Enthalpy of dilution of aqueous solutions of LiCl, NaBr, NaI, KCl, KBr, and CsCl at about 373, 423, and 473 K

A-218 J. Chem.

Thermodynamics

1982, 14,563-576

Enthalpy of dilution of aqueous solutions of LiCI, NaBr, Nal, KCI, KBr, and CsCl at about 373,423, and 473 K JAMES E. MAYRATH

and ROBERT H. WOOD”

Department of Chemistry, University of Delaware, Newark, Delaware 19711, U.S.A. (Received 14 August 1981; in revised form

16

December 1981)

The enthalpies of dilution of aqueous solutions of LiCl, NaBr, NaI, KCI, KBr, and CsCl have been measured at temperatures of about 373, 423, and 473 K. These measurements, together with literature data at lower temperatures, have been used to calculate reliable values of the relative apparent molar enthalpy .$,, the difference {4(T) - &298.15 K)) in osmotic coefficient on going from 298.15 K to T, and the logarithm ln{y(T)/y(298.15 K)] of the ratio of activity coefficients at T and 298.15 K. As temperature increases, differences in the thermodynamic properties between the individual salts diminish.

1. Introduction The measurements reported here are part of a continuing investigation of the thermodynamics of aqueous salt solutions at high temperatures using flow calorimetry which allows rapid acquisition of enthalpies of dilution.(1V2) Although there are relatively few data on aqueous salt solutions above 373 K, the properties of these solutions are of great practical and theoretical interest. This paper presents enthalpies of dilution for a variety of alkali halides. From these and previous roomtemperature measurements, osmotic and activity coefficients have been calculated from 298.15 to 473.15 K.

2. Experimental The flow calorimeter used in these experiments and its method of operation have been described in detail elsewhere. (2*3) The accuracy of the calorimeter is approximately 1 per cent and temperatures of the experiments are accurate to about 0.3 K. The pressures were kept constant at 0.1 to 0.3 MPa greater than the water vapor pressure at the experimental temperature. The sources of the chemicals used in these experiments and the manufacturer’s mass percentages are: LiCl (Merck, 99.4), NaBr (Fisher, 99.9) NaI (Allied, 99.99). 0 To whom correspondence should be addressed. 0021~9614/82/060563 + 14 .%02.00/O

0 1982 Academic Press Inc. (London) Limited

564

J. E. MAYRATH

AND

R. H. WOOD

KC1 (Fisher, 99.99). KBr (Elmer and Amend. 99.6; Mathison. 99.8; Allied. 99.8). CsCl (ROC/RIC, 99.9). The KBr from the three sources was combined into a single batch and recrystallized from water. This procedure reduced the sodium content from the original 0.02 to 0.04 to less than 0.01 mass per cent. The other salts were used as received. The KC1 was dried for 2 d at 673 K and the solutions were prepared by weighing. Stock solutions of the other salts were prepared and analyzed by a gravimetric silver-nitrate procedure with an accuracy of fO.l per cent. The stock solutions were diluted either by weighing or volumetrically. As a check on the volumetric dilutions, the concentration after a whole series of volumetric dilutions was checked to within 0.2 per cent. All weighings were corrected for buoyancy. 3. Results The results of the measurements are presented in table 1. This table gives the initial molality mi of the solution, final molality mf of the solution, and observed and calculated enthalpies of dilution AdilH. At many molalities, repeated experiments were run and table 1 gives the average result plus oe, an estimate of the accuracy of the average taking into account the scatter of the points, and the behavior of the calorimeter at the time of measurement. The experimental results for each temperature in table 1 were fitted using a leastsquares technique by the equation : Adi@ = L&)

(1)

- L+(mi ).

where the relative apparent molar enthalpy $,(m) at molality L,&m)/(J . mol - ’ ) = So-,(T)(m/m’

)I” + i

m is given by

B,(m/m”)(‘+ lb”,

(2)

i=l

where S,-,(T) is the Debye-Hiickel limiting slope (taken from the compilation by Helgeson and Kirkham)‘4’ at the experimental temperature, and m’ = 1 mol. kg- ‘. The results of the least-squares fits are presented in tables 1 and 2. No corrections were made for changes in the pressure of the experiments with temperature, since these effects are negligible at these pressures. The present measurements, together with the relative apparent molar enthalpies of Parkerc5’ at 298.15 K, can be used to calculate changes in both osmotic and activity coefficients with temperature at constant molality. For CsCl, Parker’s data were supplemented at higher molalities from Levine and Wood,‘6’ and from Stakhanova er ~1.‘~’ Standard thermodynamic manipulations give the equations : & (X,/amri2)d(i/7-), N’d$(T I= (mi’2/2W (3) sT and T: f L++ (m1’2/2)(aL,$3m112); d(l/T). (4) ln(G’N~(T,)1 = WR) sT TO tabulate values of L,, (4(T)-4(298.15 K)), and ln{y(T)/y(298.15 K); at round

ENTHALPIES TABLE

1. Enthalpies

OF

of dilution

w

DILUTION Adi,H

OF

LiCI;

LiCl;

