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Heat capacities of aqueous LiCl from 306 to 603 K at 17.5 MPa
o-232
Heat capacities of aqueous to 603 K at 17.5 MPa DOROTHY
E. WHITE,
JEFFREY
A. GATES,”
LiCl from and ROBERT
306
H. WOOD
h
Department of Chemistry, University qf Delaware. Newark, Delaware 19716, U.S.A. I Received II December 1986: in jinal,fortn
19 Februar!, 1987)
A differential flow heat-capacity calorimeter has been used to measure the heat capacity of LiCl(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 molahties found previously for NaCl(aq). NaBr(aq). and KCl(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.“-“’ Very large and negative values of the apparent molar heat capacity C,, have been found for aqueous NaCl,“*3) KU,‘@ NaBr,“’ and CaC1,.‘4’ 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.“.‘-13’ There continues to be a need for 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 boilers. In this paper we report C,,, of LiCl(aq) from 0.05 to 3.0 mol. kg- ’ and 306 to 603 K at 17.5 MPa. A two-dimensional cubic-spline representation of C’,,, 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- ’ LiCl was prepared from Fisher certified LiCl ( co.06 mass per cent of impurities excluding water). The actual molality was determined by titration with AgNO,. Other solutions were prepared by mass dilution of the stock solution. Concentrations were checked by density measurements on a Sodev OID densimeter. All molalities calculated from densities of Vaslow’i4’ agreed with literature values within 0.1 per cent. ” Present address: E. I. duPont de Nemours. Inc., Experimental U.S.A. ’ To whom correspondence should be addressed. 0071-9614/87/101037+09
SO2.00/0
Station,
(_‘, 1987 Academic
Wilmington,
Delaware
Press Inc. (London)
19898.
Limited
1038
D. E. WIlITE.
J. A. GATES.
AND
K. tt.
WOOD
The high-temperature flow heat-capacity calorimeter has been described in dctait previously. “’ For low-temperature measurements ( < 325 K) a cooling jacket was installed on the vacuum can to facilitate temperature control. The calorimctcr was operated at a water how rate of 0.033 cm’. s l and with heater power of 0.31 W resulting in temperature rises of 1.1 to 1.8 K. The reported temperatures are the average 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). A minimum of 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 of the sample solution at constant pressure cp is then calculated by the equation: c,/c;
= { 1 -,ws
- P,)lP,)
(PwlPJ.
(1)
where cp is the specific heat capacity of the solution, ( 8: 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 pw 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 factor,f‘was calculated at each temperature by using 3.0 mol. kg- ’ NaCl as a standard.‘15’ The solution densities used were those of Gates and Wood.‘16’ The densities of H,O were obtained from the equation of state of Haar, Gallagher, and Ke11.‘r7’ The apparent molar heat capacity C,., can be calculated from the specific heat capacity ratio c,/cf by using the equation: C p,. = (M2+m-‘)(c,/c,*)--m-‘c,*.
(2)
where M, is the molar mass of the salt and m is the molality. Fortier, Benson, and Picker (l*) 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 with aqueous salt solutions (m < 5.0 mol. kg- ‘). As a check far this error, the sample loop was loaded with water, followed by 2.0 cm3 of 2.9706 mol. kg-’ LiCl. At equilibrium, and before the LiCl arrives at the heater, we measured the heat-capacity ratio of waterto-water with two water-to-LiCl(aq) interfaces in the sample loop. The AP/P measured (AP/P = 0.0005) should be twice the effect of one water-to-LiCl(aq) interface. The effects of interfacial mixing (AP/P = 0.00025) were negligible at 3 mol. kg-’ compared with the chemical effects (APjP = 0.06 to 0.21 from 306 to 603 K). These effects should be even smaller at lower molalities.
