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Heat capacities of aqueous NaBr from 306 to 603 K at 17.5 MPa
O-192 .I. Chem. Thermo&namics 1987, 19, 493-503
Heat capacities of aqueous 306 to 603 K at 17.5 MPa
NaBr
from
DOROTHY E. WHITE, JEFFREY A. GATES,” and ROBERT H. WOOD’ Department of Chemistry, University qf Delaware. Newark, Delaware 19716, U.S.A. (Received 5 May 1986: in jnal form 25 September
1986)
A differential flow heat-capacity calorimeter has been used to measure the heat capacity of NaBr(aq) at molalities from 0.05 to 3.0 mol. kg-‘, temperatures from 306 to 603 K, and a pressure near 17.5 MPa. The results show the very large and negative apparent molar heat capacities at high temperatures and low molalities found for NaCl(aq) and CaCl,(aq).
1. Introduction The work presented here is part of a continuing investigation of the heat capacities of aqueous electrolytes at high temperatures using flow-calorimetric techniques.‘1-4’ Very large and negative values of the apparent molar heat capacities have been found for aqueous NaCl,‘1,3’ and CaC1,,‘4’ and this has been attributed to large interactions between ions and water, together with the changes in the properties of the water as its critical point is approached. (1,5-l l’ There continues to be a need for such information to increase our understanding of a variety of chemical processes that occur at high temperatures including mineral geochemistry, the behavior of geothermal fluids, and corrosion in electric-power-plant boilers. In this paper we report the apparent molar heat capacities of aqueous NaBr solutions from 0.05 to 3.0 mol. kg-’ and 306 to 603 K at 17.5 MPa. A twodimensional cubic-spline representation of the apparent molar heat capacity as a function of molality and temperature allows the calculation of thermodynamic properties at any temperature and molality within the range of the results.
2. Experimental A stock solution of approximately 3.0 mol. kg- ’ of NaBr was prepared from Fisher certified NaBr (total impurities were less than 0.4 mass per cent including 0.2 mass per cent of Cl and 0.12 mass per cent of K) and distilled deionized water. Actual molality was determined by titration with AgNO,(aq). All other solutions were * Present address: E. I. du Pont Delaware 19898, U.S.A. * To whom correspondence should 0021-9614!87:050493+
II
$02,00/O
de Nemours
and Co.,
Inc.,
Experimental
Station,
Wilmington,
be addressed. t(? 1987 Academic
Press Inc. (London)
Limited
494
D. E. WHITE.
J. A. GATES.
AND
R. H. WOOD
prepared by dilution of appropriate masses of the 3.0 mol. kg- ’ stock. Densities of the stock and diluted solutions were determined on the Sodev Model 01D vibratingtube densimeter. As a check all molalities were calculated from the density of the solution and the literature results of Robison and Weston.“” The molalities agreed to within 0.1 per cent. The high-temperature flow heat-capacity calorimeter has been described in detail previously. (l.13’ For low-temperature measurements (325 K) a cooling jacket was installed on the vacuum can to facilitate temperature control. The calorimeter was operated at a water flow rate of 0.033 cm3. s-’ and with heater power of 0.31 W resulting in temperature rises of 1.1 to 1.8 K. The reported temperatures are the averages of the initial and final temperatures of the solution. The back-pressure regulator was calibrated (kO.25 MPa) using a Heise CM gauge (0 to 27 MPa). At least three heat-capacity measurements were made for each molality. The instrument measures the electric power necessary to give the same temperature rise when the sample solution and pure water are flowing in the calorimeter. The specific heat capacity cp of the sample solution at constant pressure is then calculated from c,/c; = 11 -f(Ps - Rv)Ipw~(PwlPs)~
(1)
where c,, is the specific heat capacity of the solution, cf is the specific heat capacity of pure water at the experimental temperature and pressure, P, is the electric power when the sample solution is in the sample cell, P, is the power when water is in the sample cell, f is a correction factor for heat losses, and p,,, and pS are the densities of water and of the aqueous salt solution at the experimental pressure and the temperature of the sample loop (298.15 K). The correction factorfwas calculated at each temperature by using 3.0 mol. kg-’ NaCl as a chemical standard.(14’ The densities of the experimental solutions were obtained from the fit of Gates and Wood”‘) and the properties of water from the equation of state of Haar, Gallagher, and Ke11.(r6) The apparent molar heat capacity C,,, can be calculated from the specific heat capacity ratio c,/c,*: C p.e = {Of,+
llm)(c,lcf)-(llm))cf.
(2)
where M, is the molar mass of the solute and m is the molality of the aqueous salt solution. Fortier, Benson, and Picker (17) have shown that errors can arise in flow calorimeters because of mixing and volume changes at the boundary between the sample and reference solutions. This effect can be large when the sample and reference fluids are quite different but is normally negligible without aqueous salt solutions (m < 5.0 mol. kg-‘).‘3*4’
3. Results The results of the heat-capacity measurements on NaBr(aq) are given in table 1, together with estimates of the accuracy of the individual measurements. The apparent molar heat capacities were fitted by the multi-dimensional cubic-spline
HEAT CAPACITY
495
OF NaBr(aq)
TABLE 1. Apparent molar heat capacity C,, + of NaBr(aq) m mol,kg-’
p, P,
cp c:
c P.m J.K-‘,mol-’
4
6b
A’
____m mol.kg-’
-PS P,
0.0498 0.0498 0.0498 0.1003 0.1003
0.9980 0.9981 0.9983 0.9963 0.9963
0.9941 0.9942 0.9944 0.9886 0.9886
T= 306.15 K p = 17.03 MPa ,f= 1.014“ - 66.26 10.34 13.38 0.1003 0.9963 0.9886 -58.15 10.18 5.27 0.2500 0.9912 0.9723 -40.84 9.83 -12.04 0.2500 0.9913 0.9724 - 50.07 6.53 0.18 0.2500 0.9910 0.9722 - 50.66 6.54 0.77
0.501 I 0.501 I 0.501 I 1.003 I 1.0031 1.0031
0.9833 0.9833 0.9833 0.9697 0.9696 0.9698
0.9469 0.9469 0.9469 0.9016 0.9016 0.9017
T = 306.15 K p == 17.20 MPa ,/= 1.013“ - 35.20 3.53 -0.41 2.0056 0.9488 0.8280 -35.16 3.53 -0.45 2.0056 0.9488 0.8281 - 35.05 3.53 -0.57 2.0056 0.9487 0.8280 -21.95 2.96 -0.89 3.0053 0.9339 0.7708 -22.12 2.96 -0.72 3.0053 0.9339 0.7709 -21.57 2.95 - 1.27 3.0053 0.9339 0.7709
0.049x 0.0498 0.049x 0.1003 0.1003 0.1003 0.2500 0.2500 0.2500 0.501 I 0.501 I
0.9984 0.9984 0.9983 0.9967 0.9969 0.9968 0.9922 0.9921 0.9923 0.9849 0.9846
0.9944 0.9944 0.9943 0.9889 0.9890 0.9889 0.9730 0.9729 0.9732 0.9479 0.9476
T = 324.41 K p = 17.27 MPa -40.92 10.74 - 13.85 0.5011 -41.79 10.76 - 12.97 1.0031 -46.17 10.85 -8.60 1.0031 - 38.88 6.76 - 11.23 1.0031 - 32.79 6.64 - 17.32 2.0056 - 35.40 6.69 - 14.71 2.0056 - 32.43 4.32 -8.62 2.0056 -33.52 4.34 -7.53 3.0053 -29.98 4.27 -11.07 3.0053 - 26.48 3.45 -4.90 3.0053 -29.33 3.50 -2.06
/‘= 1.050“ 0.9848 0.9478 0.9717 0.9026 0.9717 0.9025 0.9717 0.9025 0.9506 0.8280 0.9507 0.8282 0.9507 0.8281 0.9347 0.7695 0.9347 0.7695 0.9347 0.7695
-27.72 - 17.72 - 17.79 - 17.79 -2.23 - 1.89 -2.03 10.35 10.30 10.35
3.47 2.92 2.92 2.92 2.47 2.46 2.46 2.19 2.19 2.19
-3.67 -0.97 -0.90 -0.90 0.16 -0.18 -0.03 -0.23 -0.19 -~0.23
0.0498 0.0498 0.0498 0.1003 0.1003 0.1003 0.2500 0.2500 0.2500 0.m 1 0.5011 05011
0.9979 0.9981 0.9980 0.9965 0.9963 0.9967 0.9917 0.9918 0.9918 0.9846 0.9846 0.9845
0.9939 0.9941 0.9940 0.9885 0.9883 0.9887 0.9723 0.9724 0.9723 0.9472 0.9471 0.9470
T = 350.30 K p = 17.75 MPa ./ = 1.082 d -88.14 12.50 31.40 1.0031 0.9719 0.9019 - 64.82 12.03 8.08 1.0031 0.9719 0.9019 -75.04 12.24 18.30 1.0031 0.9718 0.9018 - 52.38 7.44 0.99 2.0056 0.9507 0.8268 - 63.26 7.65 11.87 2.0056 0.9507 0.8268 2.0056 0.9506 0.8267 -44.38 7.28 -7.01 4.11 3.0053 0.9340 0.7673 -45.15 4.74 -43.41 4.71 2.37 3.0053 0.9342 0.7674 -43.99 4.72 2.95 3.0053 0.9343 0.7675 - 32.93 3.66 2.14 3.0053 0.9340 0.7672 - 33.36 3.67 2.58 3.0053 0.9337 0.7670 -34.53 3.70 3.74 3.0053 0.9337 0.7670
- 20.77 -20.55 - 20.98 - 5.25 - 5.25 -5.61 6.25 6.48 6.67 6.13 5.74 5.79
3.03 3.03 3.03 2.55 2.55 2.56 2.29 2.29 2.28 2.29 2.30 2.30
2.19 I .97 2.41 0.71 0.71 1.08 -- 1.34 - 1.56 .- 1.76 - 1.22 --0.82 0.87
0.0498 0.0498 0.0498 0.1003 0.1003 0.1003 0.2500 0.2500 0.2500 0.501 I
0.9982 0.9983 0.9979 0.9961 0.9962 0.9960 0.9905 0.9907 0.9905 0.9819
0.9942 0.9942 0.9938 0.9880 0.9882 0.9879 0.9710 0.9712 0.9710 0.9442
- 62.00 - 56.82 - 92.97 - 74.07 -68.93 -79.18 -68.85 -65.24 -68.33 - 59.76
- 59.50 - 59.25 -45.42 -44.79 -44.28 -26.71 - 27.29 - 26.45 - 12.59
4.75 4.75 3.82 3.81 3.80 3.16 3.17 3.15 2.80
3.62 3.36 2.10 1.47 0.96 0.86 1.43 0.60 0.00
T=
405.57 17.20 17.10 17.82 10.49 10.38 10.59 6.29 6.22 6.28 4.76
K p = 17.72 MPa - 15.10 0.5011 -20.28 0.5011 15.87 1.0031 1.10 1.0031 -4.05 1.0031 6.20 2.0056 3.94 2.0056 0.33 2.0056 3.42 3.0053 3.8X
.f = l.08gd 0.9819 0.9443 0.9819 0.9443 0.9669 0.8967 0.9670 0.8968 0.9671 0.8969 0.9421 0.8184 0.9419 0.8182 0.9423 0.8185 0.9229 0.7570