ALKALI

of aqueous salt solutions temperatures f&J”

iGi%p LiCl:

AQUEOUS

-Adi,H ___ J.mol-’

b

from

565

HALIDES molality

~ ue J.mol-’

mi to m, at various P

3 J.moll’

T = 373.15 K 9.443 4.302 2.063 1.012 0.5011 0.2494 0.1245 0.06216 0.03106

4.302 2.063 1.012 0.5011 0.2494 0.1245 0.06216 0.03106 0.01553

2 1 1 1 1 2 5 4 5

5804 2345 1275 837 614 462 344 278 211

5 5 5 5 5 20 12 22 24

0 -3 10 -11 -6 13 2 6

T = 423.65 16.508 11.312 7.590 7.181 5.092 4.866 3.850 3.563 3.188 3.186 2.829 2.613 2.087 1.927 1.798 1.539 1.3508 1.1161 0.8120 0.7934 0.5944 0.4290 0.3100 0.2200 0.1555 0.1027 0.0680 0.0469 0.0306 e

K 7.039 5.099 3.521 3.338 2.423 2.319 1.855 1.721 1.547 1.545 1.377 1.275 0.9770 0.9464 0.8840 0.7590 0.6668 0.5524 0.4020 0.3940 0.2953 0.2137 1.1545 0.1096 0.0777 0.0513 0.0340 0.0234 0.0153

2 1 1 1 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

6328 4430 3119 3019 2279 221R 1877 1801 1676 1648 1544 1492 1318 1262 1217 1129 1059 977 850 838 758 672 587 516 450 374 324 286 156

42 50 3 3 3 5 5 5 5 5 5 5 7 5 5 8 7 8 10 8 10 15 15 20 20 30 30 30 40

-6 45 -50 -76 28 23 46 27 22 50 26 - 3 36 -37 -42 -57 -59 -66 -43 -40 17 II 56 89 113 139 135 126 201

T = 472.95 16.510 10.510 6.288 5.018 3.343 1.801 1.588 0.9240 0.2469 0.1279 0.0662

K 7.040 4.737 2.955 2.389 1.618 0.8860 0.7820 0.4590 0.1232 0.0639 0.0331

1 1 1 1 1 1 1 1 1 1 1

7917 5768 4066 3499 2816 2076 1962 1578 993 810 622

10 10 10 5 3 3 3 5 10 10 40

7 19 -95 55 91 -22 -42 -96 63 107 150

-0

*

566

J. E. MAYRATH TABLE

~- mi

4

mol. kg-’

mol. kg- 1

NaBr;

NaBr;

NaBr;

’

NaI;

NaI;

T = 373.15 7.998 3.597 1.716 0.8398 0.4156 0.2067 0.10310 0.05149

K

T = 423.65 8.114 4.158 2.454 1.4525 0.9061 0.5630 0.360 0.2268 0.1532 0.1098 0.0791

K

T = 472.95 8.114 4.496 2.219 1.162 0.6152 0.3323 0.1792 0.1038 0.0581

K

T = 373.15 4.709 2.185 1.050 0.5154 0.2554 0.1271 0.0634

K

T = 423.65 4.960 3.249 2.191 1.469 0.9750 0.5460 0.3296 0.2042 0.1234 0.0794 0.0521 0.0329

K

N”

AND

R. H. WOOD

l-continued

a.

emyi’ -

3.597 1.716 0.8398 0.4156 0.2067 0.10310 0.05149 0.02574

1 1 1 2 6 4

J.mol-’

‘

‘4

d

J,mol-’

3 3 3 4 14 5

;

1882 728 513 446 406 348 294 228

3.642 1.969 1.189 0.7130 0.4478 0.2796 0.1792 0.1130 0.0764 0.0548 0.0394

1 1 1 1 1 1 1 1 1 1 3

4010 2230 1599 1252 1058 909 795 702 608 565 498

5 5 5 5 5 5 5 10 10 10 10

1 -6 12 -1 -8 -6 -7 14 -1 14

3.635 2.120 1.078 0.5726 0.3053 0.1655 0.0894 0.0518 0.0290

1 1 1 1 1 1 1 1 1

6324 4234 2905 2195 1764 1446 1222 1035 857

30 30 30 30 30 30 30 30 30

0 -4 15 -19 -13 24 10 5 -7

2.185 1.050 0.5154 0.2554 0.1271 0.0634 0.0316

9 1 7 6 6 13 9

543 368 365 357 326 286 241

4 5 3 1 6 10 17

-0

2.267 1.531 1.056 0.7150 0.4790 0.2705 0.1637 0.1017 0.0616 0.0397 0.0260 0.0164

1 1 1 1 1 1 1 1 1 1 1 3

2072 1512 1224 1058 931 806 730 668 588 547 596 502

3 3 3 3 3 5 6 7 8 9 10 20

1:

0 -2 10 -12 -12 8 13 24 -0

0 -0 0 -0 -0 1 1 -11 29 -15 -27 5 31 33 37 3 -115 -95

ENTHALPIES

OF

DILUTION

OF

TABLE mi mol.kg-’ NaI ; T = 472.95

T = 423.65

T = 472.95

T = 373.15 1.0000 0.4913 0.2436 0.1213 0.0605 0.0302

3s

l-continued -Adi,H __ J.mol-’