3. Results The results of the heat-capacity measurements on LiCl(aq) are given in table 1. together with estimates of the accuracy of the individual measurements. The
HEAT TABLE
I. Apparent
T;‘K = 306.56 0.0502 0.0502 0.0502 0.0996 0.0996 0.0996 0.2504 0.2504 0.2504 0.5009 0.5009
0.0987 0.9985 0.9988 0.9973 0.9972 0.9972 0.9932 0.9932 0.9934 0.9869 0.9869
0.9974 0.9973 0.997s 0.9949 0.9948 0.9948 0.9873 0.9872 0.9875 0.9753 0.9724
- 35.32 -46.18 -27.81 - 39.25 -42.19 -40.93 - 37.03 - 37.87 ~ 33.33 - 32.9’ - 32.25
0.0502 0.0502 0.0502
0.9983 0.9985 0.9984
0.9971 0.9972 0.9972
-66.83 - 53.49 - 55.99
0.0502 0.0502 0.0502
0.9988 0.9985 0.9988
0.9975 0.9972 0.9975
- 3 1.84 ~ 58.74 - 29.23
0.11504 0.2504 0.2504 0.5009 o.sOlI9 0.5009 I .WlO 1.OOIO
0.9936 0.9934 0.9934 0.9881 0.9875 0.9876 0.9759 0.9760
0.9874 0.9872 0.9872 0.9761 0.9755 0.9756 0.9530 0.953 1
- 34.30 - 38.49 - 37.79 -26.35 -31.61 - 30.74 -27.13 - 26.73
0.0502 0.0502 0.0502 0.0996 0.0996 0.0996 0.2504 0.2504 0.2504 0.5009 O.WY
0.9983 0.9984 0.9988 0.9967 0.9978 0.9970 0.9932 0.9932 0.993 I 0.9869 0.9872
0.9970 0.9970 0.9976 0.994 I 0.9953 0.9945 0.9869 0.9869 0.9868 0.9746 0.9749
- 70.76 - 69.26 - 26.57 - 69.05 -21.43 -55.23 - 43.46 - 43.09 -44.69 -38.82 - 36.34
1 .OOlO I.0010 1.0010 I .OOlO
0.975’ 0.9755 0.9750 0.9756
0.95 I6 0.9518 0.9513 0.9520
- 33.41 - 32.39 ~ 34.49 -31.74
T/K
T/K
T/K
TiK
T/K
CAPACITY molar
pIMPa
9.73 9.46 9.51 = 324.32 9.96 10.50 9.91 = 324.38 3.80 3.88 3.87 2.88 2.98 2.97 2.53 2.52 = 350.06
piMPa 23.04 9.70 12.20 p.!MPa - 13.01 13.89 ~ 15.61 p.iMPa -2.98 1.21 0.52 -6.14 -0.87 -1.75 0.44 0.04 piMPa
12.08 18.91 12.05 17.40 11.20 -25.29 7.53 20.57 6.57 -27.05 7.25 6.75 4.26 1.15 4.25 0.78 4.28 2.38 3.27 2.64 _3 .--7’ 0.15
=
350.27
p.‘MPa
2.70 2.68 2.72 2.67
4.67 3.66 5.76 3.01
= 17.24 0.5009 1.0010 1.0010 1.0010 2.0153 2.0153 2.0153 2.9706 2.9706 2.9706
= 17.58 0.0996 0.0996
= 17.20 0.0996 0.0996 0.0996 = 17.27 1.0010 2.0153 2.0153 2.0153 2.9706 2.9706 2.9706
= 17.79 0.5009 I.0010 I.0010 I .OOlO 2.0153 2.0153 2.0153 2.9706 2.9706 2.9706 2.9706 17.75 2.0153 2.0153 2.0153 2.9706
1039
LiCl(aq)
heat capacity
9.11 -8.44 9.32 2.41 8.96 - 15.95 5.78 -2.06 5.84 0.89 5.82 -0.38 3.67 0.10 3.68 0.94 3.59 -3.60 2.92 0.22 2.90 -0.45 = 307.78
OF
C,.,
t’=
or LiCl(aq)
1.01 I d
0.9868 0.9746 0.9746 0.9747 0.9520 0.9522 0.9522 0.9327 0.9328 0.9328
0.9753 0.9526 0.9526 0.9527 0.9114 0.9115 0.9116 0.8771 0.8772 0.8772
_ 33.26 -28.70 -28.87 -28.23 - 22.08 -21.80 -21.63 - 17.37 -17.15 - 17.19
2.92 2.51 2.52 2.51 2.25 2.25 2.24 2.13 2.13 2.13
0.56 0.99 1.17 0.53 0.14 -0.14 -0.32 -0.94 1.16 I.1 I
0.9950 0.9947
_ 32.76 -44.1 I
5.65 5.8X
-X.56 11.80
0.9946 0.9950 0.9956
-48.12 - 33.24 -8.79
6.43 6.13 5.63
5.99 ~ x.x9 ’
0.9528 0.9121 0.9122 0.9121 0.8781 0.8785 0.8785
-28.06 -20.53 -20.30 - 20.44 - 15.74 - 15.19 -- 15.24
2.55 2.25 2.24 7.24 2.12 2.1 I 7 II
1.37 0.78 0.55 0.69 0.49 - 0.05 -0.01
0.9751 0.9521 0.9523 0.9522 0.9137 0.9138 0.9138 0.8778 0.8797 0.8798 0.8796
-34.51 -31.01 -30.10 - 30.87 - 17.05 - 16.75 - 16.71 - 16.31 - 13.37 - 13.21 - 13.48
3.1x 2.68 2.67 2.68 ’ ‘I -.-2.21 2 71 2.16 2.10 2.10 2.10
- I .6X ? 3’ -._.. 1.41 2.17 ~-2.56 - 2.86 - 2.90 2.65 -0.30 -0.45 -0.1x
-
2.27 2.27 2.24 2 13
0.82 1.07 - 0.76 1.72
/ = 1.010” 0.9Y74 0.9971
/‘=
1.050”
0.9972 0.9975 0.9981 / = l.OSO* 0.9757 0.9545 0.9546 0.9545 0.9363 0.9366 0.9366
f’-
1.067’