-51.24
-44.08 -42.25 -47.07
-2.26 -2.15 -2.29 12.69 12.76 12.76
1.35 6.55 4.37 0.43 4.33 - 1.39 4.43 3.43
2.44 -0.56 2.44 -0.67 2.44 --0.53 2.12 0.62 2.12 0.55 2.12 0.55
D. E. WHITE.
496
J. A. GATES, TABLE
In
c P.0
y fib
ps
cp
mol. kg-’
P,
c;
0.0498 0.0498 0.0498 2.0056 2.0056 2.0056
0.9980 0.9919 0.9982 0.9419 0.9418 0.9417
0.9940 0.9939 0.9942 0.8193 0.8191 0.8190
-79.55 -82.08 - 62.08 -24.55 - 24.92 -25.11
0.0498 0.0498 0.0498 0.1003 0.1003 0.1003 0.1003 0.25Og 0.2500 0.2500 0.5011
0.9966 0.9911 0.9972 0.9946 0.9954 0.9950 0.9951 0.9877 0.9878 0.9879 0.9765
0.9925 0.9936 0.9932 0.9865 0.9873 0.9869 0.9871 0.9681 0.9682 0.9683 0.9389
- 207.95 - 109.76 - 150.91 - 142.57 - 107.24 - 125.83 - 118.86 - 120.20 -118.89 -117.58 - 109.63
0.0498 0.0498 0.0498 0.1003 0.1003 0.1003 0.2500 0.2500 0.2500 0.5011 0.5011
0.9969 0.9961 0.9966 0.9936 0.9938 0.9938 0.9854 0.9856 0.9858 0.9733 0.9734
0.9923 0.9921 0.9920 0.9845 0.9847 0.9847 0.9635 0.9637 0.9640 0.9317 0.9318
- 235.45 -255.58 -263.41 -239.83 -230.37 -230.37 -212.98 -208.50 -203.13 - 183.81 - 182.69
0.0498 0.0498 0.0498 0.1003 0.1003 0.1003 0.2500 0.2500 0.2500 0.5011 0.5011
0.9945 0.9943 0.9940 0.9883 0.9892 0.9885 0.9761 0.9166 0.9765 0.9584 0.9583
0.9891 0.9889 0.9885 0.9774 0.9786 0.9777 0.9510 0.9517 0.9516 0.9118 0.9117
-581.99 -609.10 -647.82 -623.21 - 566.09 -611.01 -491.39 -477.11 -479.76 -411.87 -412.52
*’
J.K-‘~rnol~’
T = 400.92
K
K
T = 500.90 K 30.45 30.85 31.01 18.74 18.55 18.55 11.26 11.17 11.06 8.37 8.35
56.72 51.26 58.03 36.14 35.00 35.90 20.89 20.61 20.66 15.09 15.11
p= - 6.54 13.60 21.43 11.15 1.70 1.70 7.80 3.32 -2.05 3.13 2.00
T = 551.90 K
~ m
-p,
cp
mol,kg-’
P,
c;
0.5011 0.5011 1.0031 1.0031 1.0031 2.0056 2.0056 2.0056 3.0053 3.0053 3.0053
17.41 MPa 0.5011 1.0031 1.0031 1.0031 2.0056 2.0056 2.0056 3.0053 3.0053 3.0053
p = 17.41 MPa
-69.51 -42.40 - 3.68 25.24 -31.87 13.05 - 10.07 -24.28 -21.70 - 1.65 -1.00
f=
0.5011 1.0031 1.0031 1.0031 2.0056 2.0056 2.0056 3.0053 3.0053 3.0053
c P.0 J,K-‘.mol-’
y
iSh
A’
1.067“
3.0053 3.0053 3.0053 3.0053 3.0053
p = 17.75 MPa
23.13 ’ 21.17 -23.22 21.99 17.93 13.38 14.98 12.67 -20.35 13.04 -1.76 12.91 -8.73 7.96 1.30 7.94 -0.01 7.91 -1.32 6.11 1.91
R. H. WOOD
lpcontinued
p = 17.48 MPa
17.26 5.79 17.31 8.32 16.91 -11.68 3.10 1.41 3.11 1.78 3.11 1.97
T = 450.37
AND
0.9195 0.9222 0.9229 0.9231 0.9227
f=
0.7553 0.7576 0.7582 0.7584 0.7581
- 15.66 -11.41 - 10.28 -9.85 - 10.51
2.85 2.77 2.74 2.13 2.15
5.04 0.78 -0.35 -0.77 -0.11
0.9400 0.9398 0.8887 0.8890 0.8887 0.8071 0.8076 0.8072 0.7432 0.7439 0.7439
-99.38 - 101.45 ~ 84.43 - 82.76 - 84.28 - 56.78 - 55.64 - 56.61 - 38.88 - 31.44 - 37.55
5.90 5.94 4.81 4.77 4.81 3.89 3.87 3.89 3.43 3.40 3.41
-8.34 -6.27 -5.24 -6.90 -5.38 -4.23 -5.38 -4.40 1.09 -0.35 -0.23
1.075’ 0.9776 0.9774 0.9585 0.9588 0.9585 0.9294 0.9299 0.9295 0.9065 0.9074 0.9073
f=
1.225d 0.9734 0.9526 0.9528 0.9520 0.9213 0.9215 0.9214 0.8979 0.8980 0.8973
j”=
0.9318 0.8762 0.8765 0.8755 0.7892 0.7893 0.7892 0.7229 0.7230 0.7223
-
182.35 150.88 149.74 154.29 108.53 108.15 108.44 -81.00 - 80.80 -82.18
8.34 6.59 6.56 6.65 5.21 5.20 5.21 4.51 4.51 4.53
1.67 1.72 0.58 5.14 -0.39 -0.77 -0.47 1.14 0.94 2.32
0.9120 0.8457 0.8448 0.8461 0.7487 0.7485 0.7484 0.6177 0.6772 0.6774
-409.92 - 334.71 - 339.63 - 332.54 -241.98 - 242.59 -242.76 - 188.08 - 188.99 - 188.59
15.05 11.48 11.58 11.44 8.63 8.64 8.65 7.25 7.21 7.26
-3.59 12.86 17.79 10.70 4.22 4.83 5.00 -3.88 -2.97 -3.31
1.281’
0.9585 0.9291 0.9284 0.9294 0.8885 0.8884 0.8883 0.8597 0.8593 0.8594
HEAT
CAPACITY TABLE
mol.kg-’
P,
(.;
J.K-‘.m,,-’
”
T = 577.87 0.0498 0.0498 0.0498 0.1003 0.1003 0.1003 0.2500 0.2500 0.2500 0.501 I 0.501 1
0.9903 0.9875 0.9884 0.9815 0.9811 0.9819 0.9635 0.9622 0.9619 0.9454 0.9305
0.9824 0.9785 0.9798 0.9662 0.9656 0.9667 0.9302 0.9284 0.9281 0.8886 0.8683
- 1390.50 -1825.13 - 1680.77 - 1306.63 - 1337.05 - 1276.20 - 1008.73 - 1048.94 -1057.11 -719.64 -954.52
0.0498 0.0498 0.0498 0. LOO3 0.1003 0.1003 0.1003 0.2500 0.2500 0.2500 0.5011
0.9862 0.9872 0.9869 0.9764 0.9765 0.9764 0.9764 0.9488 0.9491 0.9491 0.9162
0.9765 0.9778 0.9773 0.9586 0.9588 0.9586 0.9586 0.9090 0.9095 0.9095 0.8474
-2413.88 - 2234.27 - 2299.75 -2035.17 - 2023.08 -2035.17 -2035.17 - 1753.08 - 1741.09 - 1741.09 - 1408.86
-
K
T=
I-continued
mol.kg-’ p = 17.48 MPa
155.27 46.54 163.96 ’ 161.08 o 90.89 81.84 91.50 y 90.28 51.42 47.93 - 15.36 48.74 24.85 48.90 33.01 29.76 - 120.62 34.45 114.26 602.74
K
127.26 123.67 124.98 81.61 81.37 81.61 81.61 53.51 53.27 53.27 39.12
e -32.55 32.93 -25.75 -37.84 -25.75 -25.75 27.12 15.13 15.13 -8.28
497
OF NaBr(aq)
0.5011 1.0031 1.0031 1.0031 2.0056 2.0056 2.0056 3.0053 3.0053 3.0053
p = 17.55 MPa 0.5011 0.5011 1.0031 1.0031 1.0031 2.0056 2.0056 2.0056 3.0053 3.0053 3.0053
P,
c;
J.K-‘.mol-’
6b
A,
/ = 1.419 d 0.9365 0.9068 0.8970 0.9090 0.8466 0.8518 0.8532 0.8169 0.8226 0.8226
0.8765 0.8071 0.7942 0.8100 0.6832 0.6897 0.6914 0.6116 0.6183 0.6183
-859.72 - 600.68 - 678.93 -583.12 -481.96 - 460.48 -454.90 - 364.69 -348.71 -348.71
0.8473 0.8471 0.7536 0.7534 0.7529 0.6374 0.6362 0.6352 0.5625 0.5620 0.5628
-1411.12 - 1413.57 - 1090.04 - 1091.19 - 1095.18 - 747.27 -751.71 - 755.58 - 568.69 -570.13 - 567.98
32.56 19.45 21.24 --44.42 22.80 33.83 20.88 m-61.98 IS.84 22.54 15.41 1.06 15.30 -4.52 12.52 10.64 12.20 -5.35 12.20 --5.35
f = 1.435’ 0.9161 0.9160 0.8677 0.8676 0.8672 0.8117 0.8108 0.8100 0.7776 0.7771 0.7778
39.17 39.22 29.05 29.07 29.15 20.39 20.48 20.56 16.26 16.29 16.24
-6.03 -3.58 6.14 7.28 11.28 -9.61 -- 5.16 - 1.30 3.43 4.87 2.72
a The apparent molar heat capacity C,., was calculated from equation (1). ’ The estimated accuracy 6 of each value of C,,,/(J K-’ mol- ‘) was calculated assuming relative errors of 1 per cent in AP/P and an absolute error estimated from the experimental sensitivity at each temperature. The absolute error estimates varied from ~0.0001 to &O.OOlO. ’ A is the value of {C,.+(calculated)C&observed)l/(J K ’ mol ‘). The calculated value is from a cubic-spline interpolation of the knots in table 2. ’ The value of the heat-loss correction factor,fwas calculated using the heat capacity of 3.005 mol. kg- ’ for NaCl as a chemical standard.“3,‘4’ The measured values of APjP for 3.005 mol. kg-’ NaCl at the experimental pressure were -0.04813 (p = 17.03 MPa) and -0.04820 @ = 17.20 MPa) at 306.15 K, -0.04733 at 324.41 K, -0.04830 at 350.30 K. -0.05923 at 405.57 K. -0.05945 at 400.92 K. -0.07435 at 450.37 K. -0.08672 at 500.90 K, -0.12499 at 551.90 K. -0.15296 at 577.87 K, and -0.21096 at 602.74 K. ’ These values were not included in the fit. Values were discarded based on a Q-test (90 per cent confidence) or when the square of the residual for a given point was larger than 20 per cent of the overall square of the residuals.