*

N”

~ 0, J.mol-’

2.273 1.270 0.7160 0.4000 0.2161 0.1196 0.0663 0.0369 0.0209

1 1 1 1 1 I 1 1 I

4016 2740 2088 1684 1397 1189 1005 857 757

3 3 3 5 7 10 10 20 50

2.103 1.020 0.5020 0.2500 0.1244 0.0621 0.0310 0.0155

1 1 1 I 1 1 6 8

688 528 474 431 382 332 246 208

3 3 3 5 10 10 15 15

2.117 1.453 0.7820 0.5480 0.3612 0.2010 0.1322 0.0876 0.0596 0.0412 0.0285 0.0207

1 1 1 1 2 1 1 1 1 1 1 2

1985 1645 1289 1155 1011 855 786 685 630 552 556 432

5 5 5 5 5 10 10 15 20 20 30 130

2.118 1.165 0.6420 0.3564 0.1965 0.1063 0.0588 0.0326 0.0181

1 1 1 1 1 1 1 1 1

3663 2814 2307 1922 1599 1332 1132 925 740

10 10 10 10 15 15 20 30 60

0.4913 0.2436 0.1213 0.0605 0.0302 0.0151

6 3 5 8 6 12

354 350 322 282 236 194

1 1 2 5 10 18

c

A ___ J.mol-’

d

0 -2 10 -14 -3 11 21 4 -47

0 -1 5 -6 -3 -7 22 4

K 0 -1 4 -5 -2 9 -9 10 -8 -1 -70 3

K

4.533 2.414 1.308 0.7200 0.3951 0.2132 0.1179 0.0653 0.0363 KBr;

561

K

4.533 3.040 1.601 1.118 0.7300 0.4041 0.2654 0.1756 0.1195 0.0824 0.0570 e 0.0415 KCl;

HALIDES

K

4.500 2.103 1.020 0.5020 0.2500 0.1244 0.0621 0.0310 KCI;

ALKALI

4 iziqp

4.960 2.666 1.471 0.8110 0.4355 0.2403 0.1329 0.0739 0.0418 KCl ; T = 373.15

AQUEOUS

0 -0 3 -12 10 16 -11 -13 -11

K 0 -0 0 -1 1 -1

568

J. E. MAYRATH TABLE 4 mol-kg-’

KBr;

KBr;

CsCl;

CsCI;

-

T = 423.65 4.503 2.879 1.868 1.1670 0.6920 0.4660 0.2723 0.1768 0.1102 0.0667 0.0466 0.0277 e

K

T = 472.95 4.503 2.395 1.292 0.6990 0.3882 0.2152 0.1175 0.0649 0.0360

K

T = 373.15 11.030 4.421 2.003 0.9612 0.4713 0.2334 0.1162 0.0580 0.02900 0.01446

K

T = 423.65 9.043 5.718 3.670 2.446 1.685 1.188 0.8500 0.6200 0.4590 0.3193 0.2269 0.1602 0.1150 0.0833 0.0608 0.0415 = 0.0223

K

mf molkg-’

N”

AND

R. H. WOOD

l-continued -Adi,H ___ J.mol-’

2.077 1.367 0.9040 0.5720 0.3420 0.2301 0.1355 0.0881 0.0550 0.0333 0.0233 0.0138

1 1 1 1 1 1 2 3 2 1 3 4

1613 1345 1162 1016 892 820 714 658 558 506 429 298

2.077 1.147 0.6320 0.3450 0.1928 0.1072 0.0586 0.0324 0.0180

1 1 1 1 1 1 1 1 1

3335 2584 2087 1738 1477 1236 1080 843 772

4.421 2.003 0.9612 0.4713 0.2334 0.1162 0.0580 0.02900 0.01446 0.00723

2 8 6 6 13 8 9 13 11 1

736 476 382 355 336 309 271 233 188 151

3.764 2.542 1.702 1.163 0.8140 0.5800 0.4180 0.3060 0.2270 0.1586 0.1129 0.0798 0.0574 0.0416 0.0304 0.0207 0.0111

1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 3 1

2378 1854 1496 1262 1111 995 912 844 778 729 682 614 571 514 454 349 308

c

b

UC

-

J.mol-’

A

*

J.mol-’

-4 8

15 16 15 20 ,30 100 150 5 5 5 10 10 10 30 70

-2 -7 -4 8 -5 17 -12 8 66 0 -1 7 -14 -3 30 -15 34 -66 -0 0

1

-1 4

4 11 14 13 15 3

-5 -2 4 2 4 -1 -0 2 -7 8 2

10 12 15 20 25 30 35 40 35 50

-0 -6 -5 8 -3 -9 5 -4 14 64 21

ENTHALPIES

OF

DILUTION

OF

TABLE

4 mol.kg-’ C&l; T = 472.95 K 9.043 4.009 2.114 1.127 0.6110 0.3368 0.1879 0.1040 0.0574 0.0319 0.01789 0.00995

m(

AQUEOUS

569

HALIDES

l-continued -A&l J.mol-’