0.9874 0.9755 0.9757 0.9755 0.9567 0.9569 0.9569 0.9369 0.9387 0.9388 0.9387 f’=
I.081 J
0.9558 0.9557 0.9565 0.9383
0.9122 0.9120 0.9129 0.8784
20.45 20.70 18.87 15.39
1040
D. E. WHITE.
J. A. GATES. TABLE
T/K 0.0502 0.0502 0.0502 0.0996 0.0996 0.0996 0.2504 0.2504 0.2504 0.5009 0.5009
0.9980 0.9982 0.9983 0.9968 0.9968 0.9963 0.9925 0.9921 0.9919 0.9846 0.9847
0.9966 0.9968 0.9969 0.9942 0.9942 0.9936 0.9859 0.9855 0.9853 0.9718 0.9719
- 109.19 -91.65 - 83.34 - 69.42 - 69.42 -95.04 - 60.67 -67.73 - 72.38 - 64.02 -62.91
0.0502 0.0502 0.0502 0.0502
0.9980 0.9980 0.9987 0.9967
0.9967 0.9967 0.9974 0.9953
-99.97 -97.38 -40.98 -214.64
0:5009 0.5009
0.9804 0.9804
0.9675 0.9675
- 103.37 - 103.37
0.0502 0.0502 0.0502
0.9978 0.9975 0.9979
0.9964 0.9960 0.9965
- 129.55 - 158.43 -116.51
0.0996 0.0996 0.0996 0.2504 0.2504
0.9956 0.9949 0.9957 0.9895 0.9892
0.9929 0.9922 0.9930 0.9829 0.9826
- 126.17 - 157.43 - 121.97 - 115.46 -120.11
1.0010 1.0010 1.0010 2.0153 2.0153
0.9647 0.9647 0.9645 0.9400 0.9402
0.9405 0.9405 0.9402 0.8959 0.8961
-84.81 -84.67 -85.91 -59.19 -58.76
0.0502
0.9974 0.9974 0.9967 0.9942 0.9945 0.9942 0.9865 0.9865 0.9867 0.9159 0.9762
0.9956 0.9956 0.9947 0.9906 0.9908 0.9906 0.9776 0.9777 0.9179 0.9592 0.9596
-206.17 -206.17 - 284.56 -239.14 -226.71 -239.14 -217.22 -216.39 -213.11 - 185.26 - 181.17
T/K
18.97 18.62 18.45 10.63 10.63 11.14 5.85 5.99 6.09 4.41 4.39 = 401.07 18.31 18.26 17.13 20.61
T/K
T/K
T/K
T/K
T/K
0.0502 0.0996 0.0996 0.0996 0.2504 0.2504 0.2504 0.5009 0.5009
= 405.15
= 450.10 5.68 5.68 = 450.04 23.74 24.32 23.48 = 450.15
p/MPa 15.10 -2.44 - 10.75 - 18.87 - 18.87 6.75 - 16.65 -9.58 -4.94 -2.31 -3.43 p/MPa 9.56 6.96 v ” p/MPa 1.83 1.83 p/MPa -2.70 26.18 ~ 15.75
AND
I ~wtrtinurd
= 17.75 0.5009 1.0010 1.0010 1.0010 2.0153 2.0153 2.0153 2.9706 2.9706 2.9706 = 17.48 2.9706 2.9706 2.9706 = 17.65 0.0502 0.0502 = 17.51 0.0996 0.0996
p/MPa
= 17.41
0.28 31.54 -3.92 I.1 1 5.76
0.2504 0.5009 0.5009 0.5009 1.0010
= 449.89
p/MPa
= 17.34
4.36 4.35 4.38 3.39 3.39
1.37 1.22 2.46 1.20 0.76
13.91 14.54 13.83 7.83 7.92
= 500.97 30.77 30.77 32.34 19.06 18.81 19.06 11.06 11.05 10.98 7.94 7.86
p/MPa -45.78 -45.78 32.60 1.64 - 10.79 1.64 4.51 3.68 0.40 - 1.63 -- 5.71
R. H. WOOD
2.0153 2.9706 2.9706 2.9706 = 17.41 0.5009 1.0010 1.0010 1.0010 2.0153 2.0153 2.0153 2.9706 2.9706 2.9706
,f’= 1.096’ 0.9845 0.9718 0.9717 0.9718 0.9500 0.9495 0.9505 0.9336 0.9337 0.9333 f’=
4.44 3.44 3.45 3.44 2.78 2.81 2.76 2.47 2.46 2.48
-0.95 -0.94 -0.42 -0.80 -0.03 1.04 - 1.30 -0.51 -0.73 -0.13
0.8744 0.8748 0.8746
-21.98 -21.36 -21.71
2.40 2.39 2.39
-2.09 -2.71 -2.36
1.081 d
0.9976 0.9977 .f=
- 65.39 -51.87 - 52.39 - 52.01 - 36.22 -37.30 - 34.96 -24.83 - 24.61 -25.21
l.064d
0.9333 0.9337 0.9335 f‘=
0.9716 0.9475 0.9474 0.9475 0.9054 0.9049 0.9059 0.8727 0.8728 0.8724
0.9962 0.9963
- 140.80 - 132.41
23.98 23.81
8.49 0.09
0.9930 0.9929
- 121.09 - 128.14
13.88 14.02
-4.69 2.36
0.9824 0.9678 0.9668 0.9672 0.9407
-
123.46 100.63 109.33 105.87 -83.63
7.99 5.61 5.78 5.71 4.33
9.11 -0.95 1.74 4.28 -0.03
- 58.30 -40.79 - 39.86 -42.00
3.38 2.90 2.88 2.93
0.30 1.18 0.25 2.40
186.90 149.60 148.17 147.15 108.16 107.09 107.49 - 77.98 -78.91 -78.97