method described previously. (X la) The experimental pressure varied between 17.0 and 17.8 MPa. These small variations in pressure have been ignored in the representation. This isobaric assumption introduces an increase of less than 10 per cent in the estimated uncertainty of the results. The knot positions and values are presented in table 2. Table 3 gives values of C,,, at a variety of temperatures and molalities. The Debye-Hiickel limiting-law slopes for C,,, as a function of ml/‘* labeled A,, have been included in table 2. These have been calculated using Haar, Gallagher, and Kell’s equation of state for water”@ with Uematsu and Franck’s equation for the dielectric properties of water.“” As with the C,. +, surfaces for NaCl
498
D. E. WHITE.
J. A. GATES,
AND
R. H. WOOD
TABLE 2. NaBr knot positions, knot values, and DebyeeHtickel slopes A, for calculating the apparent This fit is a representation of 203 points. The sum of the squares molar heat capacities C,. ,+ of NaBr(aq). of the residuals is 73300 resulting in a standard error of the fit of k 20.0 J. K- ’ mol ‘. The minimum sum of the squares for this set is 41100 T/K:
298.15
315.00
425.00
A,:
35.15
38.26
87.24
- 57.77 -47.83 15.62
- 62.90 -46.47 12.51
- 110.24 -88.28 -21.16
500.00
560.00
603.00
216.91
718.67
3730.03
p = 17.5 MPa
{m/(mol
kg- *)}112
C,~4/(J~K-r~mol-1)
0 0.4000 1.7500
TABLE m/(mol
3. Apparent
kg- ‘):
0
molar 0.100
0.250
C,,,
of NaBr(aq)
0.500
-990.35 -693.74 -229.91
- 2947.24 - 1908.75 - 558.09
at p = 17.5 MPa 1.000
2.000
3.000
- 25.42 - 20.96 - 17.92 - 19.06 -24.59 - 37.98 - 58.92 - 87.05 - 118.09 - 146.57 - 180.23 -292.74 - 572.99 - 1000.50
- 3.68 -2.41 -2.48 -5.14 - 10.60 -21.68 - 37.86 - 59.09 -83.04 - 106.65 - 135.41 -217.39 -410.46 - 700.68
14.58 12.04 8.43 4.22 -1.00 -9.57 -21.14 - 36.37 -55.21 - 77.37 - 107.65 - 176.22 -318.91 - 525.48
C,,+/(J.K-‘.mol-‘)
T/K 298.15 313.15 333.15 353.15 373.15 398.15 423.15 448.15 473.15 498.15 523.15 548.15 573.15 598.15
heat capacity
- 279.68 -215.91 - 77.50
-
57.77 62.45 65.42 66.49 69.26 80.65 - 107.45 - 154.32 -213.97 -275.37 - 363.46 - 682.95 - 1479.60 -2692.71
-49.76 -50.01 -50.31 -51.75 - 55.99 -67.71 -89.58 - 123.99 - 169.28 - 222.52 - 302.79 - 539.20 - 1085.59 - 1900.57
-45.12 - 42.47 -40.48 -41.39 - 46.20 - 59.26 -81.99 -115.49 - 156.50 -200.37 -261.90 -452.87 -907.10 -1590.51
- 38.09 -33.71 - 30.46 -31.19 - 36.43 -50.17 - 72.84 - 104.62 - 141.26 -177.12 -223.30 - 374.58 - 744.86 - 1306.69
and CaCl, presented previously, 13*4) the NaBr surface required three m1i2 knots placed at 0, 0.4, and 1.75 mol. kg-‘, and six temperature knots placed at 298.15, 315, 425, 500, 560, and 603 K. The surface was extended to 298.15 K using the measurements of Fortier, Leduc, and Desnoyers’20’ corrected to 17.5 MPa using NaCl pressure slopes of Rogers and Pitzer.“” There were in all 203 points, of which five were eliminated (see table 1) because they were not in reasonable agreement with the other values. The fit of the remaining 198 points (and 6 additional points at 298.15 K)‘20’ to the cubic-spline surface resulted in a sum of the squares of the residuals of 73300 and a standard error of +20.0 J. K-l . mol-‘. A direct comparison of the estimated uncertainty of these results and the residuals from the fit (table 1) demonstrates the quality of the fit. Another way of showing the quality of the fit is to compare the sum of the squares of the residuals (s = 73300) with the sum of the squares of the residuals for a surface which passed through the average of each duplicate set of results (s = 41100).
HEAT CAPACITY
OF NaBr(aq)
499
4. Discussion A very small number of high-temperature heat capacities exist for NaBr(aq). Tanner and Lamb’**’ have measured specific heat capacities of NaBr(aq) from 298.15 to 358 K and 0.1 to 4.0 mol. kg-’ at the saturation vapor pressure. These values corrected to 17.5 MPa employing the C,, against p slopes of NaCl, do not agree with our fitted surfaces at temperatures above 298.15 K. We do not believe either set has substantial errors so we conclude that the assumption that the pressure dependences of C,,, of NaBr and NaCl solutions are identical is a poor assumption above 298.15 K. This assumption may not be very accurate at 298.15 K, since the deviations from our surface are systematic at 298.15 K. The errors in the pressure correction may be in excess of 50 per cent. The c,., surface for NaBr(aq) shows the same qualitative features as the NaCl and CaCl, surfaces presented previously.“, 3,4) At constant molality, C,, + increases to a maximum at about 350 K and thereafter decreases with increasing temperature. The temperature of this maximum seems to increase slightly with increasing molality. Values of C,, + at the highest temperatures and the lowest molalities in this study are very large and negative. At lower temperatures or higher molalities these large negative values do not occur. Figure 1 and table 3 show these effects. The plunge in C,,, at low molalities and elevated temperatures (above 575 K) is not surprising. In addition to the aforementioned experimental heat-capacity surfaces, several theoretical calculations indicate that C,, of an electrolyte at infinite dilution in water should approach - co as the critical temperature is approached from below.“,6-11) The C, *s presented in this paper, together with experimental results for Gibbs free enkrgies and enthalpies at 298.15 K, allow calculations of the thermodynamic properties of NaBr(aq) to 600 K at 17.5 MPa. Calculation of Gibbs free energies by this route allows the calculation of equilibrium constants for chemical reactions involving aqueous NaBr under these conditions. A comparison of the previous results for NaCl with the present results for NaBr is instructive. Table 4 shows the difference between C,,., of the two salts as a function of molality and temperature. Differences between the two salts are close to our estimated experimental errors except at the highest temperature. At the lower temperatures the differences are not random so they may be real. C,,,(NaBr) is almost always more negative than C,, ,(NaCl) at T 2 343.15 K and more positive at 298.15 K. The differences between the two salts are less at the higher molalities and lower temperatures. Because of the similarity of the two salts, it would not be a bad approximation, in the absence of these experimental values, to assume that NaBr had the same C,,, as NaCl. This leads us to the hypothesis that many (but not all) strong electrolytes will behave in a similar fashion. Recently, three groups have independently presented experimental evidence that many l-l electrolytes do have similar heat capacities ut infinite dilution.t23-25’ There are minor differences between the approaches of the three groups but they all point out that extrapolating “isocoulombic” reactions to high temperatures gives very good accuracy whereas extrapolating reactions in which there is a change in the number of ions during the reaction gives poorer
500
D. E. WHITE, J. A. GATES, AND R. H. WOOD
I
I
1.0 (m/mol.kg-‘)
0.5
I
1.5
; [)
FIGURE 1. Apparent molar heat capacity C,, of NaBr(aq) plotted as a function of m’12 at three temperatures at a pressure near 17.5 MPa. 0, Experiment; -, calculated from the two-dimensional spline fit of the results; - - -, the Debye-Hiickel limiting-law slopes at 500 and 602 K.
