AD, CS, = ACDZ-1 DS, coefficients as described p r e v i o ~ s l y . ~ ~ g ~Since ~ ~ J *1/ Y(Li,K)Br is more nearly linear than In ~ / Y ( L ~ , K ) B ~ , where A and C represent the solute cation and the the association constants were calculated from the relasolute anion which associate, S and D represent the tion solvent cation and the solvent anion, and z is the coordination number. In aqueous melts, the coordination sphere of a cation will contain water as well as solvent anions. An associated species CdBr+ may be Values of the association constants are listed in Table formed by the displacement of a water dipole rather than a nitrate ion. If the water molecules were firmly I1 for each solvent composition and temperature. The uncertainty in the association constants is estibound to the cations (and the ion-dipole forces are not mated as 5%. The molalities of the electrolyte in strong enough for this to be expected), the Helmholtz water are listed, although these concentration units free energy of association of CdBr+ in the aqueous are meaningless in such concentrated solutions, in melts, calculated with the quasi-lattice model from the measured association constants in the aqueous melts, order to indicate composition of the solutions in more familiar units. would be nearly independent of temperature at a The association constants calculated using mole given water content and this is found not to be the case.' ratio concentration units, moles of solute per mole of Hence, the water molecules may be considered as ligands competing with bromide ions for the displacement of a (Li,K)NOa, are listed in the fourth column of Table 11. These concentration units would be appropriate nitrate ion from the coordination sphere of a cadmium to a molten salt model in which the water molecules ion. The change of energy (or other thermodyare considered firmly bound to the cations. Associanamic function) in association reaction 4 in the aqueous melts is therefore some combination of the energy tion constants calculated using molal concentration units, moles of solute per kilograni of solvent mixture of association in the anhydrous molten salt and the [(Li,K)NOa HzO], are listed in the last column. The association constant of CdBr+ in anhydrous (13) J. Braunstein, M. Blander, and R . M. Lindgren, J . Am. Chem. equimolar LiNOa-KN03 has been measured at 171 Soc., 84, 1529 (1962). and at 2 4 O O . O The quasi-lattice model of molten (14) J. Braunstein and R. M. Lindgren, {bid., 84, 1534 (1962).
+
+
The Journal of Physical Chemistry
+
THELASERPHOTOLYSIS OF METHYLENE BLUE
energy of the competing hydration equilibrium. The observed increase of the association constants with decreasing water content indicates that bromide ions displace nitrate ions from the coordination sphere of cadmium ions more readily than they displace water
2633
molecules and is a measure of the tendency of the cadmium ions to become hydrated. In a subsequent paper, we shall present a statistical interpretation of the competing hydration and association equilibria of cadmium ions in aqueous molten salts.
The Laser Photolysis of Methylene Blue
by Robert M. Danziger, Kedma H. Bar-Eli, and Karl Weiss Photochemistry and Spectroacopy Laboratory, Department of Chemistry, Northeastern University, Boston, Massachusetts 021 16 (Received Janiulry SO, 1967)
~
~~
The giant pulse ruby laser flash photolysis of plain aqueous methylene blue solutions reveals three transient species (A, B, and C) with half-lives of -2, 30, and 140-psec, respectively. With a 5.5 X M dye solution a 0.5-joule, 30-nsec pulse causes almost complete conversion into transients. The photochemical change is completely reversible. M indicate that Experiments a t various concentrations in the range 5.5-294 X transients A and C are derived from the dimeric form of the dye, which exists in equilibrium with the monomer. It is proposed that transients A and B are the triplet states of the dimer and monomer, respectively, and that transient A decays primarily into the longer lived transient C, which is viewed as a charge-transfer state of the dimer. The creation of C by reaction of the monomer triplet (B) with the ground-state monomer is estimated to be slower than diffusion controlled. The establishment of the groundstate monomer-dimer equilibrium appears to be slower than all the transient decay processes. The results obtained by laser photolysis and conventional flash photolysis are compared.
Introduction The pulsed ruby laser constitutes an ideal flash photolysis source. The output is strictly monochromatic at 6493 A and with &-spoiling techniques flash durations of 30 X sec are readily achieved.’ These properties have obvious advantages for the study of very shortlived transients.2 I n this paper we report the giant pulse laser flash photolysis of aqueous methylene blue solutiohs. The dye shows strong absorption in the 5000-7000-A region, which encompasses the ruby laser emission line (eaara -1 X lo4 in water). Extensive previous photochemical studies indicate that methylene blue is readily p h o t o r e d u ~ e d ~and - ~ conventional flash photolysis has revealed two transient
It was not anticipated that the dye would show markedly different behavior with laser excitation, Rather, this study was designed to develop the tech(1) B. A. Lengyel, “Introduction to Laser Physics,” John Wiley and Sons, Inc., New York, N. Y., 1966. (2) Chemical applications of lasers, actual and potential, have recently been reviewed by D. L. Rousseau, J. Chem. Educ., 43, 566 (1966). (3) M. Koizumi, H. Obata, and 5. Hayashi, Bull. Chem. SOC. Japan. 37, 108 (1964),and previous papers cited. (4) G. Oster and N. Wotherspoon, J . Am. Chem. Soc.. 79, 4836 (1957). (5) C. A. Parker, J . Phys. Chem., 63, 26 (1959). (6) S.Kato, M. Morita, and M. Koizumi, B d . Chem. SOC..lapan, 3 7 , 117 (1964). (7) S. Matsumoto, ibid., 3 7 , 491 (1964).
Volzime 7 1 , Surnlrer 8 July 1967