N”

-

m 3.764 1.845 1.012 0.5510 0.3020 0.1673 0.0936 0.0519 0.0286 0.0159 0.00894 0.00498

ALKALI

1 1 1 1 1 1 1 1 1 1 1 1

b

0, < J,mol-’

___

4306 3051 2385 1946 1644 1388 1201 1026 886 780 642 577

5 5 5 5 5 10 10 15 20 30 40 60

--

A

d

J.mol-’

0

-3 18 -37 -8 49 44 20 -31 -95 - 102 - 158

’ N is the number of replicate experiments. * Adi,H is the average experimental enthalpy of dilution. c o, is the error of A&f estimated from the scatter of the N points and the calorimetric behavior. d A tid { A,i,H(calculated by equation 1) - A&f(expt)}. o These experiments were not included in the least-squares fit because. deviations from the fit were greater than 2~.

molalities and temperatures, the least-squares fit at each temperature was used to calculate values of L4 and aL+/am ‘/’ at round molalities. A cubic-spline routine was then used to interpolate L+ at round temperatures and to integrate equations (3) and (4) to give values of {4(?=)-b(298.15 K)} and ln{y(T)/y(298.15 K)). The results are presented in tables 2 and 3.t 4. Discussion Likke and Bromleyt’) measured the heat capacity of aqueous KC1 from 353.15 to 473.15 K. We can calculate the change in the relative apparent molar enthalpy between these temperatures by a Simpson’s rule integration of their smoothed measurements according to T

4(T)-L#$(T”)

=

(Cp,4-C~+Jd~~ f T’

where the integration is performed at a constant molality. The results of this calculation at molalities of 0.5589, 1.166, and 1.829 molekg-’ are 6.56, 8.84, and 10.66 kJ .mol- ‘, respectively. Spline fits of our measurements and the results at 298.15 K yield values of 6.37, 8.40, and 9.99 kJ. mol-’ at the same molalities. The agreement between the two sets of measurements is well within their expected error limits. Likke and Bromley estimate errors of about 0.3 per cent in heat capacity and a t More extensive tables are given in reference 3.

570

J. E. MAYRATH TABLE

T/K

2. Least-squares

polynomial

AND

R. H. WOOD

coefficients

for each salt (equation

So.,

4

5.523 9.542 16.156

- 5.603337 - 10.25433 - 17.54162

6.022988 7.804715 13.90293

- 3.47946 - 3.093078 - 5.772337

1.087011 0.6176618 1.191764

-0.1276993 - 0.048386662 - 0.095777828

5.523 9.542 16.156

- 5.415793 -9.707421 - 12.21656

3.536883 8.899019 7.619288

- 1.182334 - 4.843826 - 2.346418

0.1601006 1.408069 0.2833661

-0.1628899

5.523 9.542 16.156

-7.411318 - 6.314758 - 14.96305

8.238956

- 5.996100 3.459681 -4.141718

2.351101 - 2.013490 0.6260172

5.523 9.542 16.156

- 5.522609 -7.811296 - 10.84635

4.074286 5.198292 5.171875

- 1668038 - 1.844294 -

0.2778157 0.2658927 -0.9631749

5.523 9.542 16.156

-7.172781 - 8.650502 - 12.13972

6.142161 5.979225 6.019981

- 2.207327

-4.726118 0.3287627 - 1.125894

5.523 9.542 16.156

- 7.060084 -9.266177 - 11.20088

6.445062 7.137085 4.679660

0.9822845 0.7842288 -0.5504608

B5

2) mmal ~~mol.kg-r

L1

(T kJ.mol-’

LiCl 373.15 423.65 472.95

9.4 16.5 16.5

0.011 0.071 0.108

8.0 8.0 8.0

0.018 0.011 0.018

4.7 5.0 5.0

O.WO 0.059 0.025

4.5 4.5 4.5

0.013 0.007 0.014

0.2881418

1.0 4.5 4.5

0.002 0.010 0.037

-0.1080489 -0.077187350 0.1068934

11.0 9.0 9.0

0.004 0.010 0.081

NaBr 373.15 423.65 472.95 NaI 373.15 423.65 472.95

10.98087

- 0.3655704 0.3587895

KBl 373.15 423.65 472.95

0.2492561

KBr 373.15 423.65 472.95

2.553357

CsCl 373.15 423.65 472.95

’ mm,, is

the largest molality covered. b D is the standard error of a single point

- 3.490064 - 3.241993

in the fit.

systematic error of this magnitude would produce differences larger than those observed. By combining the present calculations of the change in osmotic coefficient with the osmotic coefficients at 298.15 K of Hamer and WU,‘~’ we can compare our results with other measurements of osmotic coefficients at high temperatures.00-12) The comparison is given in table 4. The agreement is excellent. The maximum difference, 0.026, occurs for 1 mol. kg- ’ LiCl ; all other differences are less than 0.007. All of these differences (except, possibly, for LiCI) are well within the expected experimental accuracy. Our estimate of the error limits of {4(T)--4(298.15 K)) and of ln{y(T)/y(298.15 K)) is +5 to 10 per cent, assuming the relative apparent molar enthalpy changes smoothly and regularly with temperature (as it does for NaCl, KCl, and CsCl). For LiCl, the relative apparent molar enthalpy does not change regularly, particularly at high molalities, so the error limits may be much higher. This higher

b

ENTHALPIES TABLE

OF

DILUTION

3. Relative apparent molar and changes in activity

enthalpies coefficient

m

L+

mol.kg-’ T/K:

kJ.mol-’ 373.15 423.15

OF

AQUEOUS

ALKALI

HALIDES

I& changes in osmotic coefficient ln{T(T)p;(298.15 K): for aqueous g%(T)-$(298.15

K)

571

(4(T)-+(298.15 solutions

ln(y(T)~;(298.15

K )I.