TABLE 4. Values of {C, ,(NaBr) - C,. ,&NaCI)} at various temperatures, molalities, and 17.5 M Pa T/K:
298.15
m/(mol kg- ‘) 0 0.25
343.15
398.15
{C,,(NaBr)-13 (62)
(24) -6
t-3 3.00
-3
(2)
-3
(5) -2 (3) -4 (3)
448.15
C,,(NaCI)}/(J -8 (45)
-5 (4)
-5 (4)
498.15
K-i
548.15
598.15
-62
-302 (350) -182 (15) -24 (15)
mall i)
&
(1-m
-3 (5) -6 (5)
-27 (7)
-10 (7)
’ Each figure in parentheses gives a rough estimate of the accuracy of (C,~.&NaBr)-C,,4(NaCI)]/ (J,K-i.mol-‘).
HEAT
CAPACITY
OF
NaBr(aq)
501
results, The extrapolations are based on the Gibbs free energy and enthalpy at 298.15 K. This observation implies that the heat capacities of many ions of the same charge at infinite dilution are of similar magnitude and quite different from the heat capacities of non-electrolytes. Lindsay(23’ pointed out that these ideas were not new. They received considerable attention from R. W. Gurney and others in the 193O~.‘~~-~s’ At that time only C,, s near room temperature were available so that the utility of this concept at high temperatures could not be appreciated. The present results show that on an absolute basis the difference between C,, for NaCl and NaBr increases with increasing temperature (table 4) so the salts show more individuality at higher temperature. However, on a relative scale the opposite is true; as a fraction of the total effect, the individuality decreases. The effects at high temperature are so large that the loss of relative individuality is a useful observation. Although the critical-point scaling laws predict that the heat capacities of electrolytes go to - cc as the critical point is approached from be10w,(~) the scaling laws do not give the magnitude of the effect at any given distance from the critical point so they do not predict that the heat capacities will be the same at a given temperature. Wood, Quint, and Grolier”’ calculated the properties of a hard-sphere ion in a water-like compressible dielectric fluid. This model (unlike the Born equation which does not allow for the compressibility of the solvent) shows very little dependence of the heat capacity of the ion on its radius at high temperatures. Thus, the reason for the relative similarity of the heat capacities of many 1--l electrolytes may be that the highly compressed solvent near the ion has less effect on the heat capacity of the ion than the solvent further away. This makes good sense because the solvent near the ion is at a higher pressure and is therefore further from the critical point of the water. These conclusions are only tentative because the model was unable to calculate the experimental value of the heat capacity of NaCl(aq). Since the comparison of the present results of NaBr with previous results for NaCl indicates relative similarities in the heat capacities even in concentrated solutions, one might expect the excess properties of electrolyte solutions to exhibit less relative individuality as the temperature is increased. This was suggested by Lindsay and Liu (29) from a consideration of osmotic coefficients of the alkali halides. IJsing results from more recent isopiestic experiments, Holmes and Mesmer’“O’ confirmed this trend but their results indicate that differences in activity coefficients are by no means negligible at 523.15 K. Lindsay’23’ suggested that in the absence of any better values one could estimate the activity coefficient and water activities for NaCl solutions as stand-ins for the needed but unknown values. There are other indications in the literature that the relative individuality of salt solutions becomes less at higher temperatures. The conductance values of Marshall and co-workers(31-33) sho w that many l-l electrolytes have similar association constants at supercritical temperatures and pressures. Similarly, the results of Marshall and Jones(34’ on the critical temperatures of aqueous salt solutions show that there is a group of l-l electrolytes which have similar (+ 10 per cent) critical temperatures at the same molality. Wood and Quint’@ used these values for the critical temperature of aqueous NaCl solutions, with a simple corresponding-states
502
D. E. WHITE.
J. A. GATES,
AND
R. H. WOOD
theory, to predict the heat capacities of NaCl(aq). The predictions were quite successful and led these authors to hypothesize that since many l-l electrolytes have similar critical temperatures they also have similar heat capacities. The model of a hard-sphere ion in a water-like and compressible dielectric fluid indicates that near the critical point of water each ion will have a very large region of compressed water around it with the density and dielectric constant of that water much higher than in the bulk solvent. This led Quint and Wood to hypothesize that because of the high dielectric constant near the ions, ion pairs in this temperature region spend appreciable amounts of time at fairly large distances from one another. This in turn indicates that the hard-sphere radius may not be very important in determining the association constant. Thus, the similarity in association constants at high temperatures becomes understandable. This concept can be extended to the salting out of non-electrolytes by ions at high temperatures. We suggest the hypothesis that, if the non-electrolyte is able to penetrate the solvation sphere of the ion infrequently at temperatures near the critical point of water, then the interaction of the non-electrolyte with the ion at these temperatures will be relatively independent of the radius of the ion, and many l-l electrolytes will have similar salting-out coefficients for a given non-electrolyte under these conditions. The present results allow the first accurate comparison of C,,, of two aqueous electrolytes up to 598 K. This comparison shows great relative similarities between the two salts with a different anion and there are both theoretical and experimental reasons to believe that this relative similarity will extend to other l-l electrolytes. This research was supported by the National Science Foundation under Grants CHE84-12592 and CHE8009672 and by the Office of Standard Reference Data of the National Bureau of Standards. REFERENCES 1. 2. 3. 4.
Smith-Magowan, D.; Wood, R. H. J. Chem. Thermodynamics 1981, 13, 1047. Smith-Magowan, D.; Wood, R. H.; Tillett, D. M. J. Chem. Eng. Data 1982, 27, 235. Gates, J. A.; Tillett, D. M.; White, D. E.; Wood, R. H. J. Chem. Thermodynamics 1987, 19. 131. White, D. E.; Doberstein, A. L.; Gates, J. A.; Tillett, D. M.; Wood, R. H. J. Chem. Thermodynamics 1987, 19.251.
5. 6. 7. 8. 9.
Wood, R. H.; Quint, J. R.; Grolier, J.-P. J. Phys. Chem. 1981, 85, 3944. Wood, R. H.; Quint, J. R. J. Chem. Thermodynamics 1982, 14, 1060. Wheeler, J. C. Ber. Bunsenges. Physik. Chem..1972, 76, 308. Gates. J. A.: Wood. R. H.: Ouint. J. R. J. Phvs. Chem. 1982. 86. 4948. Helgeson, H. C.; Kirkham; D. H. ‘Abstracts of papers, 174th meeting of American Chemical Society, New Orleans, LA. March 1977. 1Oa. Cobble, J. W.; Murray, R. C., Jr. Discuss. Faraday Sot. 1977, 64, 144. lob. Cobble, J. W.; Murray, R. C., Jr.; Sen, U. Nature 1981, 291, 5816. 11. Chang, R. F.; Morrison, G.; Levelt Sengers, J. M. H. J. Phys. Chem. 1984, 88, 3389. 12. Robison. S. L.: Weston. M. J. D. Solution Densifies of Sodium Bromide as a Function of Temperature and Anhydrous Salt Content. U.S. Atomic EnergyCommission. 1%7. UCRL-50257. 1 13. Smith-Magowan, D. Ph.D. Dissertation, University of Delaware. May 1980. 14. White, D. E.; Wood, R. H. J. Soln. Chem. 1982, 11, 223. 15. Gates,
J. A.; Wood,
R. H. J. Chem.
Eng. Data
1985, 30, 44. Steam Tables.
16. Haar, L.; Gallagher, J. S.; Kell, G. S. NBS/NRC Washington, DC. 1984.
Hemisphere Publishing Corp.:
HEAT
17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32 33 34
CAPACITY
OF
NaBr(aq)
503
Fortier, J.-L.; Benson, G. C.; Picker, P. J. Chem. Thermodynumics 1976, 8, 289. Gates, J. A. Ph.D. dissertation, University of Delaware, Newark. 1985. Uematsu. M.; Franck, E. U. J. Phys. Chem. Re$ Data 1980, 9, 1291. Fortier, J.-L.; Leduc, P.-A.; Desnoyers. J. E. J. Soln. Chem. 1974, 3. 323. Rogers, P. S. Z.; Pitzer, K. S. J. Phys. Chem. Re$ Data 1982, Il. 15. Tanner. J. E.: Lamb. F. W. J. Soln. Chem. 1978. 7. 303. Lindsay, W. T. 41st Annual Meeting of the ‘International Water Conference. Pittsburgh. PA. October 1980. Criss. C. M. 41st Annual Meeting of the International Water Conference, Pittsburgh. PA. October 1980. Murray, R. C., Jr.; Cobble, J. W. Electric Power Research Institute Report, August 1980. Gurney, R. W. J. Chem. Phys. 1938, 6, 499. Baughan, E. C. J. Chem. Phys. 1939, I. 951. Everett, D. H.; Wynn-Jones, W. F. K. Trans. Furadqv Sot. 1939, 35. 1380. Lindsay, W. T., Jr.; Liu, Chia-tsun. J. Phys. Chem. 1971, 75. 2723. Holmes, H. F.; Mesmer, R. F. J. Phys. Chem. 1983, 87. 1242. Dunn, A. L.: Marshall, W. L. J. Phys. Chem. 1969, 73, 723. Quist, A. S.; Marshall, W. L. J. Phys. Chem. 1969, 73, 978. Frantz. J. D.: Marshall, W. L. Am. J. Sci. 1982, 282, 1666; 1984, 284. 651. Marshall, W. L.: Jones. E. V. J. Inorg. Nucl. Chem. 1974, 36. 2319.