7.98 6.01 5.98 5.96 4.60 4.58 4.59 3.83 3.85 3.85
0.01 ~ 3.40 -4.83 -5.85 -0.02 - 1.09 -0.69 0.90 1.84 I .89
l.080d
0.9957 0.9956 ,f‘= l.072d 0.9890 0.9805 0.9796 0.9800 0.9647 ,f=
1.079’
0.9404 0.9233 0.9239 0.9226 ,f‘=
0.8963 0.8633 0.8639 0.8625
1.226“
0.9757 0.9582 0.9585 0.9587 0.9312 0.9316 0.9314 0.9148 0.9144 0.9143
0.9590 0.9277 0.9280 0.9282 0.8771 0.8775 0.8774 0.8429 0.8423 0.8423
-
HEAT
CAPACITY TABLE
5 c;
a
m molkg-‘P,
PS
c P.4 J-K-‘,mol-’
0.0502 0.0502 0.0502 0.0996 0.0996 0.0996 0.2504 0.2504 0.2504 0.5009 0.5009
0.9942 0.9940 0.9933 0.9896 0.9891 0.9887 0.9778 0.9784 0.9778 0.9614 0.9618
0.9913 0.9911 0.9903 0.9843 0.9836 0.9831 0.9657 0.9666 0.9658 0.9395 0.9400
T/K -653.00 -673.51 -761.95 - 582.85 -613.88 -641.68 -480.34 -463.83 -479.26 -405.97 -400.53
= 551.84 57.19 57.60 59.37 34.84 35.46 36.01 19.98 19.65 19.96 14.28 14.17
0.9905 0.9916 0.9915 0.9844 0.9847 0.9847 0.9684 0.9679 0.9679 0.9462 0.9454
0.9859 0.9875 0.9873 0.9766 0.9769 0.9769 0.9516 0.9509 0.9510 0.9165 0.9154
T/K - 1315.47 - 1141.01 - 1160.46 - 1065.56 -1046.09 -1046.09 -842.29 -857.53 -855.73 - 704.06 -716.21
= 577.92
0.0502 0.0502 0.0502 0.0996 0.0996 0.0996 0.2504 0.2504 0.2504 0.5009 0.5009
T/K
= 602.72
0.0502 0.0502 0.0502 0.0996 0.0996 0.0996 0.2504 0.2504 0.2504 0.5009 0.5009
0.9871 0.9873 0.9871 0.9771 0.9772 0.9780 0.9522 0.9499 0.9507 0.9204 0.9199
0.9803 0.9805 0.9802 0.9648 0.9649 0.9661 0.9260 0.9227 0.9237 0.8756 0.8748
-2268.93 -2244.82 -2281.92 -2024.77 -2018.22 -1942.41 -1661.84 - 1748.45 -1721.20 -1369.53 -1380.03
66
81.77 78.28 78.67 50.30 49.91 49.91 29.65 29.95 29.92 21.56 21.80
122.88 122.40 123.14 80.78 80.65 79.14 50.77 52.50 51.96 37.43 37.64
1041
LiCl(aq)
l-continued
A’
p/MPa 22.18 42.69 2148 33.51 e -8.77 -25.28 -9.86 -0.01 -5.45 p/MPa ’ - 14.46 4.99 11.76 -7.72 - 7.72 -31.71 - 16.41 - 18.26 -8.90 3.26 p/MPa 16.83 -7.28 29.82 -21.82 -28.37 e - 39.64 46.97 19.72 - 19.53 -9.03
OF
m ~ mol.kg’ = 17.46 0.5009 1.0010 1.0010 1.0010 2.0153 2.0153 2.0153 2.9706 2.9706 2.9706
-PS P, .f=
c P. 0 J,K-‘.mol-’
u
A’
1.283“
0.9614 0.9356 0.9354 0.9354 0.8992 0.8997 0.9003 0.8782 0.8778 0.8789
= 17.41 0.5009 1.0010 1.0010 1.0010 2.0153 2.0153 2.0153 2.9706 2.9706 2.9706
.f =
= 17.55
/‘=
0.5009 1.0010 1.0010 1.0010 2.0153 2.0153 2.0153 2.9706 2.9706 2.9706
5 c;
1.353 0.9463 0.9116 0.9120 0.9113 0.8686 0.8682 0.8686 0.8431 0.8427 0.8426
0.9395 0.8969 0.8966 0.8967 0.8340 0.8346 0.8353 0.7940 0.7936 0.7949
-405.19 -325.33 - 326.96 -326.64 -235.64 - 234.01 - 232.09 - 178.76 - 179.63 -177.11
14.27 10.59 10.62 10.62 7.78 7.75 7.71 6.34 6.36 6.31
-0.79 8.10 9.73 9.40 4.75 3.12 1.20 -5.15 - 4.28 -6.80
d 0.9166 0.8607 0.8613 0.8604 0.7876 0.7870 0.7876 0.7414 0.7408 0.7407
-702.11 - 564.84 -561.58 - 566.66 -396.37 - 397.95 -396.18 - 306.20 -307.37 - 307.53
21.52 - 10.85 16.14 19.04 16.07 15.78 16.18 20.86 I 1.48 4.28 Il.51 5.85 I 1.48 4.09 9.29 -- 7.32 9.31 -6.15 9.32 - 5.99
0.8726 0.8023 0.8025 0.8031 0.7117 0.7123 0.7128 0.6614 0.6614 0.6604
-1409.84 -1060.09 -1058.95 -1054.41 - 732.04 - 729.78 -728.15 -557.27 - 557.27 - 559.83
1.435*
0.9183 0.8750 0.8751 0.8756 0.8209 0.8214 0.8217 0.7929 0.7929 0.7921
38.24 27.53 27.51 27.41 19.14 19.09 19.06 15.09 15.09 15.15