K):

473.15

373.15

423.15

473.15

373.15

423.15

473.15

LiCl 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0

1.34 1.76 2.06 2.31 2.52 2.71 2.89 3.05 3.21 3.35 4.01 4.58 5.10 5.62 6.13 6.66 7.21 7.78 8.37 8.97 9.59 10.21 10.82 11.40 11.94 12.43

2.20 2.79 3.17 3.46 3.69 3.90 4.08 4.25 4.40 4.55 5.20 5.77 6.29 6.78 7.23 7.66 8.06 8.45 8.83 9.19 9.55 9.91 10.26 10.62 10.97 11.33

3.75 4.76 5.42 5.92 6.34 6.70 7.02 7.32 7.60 7.86 9.01 10.00 10.88 11.67 12.39 13.05 13.66 14.23 14.78 15.29 15.80 16.29 16.78 17.26 17.75 18.24

--0.014 -0.019 - 0.023 -- 0.027 - 0.030 - 0.034 -- 0.037 --0.040 -0.043 -0.046 - 0.059 - 0.073 -- 0.089 -0.108 -0.130 -0.155 --0.184 --0.214 --0.246 -- 0.277 -0.306 -0.331 -0.350 --0.361 --0.360 -.- 0.346

- 0.027 - 0.034 -0.040 - 0.045 - 0.050 - 0.055 - 0.059 -0.064 -0.068 - 0.072 - 0.093 -0.114 -0.137 -0.163 -0.193 - 0.227 - 0.265 -0.306 - 0.348 - 0.389 - 0.427 -0.461 - 0.486 - 0.501 - 0.501 - 0.483

- 0.042 - 0.052 - 0.059 - 0.065 -0.071 - 0.077 - 0.083 - 0.089 - 0.094 -0.100 -0.128 -0.155 -0.184 -0.214 - 0.248 -0.285 - 0.326 - 0.369 - 0.414 - 0.458 - 0.501 - 0.539 - 0.570 -0.591 -0.600 -0.591

-0.049 -0.065 -0.078 - 0.089 -0.099 -0.108 -0.116 -0.125 -0.132 -0.140 -0.175 - 0.208 - 0.241 - 0.278 -0.318 -0.363 -0.411 - 0.462 -0.516 - 0.570 - 0.622 -0.671 -0.714 -0.747 - 0.769 - 0.775

- 0.094 -0.122 -0.143 -0.160 -0.176 -0.190 -0.203 -0.216 - 0.228 -0.240 -0.294 -0.344 -0.395 - 0.448 - 0.506 - 0.568 - 0.635 - 0.705 -- 0.778 -0.851 - 0.923 - 0.989 -1.047 -1.094 - 1.124 ~ 1.135

-0153 -0.194 - 0.224 -0.248 - 0.269 -0.289 - 0.307 -0.324 -0.340 -0.356 -0.430 - 0.498 -0.564 -0.631 -0.700 -0.773 -0.849 -- 0.929 - I.011 - 1.093 ~ 1.174 - 1.251 - 1.320 -- 1.379 - 1.423 - 1.449

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 .o 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5

1.31 1.66 1.88 2.05 2.18 2.29 2.39 2.47 2.55 2.62 2.92 3.16 3.37 3.55 3.72 3.88 4.04 4.21 4.38 4.57 4.78 5.03 5.31

2.27 2.93 3.38 3.74 4.03 4.29 4.52 4.73 4.92 5.10 5.87 6.49 7.04 7.55 8.04 8.52 9.00 9.49 9.97 10.45 10.92 11.36 11.76

4.12 5.39 6.25 6.93 7.49 7.98 8.41 8.81 9.18 9.52 10.99 12.21 13.29 14.26 15.14 15.96 16.73 17.45 18.14 18.81 19.47 20.14 20.83

-0.010 --0.009 -- 0.007 -- 0.005 - 0.003 -- 0.001 0.000 0.002 0.003 0.004 0.009 0.012 0.015 0.018 0.019 0.020 0.018 0.014 0.005 -- 0.009 - 0.030 -- 0.030 -- 0.098

- 0.022 - 0.023 - 0.023 - 0.022 -0.021 - 0.020 - 0.019 -0.019 -0.018 -0.018 -0.017 -0.017 -0.018 - 0.019 - 0.023 - 0.028 - 0.036 - 0.047 - 0.063 - 0.085 -0.113 - 0.149 - 0.192