Heat capacities of aqueous 306 to 603 K at 17.5 MPa
NaBr
from
DOROTHY E. WHITE, JEFFREY A. GATES,” and ROBERT H. WOOD’ Department of Chemistry, University qf Delaware. Newark, Delaware 19716, U.S.A. (Received 5 May 1986: in jnal form 25 September
1986)
A differential flow heat-capacity calorimeter has been used to measure the heat capacity of NaBr(aq) at molalities from 0.05 to 3.0 mol. kg-‘, temperatures from 306 to 603 K, and a pressure near 17.5 MPa. The results show the very large and negative apparent molar heat capacities at high temperatures and low molalities found for NaCl(aq) and CaCl,(aq).
1. Introduction The work presented here is part of a continuing investigation of the heat capacities of aqueous electrolytes at high temperatures using flow-calorimetric techniques.‘1-4’ Very large and negative values of the apparent molar heat capacities have been found for aqueous NaCl,‘1,3’ and CaC1,,‘4’ and this has been attributed to large interactions between ions and water, together with the changes in the properties of the water as its critical point is approached. (1,5-l l’ There continues to be a need for such information to increase our understanding of a variety of chemical processes that occur at high temperatures including mineral geochemistry, the behavior of geothermal fluids, and corrosion in electric-power-plant boilers. In this paper we report the apparent molar heat capacities of aqueous NaBr solutions from 0.05 to 3.0 mol. kg-’ and 306 to 603 K at 17.5 MPa. A twodimensional cubic-spline representation of the apparent molar heat capacity as a function of molality and temperature allows the calculation of thermodynamic properties at any temperature and molality within the range of the results.
2. Experimental A stock solution of approximately 3.0 mol. kg- ’ of NaBr was prepared from Fisher certified NaBr (total impurities were less than 0.4 mass per cent including 0.2 mass per cent of Cl and 0.12 mass per cent of K) and distilled deionized water. Actual molality was determined by titration with AgNO,(aq). All other solutions were * Present address: E. I. du Pont Delaware 19898, U.S.A. * To whom correspondence should 0021-9614!87:050493+
II
$02,00/O
de Nemours
and Co.,
Inc.,
Experimental
Station,
Wilmington,
be addressed. t(? 1987 Academic
Press Inc. (London)
Limited
494
D. E. WHITE.
J. A. GATES.
AND
R. H. WOOD
prepared by dilution of appropriate masses of the 3.0 mol. kg- ’ stock. Densities of the stock and diluted solutions were determined on the Sodev Model 01D vibratingtube densimeter. As a check all molalities were calculated from the density of the solution and the literature results of Robison and Weston.“” The molalities agreed to within 0.1 per cent. The high-temperature flow heat-capacity calorimeter has been described in detail previously. (l.13’ For low-temperature measurements (325 K) a cooling jacket was installed on the vacuum can to facilitate temperature control. The calorimeter was operated at a water flow rate of 0.033 cm3. s-’ and with heater power of 0.31 W resulting in temperature rises of 1.1 to 1.8 K. The reported temperatures are the averages of the initial and final temperatures of the solution. The back-pressure regulator was calibrated (kO.25 MPa) using a Heise CM gauge (0 to 27 MPa). At least three heat-capacity measurements were made for each molality. The instrument measures the electric power necessary to give the same temperature rise when the sample solution and pure water are flowing in the calorimeter. The specific heat capacity cp of the sample solution at constant pressure is then calculated from c,/c; = 11 -f(Ps - Rv)Ipw~(PwlPs)~
(1)
where c,, is the specific heat capacity of the solution, cf is the specific heat capacity of pure water at the experimental temperature and pressure, P, is the electric power when the sample solution is in the sample cell, P, is the power when water is in the sample cell, f is a correction factor for heat losses, and p,,, and pS are the densities of water and of the aqueous salt solution at the experimental pressure and the temperature of the sample loop (298.15 K). The correction factorfwas calculated at each temperature by using 3.0 mol. kg-’ NaCl as a chemical standard.(14’ The densities of the experimental solutions were obtained from the fit of Gates and Wood”‘) and the properties of water from the equation of state of Haar, Gallagher, and Ke11.(r6) The apparent molar heat capacity C,,, can be calculated from the specific heat capacity ratio c,/c,*: C p.e = {Of,+
llm)(c,lcf)-(llm))cf.
(2)
where M, is the molar mass of the solute and m is the molality of the aqueous salt solution. Fortier, Benson, and Picker (17) have shown that errors can arise in flow calorimeters because of mixing and volume changes at the boundary between the sample and reference solutions. This effect can be large when the sample and reference fluids are quite different but is normally negligible without aqueous salt solutions (m < 5.0 mol. kg-‘).‘3*4’
3. Results The results of the heat-capacity measurements on NaBr(aq) are given in table 1, together with estimates of the accuracy of the individual measurements. The apparent molar heat capacities were fitted by the multi-dimensional cubic-spline
HEAT CAPACITY
495
OF NaBr(aq)
TABLE 1. Apparent molar heat capacity C,, + of NaBr(aq) m mol,kg-’
p, P,
cp c:
c P.m J.K-‘,mol-’
4
6b
A’
____m mol.kg-’
-PS P,
0.0498 0.0498 0.0498 0.1003 0.1003
0.9980 0.9981 0.9983 0.9963 0.9963
0.9941 0.9942 0.9944 0.9886 0.9886
T= 306.15 K p = 17.03 MPa ,f= 1.014“ - 66.26 10.34 13.38 0.1003 0.9963 0.9886 -58.15 10.18 5.27 0.2500 0.9912 0.9723 -40.84 9.83 -12.04 0.2500 0.9913 0.9724 - 50.07 6.53 0.18 0.2500 0.9910 0.9722 - 50.66 6.54 0.77
0.501 I 0.501 I 0.501 I 1.003 I 1.0031 1.0031
0.9833 0.9833 0.9833 0.9697 0.9696 0.9698
0.9469 0.9469 0.9469 0.9016 0.9016 0.9017
T = 306.15 K p == 17.20 MPa ,/= 1.013“ - 35.20 3.53 -0.41 2.0056 0.9488 0.8280 -35.16 3.53 -0.45 2.0056 0.9488 0.8281 - 35.05 3.53 -0.57 2.0056 0.9487 0.8280 -21.95 2.96 -0.89 3.0053 0.9339 0.7708 -22.12 2.96 -0.72 3.0053 0.9339 0.7709 -21.57 2.95 - 1.27 3.0053 0.9339 0.7709
0.049x 0.0498 0.049x 0.1003 0.1003 0.1003 0.2500 0.2500 0.2500 0.501 I 0.501 I
0.9984 0.9984 0.9983 0.9967 0.9969 0.9968 0.9922 0.9921 0.9923 0.9849 0.9846
0.9944 0.9944 0.9943 0.9889 0.9890 0.9889 0.9730 0.9729 0.9732 0.9479 0.9476
T = 324.41 K p = 17.27 MPa -40.92 10.74 - 13.85 0.5011 -41.79 10.76 - 12.97 1.0031 -46.17 10.85 -8.60 1.0031 - 38.88 6.76 - 11.23 1.0031 - 32.79 6.64 - 17.32 2.0056 - 35.40 6.69 - 14.71 2.0056 - 32.43 4.32 -8.62 2.0056 -33.52 4.34 -7.53 3.0053 -29.98 4.27 -11.07 3.0053 - 26.48 3.45 -4.90 3.0053 -29.33 3.50 -2.06
/‘= 1.050“ 0.9848 0.9478 0.9717 0.9026 0.9717 0.9025 0.9717 0.9025 0.9506 0.8280 0.9507 0.8282 0.9507 0.8281 0.9347 0.7695 0.9347 0.7695 0.9347 0.7695
-27.72 - 17.72 - 17.79 - 17.79 -2.23 - 1.89 -2.03 10.35 10.30 10.35
3.47 2.92 2.92 2.92 2.47 2.46 2.46 2.19 2.19 2.19
-3.67 -0.97 -0.90 -0.90 0.16 -0.18 -0.03 -0.23 -0.19 -~0.23
0.0498 0.0498 0.0498 0.1003 0.1003 0.1003 0.2500 0.2500 0.2500 0.m 1 0.5011 05011
0.9979 0.9981 0.9980 0.9965 0.9963 0.9967 0.9917 0.9918 0.9918 0.9846 0.9846 0.9845
0.9939 0.9941 0.9940 0.9885 0.9883 0.9887 0.9723 0.9724 0.9723 0.9472 0.9471 0.9470
T = 350.30 K p = 17.75 MPa ./ = 1.082 d -88.14 12.50 31.40 1.0031 0.9719 0.9019 - 64.82 12.03 8.08 1.0031 0.9719 0.9019 -75.04 12.24 18.30 1.0031 0.9718 0.9018 - 52.38 7.44 0.99 2.0056 0.9507 0.8268 - 63.26 7.65 11.87 2.0056 0.9507 0.8268 2.0056 0.9506 0.8267 -44.38 7.28 -7.01 4.11 3.0053 0.9340 0.7673 -45.15 4.74 -43.41 4.71 2.37 3.0053 0.9342 0.7674 -43.99 4.72 2.95 3.0053 0.9343 0.7675 - 32.93 3.66 2.14 3.0053 0.9340 0.7672 - 33.36 3.67 2.58 3.0053 0.9337 0.7670 -34.53 3.70 3.74 3.0053 0.9337 0.7670
- 20.77 -20.55 - 20.98 - 5.25 - 5.25 -5.61 6.25 6.48 6.67 6.13 5.74 5.79
3.03 3.03 3.03 2.55 2.55 2.56 2.29 2.29 2.28 2.29 2.30 2.30
2.19 I .97 2.41 0.71 0.71 1.08 -- 1.34 - 1.56 .- 1.76 - 1.22 --0.82 0.87
0.0498 0.0498 0.0498 0.1003 0.1003 0.1003 0.2500 0.2500 0.2500 0.501 I
0.9982 0.9983 0.9979 0.9961 0.9962 0.9960 0.9905 0.9907 0.9905 0.9819
0.9942 0.9942 0.9938 0.9880 0.9882 0.9879 0.9710 0.9712 0.9710 0.9442
- 62.00 - 56.82 - 92.97 - 74.07 -68.93 -79.18 -68.85 -65.24 -68.33 - 59.76
- 59.50 - 59.25 -45.42 -44.79 -44.28 -26.71 - 27.29 - 26.45 - 12.59
4.75 4.75 3.82 3.81 3.80 3.16 3.17 3.15 2.80
3.62 3.36 2.10 1.47 0.96 0.86 1.43 0.60 0.00
T=
405.57 17.20 17.10 17.82 10.49 10.38 10.59 6.29 6.22 6.28 4.76
K p = 17.72 MPa - 15.10 0.5011 -20.28 0.5011 15.87 1.0031 1.10 1.0031 -4.05 1.0031 6.20 2.0056 3.94 2.0056 0.33 2.0056 3.42 3.0053 3.8X
.f = l.08gd 0.9819 0.9443 0.9819 0.9443 0.9669 0.8967 0.9670 0.8968 0.9671 0.8969 0.9421 0.8184 0.9419 0.8182 0.9423 0.8185 0.9229 0.7570