20.79 4.17 3.03 - 1.52 -0.53 ~~ 2.79 -4.42 0.22 0.22 2.78
’ The apparent molar heat capacity C,, was calculated from equations (1) and (2). h 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 absolute errors estimated from the experimental sensitivity at each temperature. The absolute error estimates varied from +O.OOOl to +0.0005. ‘ A is the value of [C, +(calc.) - C,, ,+}/(J K - t mol - ‘), The calculated value is from a cubic-spline interpolation of the knots in table 2. d The value of the heat-loss correction factorjwas calculated using the heat capacity of 3.005 mol. kg 1 NaCl as a standard.‘3.15’ The measured values of APjP for 3.005 mol. kg-’ NaCl at the experimental pressure were -0.04828 at 306.56 K, -0.04830 at 307.78 K, -0.04733 at 324.32 K. -0.04734 at 324.38 K, -0.04893 at 350.06 K, ~-0.04833 at 350.27 K, -0.05897 at 405.15 K, -0.05961 at 401.07 K, -0.07411 at 450.10 K. -0.07488 at 450.04 K, -0.07481 at 450.15 K, -0.07426 at 449.89 K. -0.08671 at 500.97 K. -0.12465 at 551.84 K, -0.16077 at 577.92 K. and -0.21096 at 602.72 K.
1042
D. E. WHITE,
J. A. GATES.
AND
R. H. WOOD
apparent molar heat capacities were fitted by the multi-dimensional cubic-splint method described previously. ‘3.19’ The experimental pressure varied between 17.2 and 17.8 MPa. These small variations in pressure have been ignored in the representation of the results. This isobaric assumption introduces an increase of less than 10 per cent in the estimated uncertainties. The knot positions and fitted 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,.,/(J K - ’ . mol- ‘) as a function of (m/m”)1i2 with mu = 1 mol. kg-‘, labeled A,, have been included in table 2. These have been calculated using Haar, Gallagher, and Kelps equation of state for water’r7’ with Uematsu and Franck’s equation for the dielectric properties of water.‘*” As with the C,,, surfaces presented previously,‘3-6’ the LiCl surface required three m ‘I2 knots placed at 0, 0.4, and 1.75 mol. kg- ’ and six temperature TABLE
2. LiCl
knot
positions,
knot
values,
T/K:
298.15
350.00
A,:
35.15
47.88
-50.58 - 39.33 - 19.70
-61.41 -45.54 -13.15
and DebyeHuckel
slopes A, for calculating
425.00
C,,,
of LiCl(aq)
550.00
575.00
603.00
559.45
1116.19
3730.03
-735.13 - 520.08 - 114.42
- 1305.77 ~ 889.47 - 286.08
- 2944.50 ~ 1891.58 - 545.51
p = 17.5 MPa
(m/(mol
kg
81.24
l))‘/*
C,,S/(J.kgm’,molF’)
0 0.4000 1.7500
- 128.72 -99.40 - 30.40
’ This fit is a representation of 216 points. The sum of the squares of the residuals a standard error of the fit of 12.3 J. Km ’ mol- I. The minimum sum of the squares
TABLE m/(mol.
3. Apparent kg-‘)
molar 0
heat capacity 0.100
of LiCl
0.250
from 0.500
298.15
to 598.15 1.ooo
K at 17.50 MPa Loo0
3.000
~ 23.28 - 22.52 -21.09 - 19.95 ~ 19.27 - 19.25 ~ 20.08 - 21.82 -24.31 - 33.43 -44.74 -57.31 - 75.32 - 104.49 - 150.59 -219.36 - 347.90 -665.70
- 19.88 - 18.88 - 16.96 -. 15.30 - 14.08 ~ 13.47 - 13.64 ~ 14.66 - 16.40 -22.89 ~ 30.65 - 38.46 ~ 50.54 - 72.80 --Ill.16 -171.52 ~~277.60 ~ 503.53
C,,+,/(J.K~‘.molJ’)
T/K 298.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15 398.15 423.15 448.15 473.15 498.15 523.15 548.15 573.15 598.15
C,,,
is 30000 resulting in for this set is 17700.