-0.040 - 0.045 - 0.047 - 0.049 - 0.050 -0.051 - 0.052 - 0.053 - 0.054 - 0.055 -0.061 - 0.067 - 0.074 - 0.082 -0.091 -0.104 -0.119 -0.138 -0.161 -0.189 -0.222 - 0.261 - 0.305

-0.040 - 0.045 - 0.047 - 0.047 -0.046 -0.044 - 0.043 -0.041 - 0.039 - 0.038 -0.031 - 0.024 -0.018 -0.013 - 0.008 -0.005 -0.004 - 0.007 -0.015 - 0.029 -0.051 - 0.084 -0.128

- 0.085 -0.102 -0.111 -0.116 -0.120 -0.123 -0.126 -0.128 -0.129 -0.131 -0.137 -0.142 -0.146 -0.152 -0.158 -0.166 -0.178 -0.194 -0.215 - 0.243 - 0.279 -0.324 - 0.380

-0.149 -0.184 - 0.205 - 0.220 - 0.232 - 0.242 -0.251 - 0.259 - 0.266 -- 0.273 - 0.302 - 0.327 - 0.349 - 0.372 - 0.395 - 0.420 - 0.448 - 0.480 -0.518 -0.561 -0.611 - 0.661 -0.731

NaBr

3s *

J. E. MAYRATH

572

AND

TABLE 111

4

T/K:

3-continued

4(T)-4(298X

kJ

m

R. H. WOOD

373.15

423.15

473.15

1.21 1.52 1.72 1.87 1.98 2.08 2.16 2.23 2.29 2.34 2.54 2.68 2.82 2.96 3.10 3.21 3.28

2.40 3.09 3.53 3.86 4.12 4.34 4.53 4.70 4.86 5.00 5.62 6.14 6.59 6.97 7.32 7.66 8.03

3.93 5.07 5.83 6.42 6.91 7.34 7.72 8.06 8.38 8.68 9.94 10.98 11.87 12.66 13.40 14.10 14.81

K)

ln(p(T)/y(298.15

K)I

373.15

423.15

473.15

373.15

423.15

473.15

-0.007 -0.006 -0.004 -0.002 -0.001 0.001 0.004 0.006 0.008 0.010 0.020 0.025 0.026 0.024 0.025 0.035 0.060

-0.019 -0.020 -0.019 -0.018 -0.016 -0.015 -0.013 -0.011 -0.009 -0.007 -o.ooo 0.002 0.001 -0.004 -0.005 0.002 0.026

-0.037 -0.041 -0.042 -0.042 -0.041 -0041 -0.040 -0.039 -0.039 -0.038 -0.037 - 0.039 -0.045 -0.052 - 0.058 - 0.059 - 0.059

-0.032 -0.036 -0.036 -0.035 -0.034 -0.032 -0.029 - 0.026 -0.023 -0.020 -0.005 0.007 0.014 0.017 0.021 0.034 0.066

-0.078 -0.092 -0.099 -0.103 -0.106 -0.107 -0.107 - 0.107 -0.106 -0.105 -0.100 -0.097 -0.098 -0.102 -0.105 -0.098 -0.073

-0.143 -0.173 -0.191 -0.203 -0.212 -0.219 -0.224 - 0.229 -0.233 -0.236 -0.250 -0.263 -0.278 -0.294 -0.308 -0.317 -0.316

NaI 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

KC1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

1.31 1.67 1.90 2.08 2.22 2.33 2.44 2.53 2.61 2.68 2.98 3.19 3.35 3.49 3.61 3.75 3.91

2.37 3.08 3.56 3.93 4.24 4.50 4.74 4.95 5.14 5.32 6.06 6.66 7.16 7.60 8.00 8.37 8.73

4.19 5.52 6.42 7.12 7.71 8.21 8.66 9.07 9.44 9.79 11.23 12.36 13.28 14.06 14.77 15.47 16.21

-0.009 -0.009 -0.008 -0.007 -0.006 -0.005 -0.003 -0.002 -0.001 0.040 0.006 0.012 0.017 0.019 0.017 0.010 -0.003

-0.023 -0.025 -0.025 -0.025 -0.025 -0.024 -0.024 -0.023 -0.022 -0.022 -0.018 -0.014 -0.012 -0.011 -0.016 -0.027 -0.047

-0.042 -0.048 -0.051 - 0.053 -0.054 -0.055 -0.056 -0.057 -0.058 -0.058 -0.060 -0.060 -0.060 -0.063 -0.071 -0.089 -0.120

-0.040 -0.046 -0.048 -0.049 -0.050 -0.049 -0.049 -0.048 -0.047 -0.045 -0.038 -0.030 -0.022 -0.017 -0.015 -0.020 -0.033

-0.086 -0.105 -0.115 -0.122 -0.127 -0.131 -0.134 -0.137 -0.139 -0.141 -0.145 -0.146 -0.146 -0.148 -0.155 -0.169 -0.193

-0.153 -0.190 -0.214 -0.230 -0.244 -0.255 -0.264 -0.273 -0.280 -0.287 -0.313 -0.330 -0.343 -0.357 -0.375 -0.404 -0.447