-51.24
-44.08 -42.25 -47.07
-2.26 -2.15 -2.29 12.69 12.76 12.76
1.35 6.55 4.37 0.43 4.33 - 1.39 4.43 3.43
2.44 -0.56 2.44 -0.67 2.44 --0.53 2.12 0.62 2.12 0.55 2.12 0.55
D. E. WHITE.
496
J. A. GATES, TABLE
In
c P.0
y fib
ps
cp
mol. kg-’
P,
c;
0.0498 0.0498 0.0498 2.0056 2.0056 2.0056
0.9980 0.9919 0.9982 0.9419 0.9418 0.9417
0.9940 0.9939 0.9942 0.8193 0.8191 0.8190
-79.55 -82.08 - 62.08 -24.55 - 24.92 -25.11
0.0498 0.0498 0.0498 0.1003 0.1003 0.1003 0.1003 0.25Og 0.2500 0.2500 0.5011
0.9966 0.9911 0.9972 0.9946 0.9954 0.9950 0.9951 0.9877 0.9878 0.9879 0.9765
0.9925 0.9936 0.9932 0.9865 0.9873 0.9869 0.9871 0.9681 0.9682 0.9683 0.9389
- 207.95 - 109.76 - 150.91 - 142.57 - 107.24 - 125.83 - 118.86 - 120.20 -118.89 -117.58 - 109.63
0.0498 0.0498 0.0498 0.1003 0.1003 0.1003 0.2500 0.2500 0.2500 0.5011 0.5011
0.9969 0.9961 0.9966 0.9936 0.9938 0.9938 0.9854 0.9856 0.9858 0.9733 0.9734
0.9923 0.9921 0.9920 0.9845 0.9847 0.9847 0.9635 0.9637 0.9640 0.9317 0.9318
- 235.45 -255.58 -263.41 -239.83 -230.37 -230.37 -212.98 -208.50 -203.13 - 183.81 - 182.69
0.0498 0.0498 0.0498 0.1003 0.1003 0.1003 0.2500 0.2500 0.2500 0.5011 0.5011
0.9945 0.9943 0.9940 0.9883 0.9892 0.9885 0.9761 0.9166 0.9765 0.9584 0.9583
0.9891 0.9889 0.9885 0.9774 0.9786 0.9777 0.9510 0.9517 0.9516 0.9118 0.9117
-581.99 -609.10 -647.82 -623.21 - 566.09 -611.01 -491.39 -477.11 -479.76 -411.87 -412.52
*’
J.K-‘~rnol~’
T = 400.92
K
K
T = 500.90 K 30.45 30.85 31.01 18.74 18.55 18.55 11.26 11.17 11.06 8.37 8.35
56.72 51.26 58.03 36.14 35.00 35.90 20.89 20.61 20.66 15.09 15.11
p= - 6.54 13.60 21.43 11.15 1.70 1.70 7.80 3.32 -2.05 3.13 2.00
T = 551.90 K
~ m
-p,
cp
mol,kg-’
P,
c;
0.5011 0.5011 1.0031 1.0031 1.0031 2.0056 2.0056 2.0056 3.0053 3.0053 3.0053
17.41 MPa 0.5011 1.0031 1.0031 1.0031 2.0056 2.0056 2.0056 3.0053 3.0053 3.0053
p = 17.41 MPa
-69.51 -42.40 - 3.68 25.24 -31.87 13.05 - 10.07 -24.28 -21.70 - 1.65 -1.00
f=
0.5011 1.0031 1.0031 1.0031 2.0056 2.0056 2.0056 3.0053 3.0053 3.0053
c P.0 J,K-‘.mol-’
y
iSh
A’
1.067“
3.0053 3.0053 3.0053 3.0053 3.0053
p = 17.75 MPa
23.13 ’ 21.17 -23.22 21.99 17.93 13.38 14.98 12.67 -20.35 13.04 -1.76 12.91 -8.73 7.96 1.30 7.94 -0.01 7.91 -1.32 6.11 1.91
R. H. WOOD
lpcontinued
p = 17.48 MPa
17.26 5.79 17.31 8.32 16.91 -11.68 3.10 1.41 3.11 1.78 3.11 1.97
T = 450.37
AND
0.9195 0.9222 0.9229 0.9231 0.9227
f=
0.7553 0.7576 0.7582 0.7584 0.7581
- 15.66 -11.41 - 10.28 -9.85 - 10.51
2.85 2.77 2.74 2.13 2.15
5.04 0.78 -0.35 -0.77 -0.11
0.9400 0.9398 0.8887 0.8890 0.8887 0.8071 0.8076 0.8072 0.7432 0.7439 0.7439
-99.38 - 101.45 ~ 84.43 - 82.76 - 84.28 - 56.78 - 55.64 - 56.61 - 38.88 - 31.44 - 37.55
5.90 5.94 4.81 4.77 4.81 3.89 3.87 3.89 3.43 3.40 3.41
-8.34 -6.27 -5.24 -6.90 -5.38 -4.23 -5.38 -4.40 1.09 -0.35 -0.23
1.075’ 0.9776 0.9774 0.9585 0.9588 0.9585 0.9294 0.9299 0.9295 0.9065 0.9074 0.9073
f=
1.225d 0.9734 0.9526 0.9528 0.9520 0.9213 0.9215 0.9214 0.8979 0.8980 0.8973
j”=
0.9318 0.8762 0.8765 0.8755 0.7892 0.7893 0.7892 0.7229 0.7230 0.7223
-
182.35 150.88 149.74 154.29 108.53 108.15 108.44 -81.00 - 80.80 -82.18
8.34 6.59 6.56 6.65 5.21 5.20 5.21 4.51 4.51 4.53
1.67 1.72 0.58 5.14 -0.39 -0.77 -0.47 1.14 0.94 2.32
0.9120 0.8457 0.8448 0.8461 0.7487 0.7485 0.7484 0.6177 0.6772 0.6774
-409.92 - 334.71 - 339.63 - 332.54 -241.98 - 242.59 -242.76 - 188.08 - 188.99 - 188.59
15.05 11.48 11.58 11.44 8.63 8.64 8.65 7.25 7.21 7.26
-3.59 12.86 17.79 10.70 4.22 4.83 5.00 -3.88 -2.97 -3.31
1.281’
0.9585 0.9291 0.9284 0.9294 0.8885 0.8884 0.8883 0.8597 0.8593 0.8594
HEAT
CAPACITY TABLE
mol.kg-’
P,
(.;
J.K-‘.m,,-’
”
T = 577.87 0.0498 0.0498 0.0498 0.1003 0.1003 0.1003 0.2500 0.2500 0.2500 0.501 I 0.501 1
0.9903 0.9875 0.9884 0.9815 0.9811 0.9819 0.9635 0.9622 0.9619 0.9454 0.9305
0.9824 0.9785 0.9798 0.9662 0.9656 0.9667 0.9302 0.9284 0.9281 0.8886 0.8683
- 1390.50 -1825.13 - 1680.77 - 1306.63 - 1337.05 - 1276.20 - 1008.73 - 1048.94 -1057.11 -719.64 -954.52
0.0498 0.0498 0.0498 0. LOO3 0.1003 0.1003 0.1003 0.2500 0.2500 0.2500 0.5011
0.9862 0.9872 0.9869 0.9764 0.9765 0.9764 0.9764 0.9488 0.9491 0.9491 0.9162
0.9765 0.9778 0.9773 0.9586 0.9588 0.9586 0.9586 0.9090 0.9095 0.9095 0.8474
-2413.88 - 2234.27 - 2299.75 -2035.17 - 2023.08 -2035.17 -2035.17 - 1753.08 - 1741.09 - 1741.09 - 1408.86
-
K
T=
I-continued
mol.kg-’ p = 17.48 MPa
155.27 46.54 163.96 ’ 161.08 o 90.89 81.84 91.50 y 90.28 51.42 47.93 - 15.36 48.74 24.85 48.90 33.01 29.76 - 120.62 34.45 114.26 602.74
K
127.26 123.67 124.98 81.61 81.37 81.61 81.61 53.51 53.27 53.27 39.12
e -32.55 32.93 -25.75 -37.84 -25.75 -25.75 27.12 15.13 15.13 -8.28
497
OF NaBr(aq)
0.5011 1.0031 1.0031 1.0031 2.0056 2.0056 2.0056 3.0053 3.0053 3.0053
p = 17.55 MPa 0.5011 0.5011 1.0031 1.0031 1.0031 2.0056 2.0056 2.0056 3.0053 3.0053 3.0053
P,
c;
J.K-‘.mol-’
6b
A,
/ = 1.419 d 0.9365 0.9068 0.8970 0.9090 0.8466 0.8518 0.8532 0.8169 0.8226 0.8226
0.8765 0.8071 0.7942 0.8100 0.6832 0.6897 0.6914 0.6116 0.6183 0.6183
-859.72 - 600.68 - 678.93 -583.12 -481.96 - 460.48 -454.90 - 364.69 -348.71 -348.71
0.8473 0.8471 0.7536 0.7534 0.7529 0.6374 0.6362 0.6352 0.5625 0.5620 0.5628
-1411.12 - 1413.57 - 1090.04 - 1091.19 - 1095.18 - 747.27 -751.71 - 755.58 - 568.69 -570.13 - 567.98
32.56 19.45 21.24 --44.42 22.80 33.83 20.88 m-61.98 IS.84 22.54 15.41 1.06 15.30 -4.52 12.52 10.64 12.20 -5.35 12.20 --5.35
f = 1.435’ 0.9161 0.9160 0.8677 0.8676 0.8672 0.8117 0.8108 0.8100 0.7776 0.7771 0.7778
39.17 39.22 29.05 29.07 29.15 20.39 20.48 20.56 16.26 16.29 16.24
-6.03 -3.58 6.14 7.28 11.28 -9.61 -- 5.16 - 1.30 3.43 4.87 2.72
a The apparent molar heat capacity C,., was calculated from equation (1). ’ The estimated accuracy 6 of each value of C,,,/(J K-’ mol- ‘) was calculated assuming relative errors of 1 per cent in AP/P and an absolute error estimated from the experimental sensitivity at each temperature. The absolute error estimates varied from ~0.0001 to &O.OOlO. ’ A is the value of {C,.+(calculated)C&observed)l/(J K ’ mol ‘). The calculated value is from a cubic-spline interpolation of the knots in table 2. ’ The value of the heat-loss correction factor,fwas calculated using the heat capacity of 3.005 mol. kg- ’ for NaCl as a chemical standard.“3,‘4’ The measured values of APjP for 3.005 mol. kg-’ NaCl at the experimental pressure were -0.04813 (p = 17.03 MPa) and -0.04820 @ = 17.20 MPa) at 306.15 K, -0.04733 at 324.41 K, -0.04830 at 350.30 K. -0.05923 at 405.57 K. -0.05945 at 400.92 K. -0.07435 at 450.37 K. -0.08672 at 500.90 K, -0.12499 at 551.90 K. -0.15296 at 577.87 K, and -0.21096 at 602.74 K. ’ These values were not included in the fit. Values were discarded based on a Q-test (90 per cent confidence) or when the square of the residual for a given point was larger than 20 per cent of the overall square of the residuals.