- 50.58 - 50.86 -51.58 - 52.82 - 54.93 - 58.26 -63.14 - 69.68 - 77.60 - 101.39 - 126.90 - 153.20 - 199.42 - 290.96 -453.19 -711.50 - 1234.89 -2617.30
-41.31 -41.29 -41.40 -42.00 -43.39 -45.90 - 49.84 -55.31 - 62.03 - 82.22 - 103.37 - 123.87 - 158.39 -226.71 - 348.58 -543.77 -919.96 - 1841.73
-37.14 - 37.01 ~ 36.90 - 37.20 - 38.22 -40.22 -43.48 -48.1 I - 53.88 -71.80 -91.73 - 112.41 - 144.84 -203.79 - 304.09 -460.52 ~ 764.33 -1531.93
-33.13 - 32.87 - 32.48 - 32.46 - 33.07 ~ 34.54 -37.14 -40.94 - 45.80 -61.39 -79.71 - 99.75 - 129.46 - 179.56 - 260.77 -383.82 -624.33 -1250.50
~ 28.46 - 28.01 - 27.20 -26.72 -26.78 - 27.59 - 29.37 - 32.20 - 35.98 - 48.66 -64.30 ~ 82.05 - 107.28 - 147.30 - 209.40 - 300.90 -479.20 -951.11
HEAT
CAPACITY
OF
1043
LiCI(aq)
knots placed at 298.15, 350.00, 425,00, 500.00, 575.00, and 603.00 K. The surface was extended to 298.15 K using the measurements of Fortier, Leduc, and Desnoyers’21) corrected to 17.5 MPa using the pressure dependence of C,., of NaCl(aq).‘22’ There were a total of 217 points, of which 7 were eliminated (see table 1) because they were not in reasonable agreement with the other results. The fit of the remaining 210 points (and 6 additional points at 298.15 K)“” to the cubic-spline surface resulted in a sum of the squares of the residuals of 30000 and a standard error of 12.3 J. K- ’ . 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 = 30000) with the sum of the squares of the residuals for a surface which passed through the average of each duplicate set of results (s = 17700). 4. Discussion There are no other high-temperature heat capacities available in the literature for LiCl(aq). The heat capacities presented herein complete a series for the alkali-metal halides (LiCl, NaCl, KCl. and NaBr). At lower temperatures, between 298 and 373 K at 17.5 MPa, there may be real differences between the shapes of the C,,, surfaces. At infinite dilution the LiCl and NaBr surfaces do not have the maximum in Cc,, observed for both the NaCl and KC1 surfaces as a function of temperature but as the molalities increase maxima occur in C,,, for all of these aqueous salts. At low pressures, maxima are typically found for C’z, of aqueous l-l electrolytes between 300 and 400 K.(23-2s’ It is quite possible that more accurate experiments will show that there are maxima in C’z, for LiCl(aq) and NaBr(aq) in this temperature range since the present results show only very small decreases in C& from 298 to 340 K. It is also possible that these salts would have maxima if either the temperature or the pressure were lowered. A comparison of the molality dependence given in table 4 shows that the TABLE
4. Values
T,‘K 298. I5 373.15 473.15 573.15 598.15
of {(C’,+(3.0
kg- ’ )
m/(mol 0 0.5 0 0.5 0 0.5 0 0.5 0 0.5
mol.
kg-I)-C,,+(m,)}/(J. 17.1 MPa
K--’
‘mol-‘1
for
some
I-1
salts
at about
LiCl
NaCl
KCI
NaBr
21 13 61 29 149 19 951 347 2110 141
89 53 55 36 148 82 x00 330 1850 690
55 38 57 31 I46 6X 770 321 2030 701
72 53 6X 35 149 X6 1160 426 2170 781
1044
D. E. WHITE. J. A. GATES, AND R. H. WOOD
differences in values of (C,,,(m,) -Cp,+(m,)) for the four salts increases with temperature but the fractional differences decrease. The differences at the higher temperatures are only slightly larger than our estimates of the experimental errors. In previous papers’5*6’ we have noted the similarity of Cz, for aqueous NaCI, KCI, and NaBr. As expected, the present results for C;, of LiCl are similar to those for the other three salts at the higher temperatures. There still are real differences between these 1- 1 salts but the fractional differences between both Czd and {C~+(Q) - CF,(m,)} decrease with increasing temperature. These similarities should be very useful in estimating the properties of other 1-l salts at high temperatures. Helgeson, Kirkham, and Flowers(23’ and recently Tanger and Helgeson’24’ have published predictive equations for the standard partial molar properties of electrolytes. A comparison of Helgeson, Kirkham, and Flower’s surface with the extrapolation of our heat-capacity surface to m = 0 shows excellent agreement below 573.15 K. Above 573.15 K the predicted values tend to be too negative although the qualitative shape of the curve is correct. Tanger and Helgeson’24’ have improved upon Helgeson et al.‘23’ using many of the recent higher-temperature values (including the present results). The agreement of this improved surface and our results is excellent. A more thorough discussion is included in Tanger and Helgeson’s paper. In view of the similarities in the molality dependence of C,,, it seemed very unusual that the relative apparent molar enthalpy of LiCl(aq) measured earlier in this laboratory’26’ is so different from that of other l-l salts. At high molalities L, of LiCl decreases between 373 and 423 K rather than increasing like the other salts. Holmes and Mesmer’27’ found that the L, measurements above 373.15 K were not consistent with their high-temperature isopiestic measurements on LiCl(aq) and that a steadily increasing L, with temperature was necessary to fit their results. If we neglect the large pressure difference between the L, and C,, measurements (< 2 MPa compared with 17.5 MPa) we can calculate {ALb(T2)-AL,+,(T1)} where AL, = {L,(3.0 mol. kg-‘) - L,(O.5 mol. kg- I)>. The two sets of results give good agreement for LiCl between 298.15 and 373.15 K and no agreement above 373.15 K. In contrast, a check calculation using results for NaCl gave good agreement at all temperatures. We conclude that the enthalpy of dilution results of Mayrath and Wood’26’ are in error at 423 and 473 K. Since other results run at the same time have proved reliable we suspect an error in the preparation of the LiCl solutions used above 373 K. 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. The authors thank Mark A. Ryan, David M. Tillet, and Anne L. Doberstein for help with the experimental measurements. REFERENCES 1. Smith-Magowan. 2. Smith-Magowan,
1981, 13, 1047. D.; Wood, R. H. J. Chem. Thermodynamics D.: Wood, R. H.: Tillett, D. M. J. Chem. Eng. Data 1982, 27, 235.