0.1 0.2 9.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

1.21 1.52 1.72 1.86 1.97 2.06 2.14 2.20 2.26 2.32

2.31 2.97 3.41 3.74 4.02 4.25 4.45 4.64 4.80 4.96

4.09 5.33 6.16 6.80 7.34 7.79

-0.007 -0.006 -0.004 -0.002 0.ooo~ 0.003 0.005 0.007 0.007 0.005

-0.019 -0.020 -0.019 -0.018 -0.015 -0.013 -0.011 -0.010 -0.011 -0.014

-0.037 -0.041 -0.043 -0.043 -0.042 -0.041 -0.041 -0.041 -0.043 -0.047

-0.034 - 0.037 -0.037 -0.036 -0.034 -0,031 -0.028 -0.026 -0.025 -0.026

-0.078 -0.092 -0.099 -0.103 -0.104 -0.105 -0.105 -0.105 -0.107 -0.112

-0.142 -0.174 -0.193 -0.205 -0.214 -0.220 -0.226 -0.232 -0.238 -0.247

KBr

8.K) 8.57 8.91 9.22

ENTHALPIES

OF

DILUTION

OF

TABLE m

4 kJ.mol-i

-I-i T/K:

AQUEOUS

423.15

473.15

1.21 1.51 1.70 1.83 1.94 2.03 2.11 2.18 2.24 2.29 2.50 2.65 2.76 2.86 2.95 3.04 3.15 3.26

2.27 2.92 3.34 3.67 3.93 4.16 4.35 4.53 4.69 4.84 5.47 5.96 6.37 6.73 7.05 7.35 7.62 7.89

4.14 5.41 6.25 6.89 7.41 7.86 8.25 8.60 8.92 9.21 10.45 11.45 12.30 13.03 13.66 14.21 14.67 15.07

HALIDES

573

3-continued

b(T)-+(298X

373.15

ALKALI

K)

ln{y(T)k;(298.15

K);

373.15

423.15

473.15

373.15

423.15

473.15

-0.006 -0.005 - 0.003 - 0.001 0.001 0.003 0.004 0.006 0.007 0.009 0.016 0.021 0.025 0.027 0.026 0.024 0.020 0.016

-0.018 -0.018 -0.017 -0.016 -0.014 -0.013 -0.012 -0.011 - 0.010 -0.009 -0.004 0.000 0.003 0.003 0.001 -0.005 -0.012 - 0.020

- 0.036 - 0.039 -0.040 -0.040 -0.041 -0.041 -0.040 -0.040 -0.040 -0.040 -0.040 - 0.039 - 0.039 -0.041 - 0.045 -0.051 - 0.059 - 0.067

- 0.032 - 0.034 - 0.034 -0.032 -0.031 - 0.029 - 0.026 - 0.024 - 0.022 -0.020 -0.008 0.003 0.012 0.019 0.022 0.023 0.022 0.019

- 0.076 - 0.088 - 0.094 - 0.097 -0.100 -0.101 -0.102 -0.102 -0.103 -0.103 -0.100 - 0.096 - 0.093 - 0.092 - 0.095 -0.100 -0.109 -0.119

-0.140 -0.170 -0.187 -0.199 - 0.208 -0.215 - 0.221 - 0.227 -0.231 - 0.235 -0.251 - 0.262 -0.271 - 0.280 -0.290 -0.303 -0.317 -0.332

CSCI 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

error for LiCl is compatible with the greater disagreement found with the results of Lindsay and Liu for LiCl.‘“’ Lindsay and Liu measured only one molality of LiCl and CsCl (1 .O mol. kg- ’ ). Our agreement with their results shows that we now have osmotic coefficients over a range of molalities for these two salts with an accuracy of about +0.03 for LiCl and +O.Ol for CsCI. TABLE

Salt LiCl NaCl CsCl KCI

4. Comparison

of calculated

osmotic

coefficients

with

m

literature

results

at 473.15

K

4

mol.kg-’

obs.”

lit?

1.0 1.0 1.0 0.1 0.5 1.0 2.0 3.0

0.920 0.865 0.821 0.885 0.846 0.840 0.852 0.874

0.894’ 0.864’ 0.823 0.889 0.852 0.847 0.856 0.874

’ Calculated from the present values (for NaCI. the previous results from this laboratory the osmotic coefficients at 298.15 K of Hamer and WU.‘~’ b Osmotic coefficients from the literature. The references are given in the footnotes. ’ Reference 10. ’ Reference 11. e Reference 12.