method described previously. (X la) The experimental pressure varied between 17.0 and 17.8 MPa. These small variations in pressure have been ignored in the representation. This isobaric assumption introduces an increase of less than 10 per cent in the estimated uncertainty of the results. The knot positions and values are presented in table 2. Table 3 gives values of C,,, at a variety of temperatures and molalities. The Debye-Hiickel limiting-law slopes for C,,, as a function of ml/‘* labeled A,, have been included in table 2. These have been calculated using Haar, Gallagher, and Kell’s equation of state for water”@ with Uematsu and Franck’s equation for the dielectric properties of water.“” As with the C,. +, surfaces for NaCl
498
D. E. WHITE.
J. A. GATES,
AND
R. H. WOOD
TABLE 2. NaBr knot positions, knot values, and DebyeeHtickel slopes A, for calculating the apparent This fit is a representation of 203 points. The sum of the squares molar heat capacities C,. ,+ of NaBr(aq). of the residuals is 73300 resulting in a standard error of the fit of k 20.0 J. K- ’ mol ‘. The minimum sum of the squares for this set is 41100 T/K:
298.15
315.00
425.00
A,:
35.15
38.26
87.24
- 57.77 -47.83 15.62
- 62.90 -46.47 12.51
- 110.24 -88.28 -21.16
500.00
560.00
603.00
216.91
718.67
3730.03
p = 17.5 MPa
{m/(mol
kg- *)}112
C,~4/(J~K-r~mol-1)
0 0.4000 1.7500
TABLE m/(mol
3. Apparent
kg- ‘):
0
molar 0.100
0.250
C,,,
of NaBr(aq)
0.500
-990.35 -693.74 -229.91
- 2947.24 - 1908.75 - 558.09
at p = 17.5 MPa 1.000
2.000
3.000
- 25.42 - 20.96 - 17.92 - 19.06 -24.59 - 37.98 - 58.92 - 87.05 - 118.09 - 146.57 - 180.23 -292.74 - 572.99 - 1000.50
- 3.68 -2.41 -2.48 -5.14 - 10.60 -21.68 - 37.86 - 59.09 -83.04 - 106.65 - 135.41 -217.39 -410.46 - 700.68
14.58 12.04 8.43 4.22 -1.00 -9.57 -21.14 - 36.37 -55.21 - 77.37 - 107.65 - 176.22 -318.91 - 525.48
C,,+/(J.K-‘.mol-‘)
T/K 298.15 313.15 333.15 353.15 373.15 398.15 423.15 448.15 473.15 498.15 523.15 548.15 573.15 598.15
heat capacity
- 279.68 -215.91 - 77.50
-
57.77 62.45 65.42 66.49 69.26 80.65 - 107.45 - 154.32 -213.97 -275.37 - 363.46 - 682.95 - 1479.60 -2692.71
-49.76 -50.01 -50.31 -51.75 - 55.99 -67.71 -89.58 - 123.99 - 169.28 - 222.52 - 302.79 - 539.20 - 1085.59 - 1900.57
-45.12 - 42.47 -40.48 -41.39 - 46.20 - 59.26 -81.99 -115.49 - 156.50 -200.37 -261.90 -452.87 -907.10 -1590.51
- 38.09 -33.71 - 30.46 -31.19 - 36.43 -50.17 - 72.84 - 104.62 - 141.26 -177.12 -223.30 - 374.58 - 744.86 - 1306.69
and CaCl, presented previously, 13*4) the NaBr surface required three m1i2 knots placed at 0, 0.4, and 1.75 mol. kg-‘, and six temperature knots placed at 298.15, 315, 425, 500, 560, and 603 K. The surface was extended to 298.15 K using the measurements of Fortier, Leduc, and Desnoyers’20’ corrected to 17.5 MPa using NaCl pressure slopes of Rogers and Pitzer.“” There were in all 203 points, of which five were eliminated (see table 1) because they were not in reasonable agreement with the other values. The fit of the remaining 198 points (and 6 additional points at 298.15 K)‘20’ to the cubic-spline surface resulted in a sum of the squares of the residuals of 73300 and a standard error of +20.0 J. K-l . mol-‘. A direct comparison of the estimated uncertainty of these results and the residuals from the fit (table 1) demonstrates the quality of the fit. Another way of showing the quality of the fit is to compare the sum of the squares of the residuals (s = 73300) with the sum of the squares of the residuals for a surface which passed through the average of each duplicate set of results (s = 41100).
HEAT CAPACITY
OF NaBr(aq)
499
4. Discussion A very small number of high-temperature heat capacities exist for NaBr(aq). Tanner and Lamb’**’ have measured specific heat capacities of NaBr(aq) from 298.15 to 358 K and 0.1 to 4.0 mol. kg-’ at the saturation vapor pressure. These values corrected to 17.5 MPa employing the C,, against p slopes of NaCl, do not agree with our fitted surfaces at temperatures above 298.15 K. We do not believe either set has substantial errors so we conclude that the assumption that the pressure dependences of C,,, of NaBr and NaCl solutions are identical is a poor assumption above 298.15 K. This assumption may not be very accurate at 298.15 K, since the deviations from our surface are systematic at 298.15 K. The errors in the pressure correction may be in excess of 50 per cent. The c,., surface for NaBr(aq) shows the same qualitative features as the NaCl and CaCl, surfaces presented previously.“, 3,4) At constant molality, C,, + increases to a maximum at about 350 K and thereafter decreases with increasing temperature. The temperature of this maximum seems to increase slightly with increasing molality. Values of C,, + at the highest temperatures and the lowest molalities in this study are very large and negative. At lower temperatures or higher molalities these large negative values do not occur. Figure 1 and table 3 show these effects. The plunge in C,,, at low molalities and elevated temperatures (above 575 K) is not surprising. In addition to the aforementioned experimental heat-capacity surfaces, several theoretical calculations indicate that C,, of an electrolyte at infinite dilution in water should approach - co as the critical temperature is approached from below.“,6-11) The C, *s presented in this paper, together with experimental results for Gibbs free enkrgies and enthalpies at 298.15 K, allow calculations of the thermodynamic properties of NaBr(aq) to 600 K at 17.5 MPa. Calculation of Gibbs free energies by this route allows the calculation of equilibrium constants for chemical reactions involving aqueous NaBr under these conditions. A comparison of the previous results for NaCl with the present results for NaBr is instructive. Table 4 shows the difference between C,,., of the two salts as a function of molality and temperature. Differences between the two salts are close to our estimated experimental errors except at the highest temperature. At the lower temperatures the differences are not random so they may be real. C,,,(NaBr) is almost always more negative than C,, ,(NaCl) at T 2 343.15 K and more positive at 298.15 K. The differences between the two salts are less at the higher molalities and lower temperatures. Because of the similarity of the two salts, it would not be a bad approximation, in the absence of these experimental values, to assume that NaBr had the same C,,, as NaCl. This leads us to the hypothesis that many (but not all) strong electrolytes will behave in a similar fashion. Recently, three groups have independently presented experimental evidence that many l-l electrolytes do have similar heat capacities ut infinite dilution.t23-25’ There are minor differences between the approaches of the three groups but they all point out that extrapolating “isocoulombic” reactions to high temperatures gives very good accuracy whereas extrapolating reactions in which there is a change in the number of ions during the reaction gives poorer
500
D. E. WHITE, J. A. GATES, AND R. H. WOOD
I
I
1.0 (m/mol.kg-‘)
0.5
I
1.5
; [)
FIGURE 1. Apparent molar heat capacity C,, of NaBr(aq) plotted as a function of m’12 at three temperatures at a pressure near 17.5 MPa. 0, Experiment; -, calculated from the two-dimensional spline fit of the results; - - -, the Debye-Hiickel limiting-law slopes at 500 and 602 K.