HEAT CAPACITY
OF LiCl(aq)
1045
3. Gates. J. A.: Tillett. D. M.: White. D. E.: Wood. R. H. J. Chem. Thermodvnamics 1987. 19. 131. 4. White. D. E.: Doberstein. A. L.; Gates. J. A.; Tillett, D. M.; Wood, R. H. j. Chem. Theimodvnamics 1987, 19, 251.
5. White, D. E.: Gates, J. A.; Wood. R. H. J. Chem. Thermo&namics 1987, 19. 493. 6. White. D. E.; Ryan, M. A.; Armstrong, M. V. C.; Gates, J. A.; Wood. R. H. J. Chem. Thermodynamics 1987, 19, 1023. 7. Wood, R. H.; Quint, J. R.; Grolier, J.-P. J. Phys. Chem. 1981, 85, 3944. 8. Wood, R. H.; Quint, J. R. J. Chem. Thermod.vnamics 1982, 14, 1069. 9. Wheeler, J. C. Ber. Bunsenges. Physik. Chem. 1972, 76, 308. IO. Gates, J. A.: Wood, R. H.; Quint, J. R. J. Phvs. Chem. 1982, 86. 4948. II. Helgeson, H. C.; Kirkham, D. H. Abstracts c>fpapers, 174th meeting. American Chemical Society: New Orleans, LA: March 1977. 12. Cobble, J. W.; Murray, R. C., Jr. Discuss. Furaday Sot. 1977, 64, 144. 13. Chang, R. F.; Morrison, G.; Levelt-Sengers, J. M. H. J. Phys. Chem. 19&(, 88, 3389. 14. Vaslow, F. J. Phys. Chem. 1966, 70, 2286. 15. White, D. E.; Wood, R. H. J. Solution Chom. 1982, I I. 223. 16. Gates, J. A.; Wood, R. H. J. Chem. Eng. Data 1985, 30. 44. 17. Haar. L.; Gallagher, J. S.; Kell. G. S. NBS/NRC Steam Tables. Hemisphere Publishing Corp.: Washington, DC. 1984. 18. Fortier, J.-L.; Benson, G. C.; Picker, P. J. Chem. Thermodynamics 1976, 8, 289. 19. Gates, J. A. Ph.D. dissertation, University of Delaware. January 1985. 20. Uematsu, M.; Franck, E. U. J. Phys. Chem. Ref. Dafa 1980,9, 1291. 21. Fortier, J.-L.; Leduc, P.-A.; Desnoyers, J. E. J. So&ion Chem. 1974, 3. 323. 22. Rogers, P. S. Z.; Pitzer, K. S. J. Phys. Chem. Ref. Data 1982, Il. 15. 23. Helneson. H. C.: Kirkham. D. H.: Flowers. G. C. Am. J. Sci. 1981., 281. 1249 24. Tanger, J. C., IV; Helgeson, H. C. Am. J. Sri., in press, 25. Saluja, P. P. S.; Pitzer, K. S.; Phutela, R. C. Can. J. Chem. 1986, 64, 1328. 26. Mayrath, J. E.; Wood, R. H. J. Chem. Thermodynamics 1982, 14, 15. 17. Holmes. H. F.; Mesmer. R. F. J. Phys. Chem. 1983, 87. 1242.