’ ’ e ’ * ’

were used) and

J. E. MAYRATH

574

AND R. H. WOOD

The present measurements allow calculation of the relative apparent molar enthalpies, osmotic coefficients, and activity coefficients of a variety of I 1 electrolytes at temperatures up to 473 K. Now that these are available, it is possible to see some trends in the variation of these quantities with temperature. At very low molalities, the variation is determined by changes in the Debye-Hiickel limiting-law slopes and, thus, ultimately by the temperature dependence of the dielectric constant and density of the solvent. With water as a solvent, this dictates a large increase in the relative apparent molar enthalpy and a large decrease in osmotic and activity coefficients. At higher molalities, the changes reflect pair-wise and higher-order interactions between the ions and it is here that the individual differences between various salts are found. As shown in figure 1, there is a very large increase in relative apparent molar enthalpy with increasing temperature. All of the 1 1 electrolytes investigated have much higher relative apparent molar enthalpies at 473.15 than at 298.15 K. At 298.15 K, LiCl has a much higher value of L, than other salts in this study but at 473.15 K, LiCl is lower but not far from the other salts. It appears that LiCl loses its individuality as the temperature rises. At molalities above 6 mol. kg- ’ LiCl behaves irregularly : L+(423.15 IS) < tJ373.15 K) < L,(473.15 K). There are

O-

D-

298.15 K +/-+-

+-

+’

+-----+

I-

I

O

I

I

2

4

,

J h

m/(mol-kg-‘)

FIGURE 1. Relative apparent molar enthalpy L, at 298.15 K (lower group) and 473.15 K (upper group) plotted against molality. + . LiCl ; 0, NaCl ; 0, NaBr ; x . NaI ; A, KC1 ; 0, KBr ; V. CsCl. For clarity, curves are omitted for KC1 and NaI at both temperatures and for CsCl at 298.15 K. For KBr there is only one point at 1 mol.kg-’ at 473.15 K.

ENTHALPIES

OF DILUTION

OF AQUEOUS

ALKALI

HALIDES

575

1.2

1.0

0.6

. . \ 0.4

0

1

2

3

m/(mol-kg-‘)

FIGURE 2. Activity coefficient 7 at 298.15 K (solid lines) and 473.15 K (dashed lines) plotted against molality.+,LiCl;O,NaCI;x.NaBr;~,NaI;~,KCI;~.KBr;~.CsCI.At473.15KtheKBrcurve is omitted because it is so close to the NaCl curve.

many possible explanations for this behavior. One possibility is changes in the primary coordination sphere of the lithium ion at high molalities. The activity coefficients at 473.15 K are plotted in figure 2. All of the l-l salts shift downward to lower activity coefficients at the higher temperature. At low molalities this is required by the Debye-Htickel limiting law. Except for LiCl, the sequence of activity coefficients is the same, but tke.spread of values is a little narrower. At room temperature, LiCl has the highest activity coefficient in this group and at 473 K it is second highest. At both temperatures, the activity coefficients form a regular family of curves that do not cross one another. From their studies on LiCl, NaCl, and CsCl, Liu and Lindsay”O*“’ concluded there were smaller individual differences between osmotic coefficients at the higher temperatures, and the present results extend this observation to enthalpies and activity coefficients.

J. E. MAYRATH

576

AND R. H. WOOD

This material is based upon work supported by the National Science Foundation under Grants CHE77-10624 and CHE 8009672. The authors thank Peter T. Thompson and David Smith-Magowan for assistance with the runs at 473 K. REFERENCES 1. Messikomer, E. E.; Wood, R. H. J. Chem. Thermodynamics 1975, 7, 119. 2. Mayrath, J. E.; Wood, R. H. J. Chem. Thermo&uzmics 1982, 14. 15. 3. Mayrath, J. E. Ph.D. Dissertation, University of Delaware. May 1980. 4. Helgesen, H. C.; Kirkham, D. H. Am. J. Sci. 1974,274, 1199. 5. Parker, V. B. Thermal Properties of Aqueous Uni-univalent Electro(vtes. NSRDS-NBS 2. IJ.S. Government Printing Office: Washington, D.C. 1965. 6. Levine, A. S.; Wood. R. H. J. Chem. Enn. Data 1970. 15. 33. 7. Stakhanova, h. S.; Vlasenko, K. K.; K&apet’yants,‘M. Kh.; Bazlova, I. V. Russ. J. Phys. Chem. 1968,42,

8. 9. 10. 11. 12.

214.

Likke, S.; Bromley, L. A. J. Chem. Eng. Data 1973, 18, 189. Hamer. W. J.: Wu. Y. C. J. Phvs. Chem. Ref. Data 1972. 1. 1047. Lindsay, W. i., Jr.; Liu, C.-T. >. Phys. Chek. 1971, 75. i7;3. Liu, C.-T.; Lindsay. W. T., Jr. J. Solution Chem. 1972, 1, 45. Holmes, H. F.; Baes, C. F.. Jr.; Mesmer, R. E. J. Chem. Thermodsvnamics

1978,

10. 983.

Note added in proof

Recent measurements of R. F. Holmes and R. E. Mesmer (J. Chem. Thermodynamics 1981, 13, 1035) on LiCl and CsCl are in excellent agreement with Lindsay and Liu’s results (lo) (A = 0.001 and 0.003, respectively). The agreement with the present results is excellent for CsCl below 3 mol. kg- 1 (A = 0.002) and reasonable at 5 mol. kg- ’ (A = 0.030). For LiCl, the agreement is as expected (A = 0.02 to 0.04). The higher error for 5 mol. kg-r CsCl might be due to a lack of dilution experiments to define accurately at the higher molalities. (qp?l”2)p