TABLE 4. Values of {C, ,(NaBr) - C,. ,&NaCI)} at various temperatures, molalities, and 17.5 M Pa T/K:
298.15
m/(mol kg- ‘) 0 0.25
343.15
398.15
{C,,(NaBr)-13 (62)
(24) -6
t-3 3.00
-3
(2)
-3
(5) -2 (3) -4 (3)
448.15
C,,(NaCI)}/(J -8 (45)
-5 (4)
-5 (4)
498.15
K-i
548.15
598.15
-62
-302 (350) -182 (15) -24 (15)
mall i)
&
(1-m
-3 (5) -6 (5)
-27 (7)
-10 (7)
’ Each figure in parentheses gives a rough estimate of the accuracy of (C,~.&NaBr)-C,,4(NaCI)]/ (J,K-i.mol-‘).
HEAT
CAPACITY
OF
NaBr(aq)
501
results, The extrapolations are based on the Gibbs free energy and enthalpy at 298.15 K. This observation implies that the heat capacities of many ions of the same charge at infinite dilution are of similar magnitude and quite different from the heat capacities of non-electrolytes. Lindsay(23’ pointed out that these ideas were not new. They received considerable attention from R. W. Gurney and others in the 193O~.‘~~-~s’ At that time only C,, s near room temperature were available so that the utility of this concept at high temperatures could not be appreciated. The present results show that on an absolute basis the difference between C,, for NaCl and NaBr increases with increasing temperature (table 4) so the salts show more individuality at higher temperature. However, on a relative scale the opposite is true; as a fraction of the total effect, the individuality decreases. The effects at high temperature are so large that the loss of relative individuality is a useful observation. Although the critical-point scaling laws predict that the heat capacities of electrolytes go to - cc as the critical point is approached from be10w,(~) the scaling laws do not give the magnitude of the effect at any given distance from the critical point so they do not predict that the heat capacities will be the same at a given temperature. Wood, Quint, and Grolier”’ calculated the properties of a hard-sphere ion in a water-like compressible dielectric fluid. This model (unlike the Born equation which does not allow for the compressibility of the solvent) shows very little dependence of the heat capacity of the ion on its radius at high temperatures. Thus, the reason for the relative similarity of the heat capacities of many 1--l electrolytes may be that the highly compressed solvent near the ion has less effect on the heat capacity of the ion than the solvent further away. This makes good sense because the solvent near the ion is at a higher pressure and is therefore further from the critical point of the water. These conclusions are only tentative because the model was unable to calculate the experimental value of the heat capacity of NaCl(aq). Since the comparison of the present results of NaBr with previous results for NaCl indicates relative similarities in the heat capacities even in concentrated solutions, one might expect the excess properties of electrolyte solutions to exhibit less relative individuality as the temperature is increased. This was suggested by Lindsay and Liu (29) from a consideration of osmotic coefficients of the alkali halides. IJsing results from more recent isopiestic experiments, Holmes and Mesmer’“O’ confirmed this trend but their results indicate that differences in activity coefficients are by no means negligible at 523.15 K. Lindsay’23’ suggested that in the absence of any better values one could estimate the activity coefficient and water activities for NaCl solutions as stand-ins for the needed but unknown values. There are other indications in the literature that the relative individuality of salt solutions becomes less at higher temperatures. The conductance values of Marshall and co-workers(31-33) sho w that many l-l electrolytes have similar association constants at supercritical temperatures and pressures. Similarly, the results of Marshall and Jones(34’ on the critical temperatures of aqueous salt solutions show that there is a group of l-l electrolytes which have similar (+ 10 per cent) critical temperatures at the same molality. Wood and Quint’@ used these values for the critical temperature of aqueous NaCl solutions, with a simple corresponding-states
502
D. E. WHITE.
J. A. GATES,
AND
R. H. WOOD
theory, to predict the heat capacities of NaCl(aq). The predictions were quite successful and led these authors to hypothesize that since many l-l electrolytes have similar critical temperatures they also have similar heat capacities. The model of a hard-sphere ion in a water-like and compressible dielectric fluid indicates that near the critical point of water each ion will have a very large region of compressed water around it with the density and dielectric constant of that water much higher than in the bulk solvent. This led Quint and Wood to hypothesize that because of the high dielectric constant near the ions, ion pairs in this temperature region spend appreciable amounts of time at fairly large distances from one another. This in turn indicates that the hard-sphere radius may not be very important in determining the association constant. Thus, the similarity in association constants at high temperatures becomes understandable. This concept can be extended to the salting out of non-electrolytes by ions at high temperatures. We suggest the hypothesis that, if the non-electrolyte is able to penetrate the solvation sphere of the ion infrequently at temperatures near the critical point of water, then the interaction of the non-electrolyte with the ion at these temperatures will be relatively independent of the radius of the ion, and many l-l electrolytes will have similar salting-out coefficients for a given non-electrolyte under these conditions. The present results allow the first accurate comparison of C,,, of two aqueous electrolytes up to 598 K. This comparison shows great relative similarities between the two salts with a different anion and there are both theoretical and experimental reasons to believe that this relative similarity will extend to other l-l electrolytes. This research was supported by the National Science Foundation under Grants CHE84-12592 and CHE8009672 and by the Office of Standard Reference Data of the National Bureau of Standards. REFERENCES 1. 2. 3. 4.
Smith-Magowan, D.; Wood, R. H. J. Chem. Thermodynamics 1981, 13, 1047. Smith-Magowan, D.; Wood, R. H.; Tillett, D. M. J. Chem. Eng. Data 1982, 27, 235. Gates, J. A.; Tillett, D. M.; White, D. E.; Wood, R. H. J. Chem. Thermodynamics 1987, 19. 131. White, D. E.; Doberstein, A. L.; Gates, J. A.; Tillett, D. M.; Wood, R. H. J. Chem. Thermodynamics 1987, 19.251.
5. 6. 7. 8. 9.
Wood, R. H.; Quint, J. R.; Grolier, J.-P. J. Phys. Chem. 1981, 85, 3944. Wood, R. H.; Quint, J. R. J. Chem. Thermodynamics 1982, 14, 1060. Wheeler, J. C. Ber. Bunsenges. Physik. Chem..1972, 76, 308. Gates. J. A.: Wood. R. H.: Ouint. J. R. J. Phvs. Chem. 1982. 86. 4948. Helgeson, H. C.; Kirkham; D. H. ‘Abstracts of papers, 174th meeting of American Chemical Society, New Orleans, LA. March 1977. 1Oa. Cobble, J. W.; Murray, R. C., Jr. Discuss. Faraday Sot. 1977, 64, 144. lob. Cobble, J. W.; Murray, R. C., Jr.; Sen, U. Nature 1981, 291, 5816. 11. Chang, R. F.; Morrison, G.; Levelt Sengers, J. M. H. J. Phys. Chem. 1984, 88, 3389. 12. Robison. S. L.: Weston. M. J. D. Solution Densifies of Sodium Bromide as a Function of Temperature and Anhydrous Salt Content. U.S. Atomic EnergyCommission. 1%7. UCRL-50257. 1 13. Smith-Magowan, D. Ph.D. Dissertation, University of Delaware. May 1980. 14. White, D. E.; Wood, R. H. J. Soln. Chem. 1982, 11, 223. 15. Gates,
J. A.; Wood,
R. H. J. Chem.
Eng. Data
1985, 30, 44. Steam Tables.
16. Haar, L.; Gallagher, J. S.; Kell, G. S. NBS/NRC Washington, DC. 1984.
Hemisphere Publishing Corp.:
HEAT
17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32 33 34
CAPACITY
OF
NaBr(aq)
503
Fortier, J.-L.; Benson, G. C.; Picker, P. J. Chem. Thermodynumics 1976, 8, 289. Gates, J. A. Ph.D. dissertation, University of Delaware, Newark. 1985. Uematsu. M.; Franck, E. U. J. Phys. Chem. Re$ Data 1980, 9, 1291. Fortier, J.-L.; Leduc, P.-A.; Desnoyers. J. E. J. Soln. Chem. 1974, 3. 323. Rogers, P. S. Z.; Pitzer, K. S. J. Phys. Chem. Re$ Data 1982, Il. 15. Tanner. J. E.: Lamb. F. W. J. Soln. Chem. 1978. 7. 303. Lindsay, W. T. 41st Annual Meeting of the ‘International Water Conference. Pittsburgh. PA. October 1980. Criss. C. M. 41st Annual Meeting of the International Water Conference, Pittsburgh. PA. October 1980. Murray, R. C., Jr.; Cobble, J. W. Electric Power Research Institute Report, August 1980. Gurney, R. W. J. Chem. Phys. 1938, 6, 499. Baughan, E. C. J. Chem. Phys. 1939, I. 951. Everett, D. H.; Wynn-Jones, W. F. K. Trans. Furadqv Sot. 1939, 35. 1380. Lindsay, W. T., Jr.; Liu, Chia-tsun. J. Phys. Chem. 1971, 75. 2723. Holmes, H. F.; Mesmer, R. F. J. Phys. Chem. 1983, 87. 1242. Dunn, A. L.: Marshall, W. L. J. Phys. Chem. 1969, 73, 723. Quist, A. S.; Marshall, W. L. J. Phys. Chem. 1969, 73, 978. Frantz. J. D.: Marshall, W. L. Am. J. Sci. 1982, 282, 1666; 1984, 284. 651. Marshall, W. L.: Jones. E. V. J. Inorg. Nucl. Chem. 1974, 36. 2319.