Heat capacities of aqueous to 603 K at 17.5 MPa DOROTHY
E. WHITE,
JEFFREY
A. GATES,”
LiCl from and ROBERT
306
H. WOOD
h
Department of Chemistry, University qf Delaware. Newark, Delaware 19716, U.S.A. I Received II December 1986: in jinal,fortn
19 Februar!, 1987)
A differential flow heat-capacity calorimeter has been used to measure the heat capacity of LiCl(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 molahties found previously for NaCl(aq). NaBr(aq). and KCl(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.“-“’ Very large and negative values of the apparent molar heat capacity C,, have been found for aqueous NaCl,“*3) KU,‘@ NaBr,“’ and CaC1,.‘4’ 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.“.‘-13’ There continues to be a need for 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 boilers. In this paper we report C,,, of LiCl(aq) from 0.05 to 3.0 mol. kg- ’ and 306 to 603 K at 17.5 MPa. A two-dimensional cubic-spline representation of C’,,, 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- ’ LiCl was prepared from Fisher certified LiCl ( co.06 mass per cent of impurities excluding water). The actual molality was determined by titration with AgNO,. Other solutions were prepared by mass dilution of the stock solution. Concentrations were checked by density measurements on a Sodev OID densimeter. All molalities calculated from densities of Vaslow’i4’ agreed with literature values within 0.1 per cent. ” Present address: E. I. duPont de Nemours. Inc., Experimental U.S.A. ’ To whom correspondence should be addressed. 0071-9614/87/101037+09
SO2.00/0
Station,
(_‘, 1987 Academic
Wilmington,
Delaware
Press Inc. (London)
19898.
Limited
1038
D. E. WIlITE.
J. A. GATES.
AND
K. tt.
WOOD
The high-temperature flow heat-capacity calorimeter has been described in dctait previously. “’ For low-temperature measurements ( < 325 K) a cooling jacket was installed on the vacuum can to facilitate temperature control. The calorimctcr was operated at a water how rate of 0.033 cm’. s l and with heater power of 0.31 W resulting in temperature rises of 1.1 to 1.8 K. The reported temperatures are the average 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). A minimum of 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 of the sample solution at constant pressure cp is then calculated by the equation: c,/c;
= { 1 -,ws
- P,)lP,)
(PwlPJ.
(1)
where cp is the specific heat capacity of the solution, ( 8: 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 pw 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 factor,f‘was calculated at each temperature by using 3.0 mol. kg- ’ NaCl as a standard.‘15’ The solution densities used were those of Gates and Wood.‘16’ The densities of H,O were obtained from the equation of state of Haar, Gallagher, and Ke11.‘r7’ The apparent molar heat capacity C,., can be calculated from the specific heat capacity ratio c,/cf by using the equation: C p,. = (M2+m-‘)(c,/c,*)--m-‘c,*.
(2)
where M, is the molar mass of the salt and m is the molality. Fortier, Benson, and Picker (l*) 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 with aqueous salt solutions (m < 5.0 mol. kg- ‘). As a check far this error, the sample loop was loaded with water, followed by 2.0 cm3 of 2.9706 mol. kg-’ LiCl. At equilibrium, and before the LiCl arrives at the heater, we measured the heat-capacity ratio of waterto-water with two water-to-LiCl(aq) interfaces in the sample loop. The AP/P measured (AP/P = 0.0005) should be twice the effect of one water-to-LiCl(aq) interface. The effects of interfacial mixing (AP/P = 0.00025) were negligible at 3 mol. kg-’ compared with the chemical effects (APjP = 0.06 to 0.21 from 306 to 603 K). These effects should be even smaller at lower molalities.
3. Results The results of the heat-capacity measurements on LiCl(aq) are given in table 1. together with estimates of the accuracy of the individual measurements. The
HEAT TABLE
I. Apparent
T;‘K = 306.56 0.0502 0.0502 0.0502 0.0996 0.0996 0.0996 0.2504 0.2504 0.2504 0.5009 0.5009
0.0987 0.9985 0.9988 0.9973 0.9972 0.9972 0.9932 0.9932 0.9934 0.9869 0.9869
0.9974 0.9973 0.997s 0.9949 0.9948 0.9948 0.9873 0.9872 0.9875 0.9753 0.9724
- 35.32 -46.18 -27.81 - 39.25 -42.19 -40.93 - 37.03 - 37.87 ~ 33.33 - 32.9’ - 32.25
0.0502 0.0502 0.0502
0.9983 0.9985 0.9984
0.9971 0.9972 0.9972
-66.83 - 53.49 - 55.99
0.0502 0.0502 0.0502
0.9988 0.9985 0.9988
0.9975 0.9972 0.9975
- 3 1.84 ~ 58.74 - 29.23
0.11504 0.2504 0.2504 0.5009 o.sOlI9 0.5009 I .WlO 1.OOIO
0.9936 0.9934 0.9934 0.9881 0.9875 0.9876 0.9759 0.9760
0.9874 0.9872 0.9872 0.9761 0.9755 0.9756 0.9530 0.953 1
- 34.30 - 38.49 - 37.79 -26.35 -31.61 - 30.74 -27.13 - 26.73
0.0502 0.0502 0.0502 0.0996 0.0996 0.0996 0.2504 0.2504 0.2504 0.5009 O.WY
0.9983 0.9984 0.9988 0.9967 0.9978 0.9970 0.9932 0.9932 0.993 I 0.9869 0.9872
0.9970 0.9970 0.9976 0.994 I 0.9953 0.9945 0.9869 0.9869 0.9868 0.9746 0.9749
- 70.76 - 69.26 - 26.57 - 69.05 -21.43 -55.23 - 43.46 - 43.09 -44.69 -38.82 - 36.34
1 .OOlO I.0010 1.0010 I .OOlO
0.975’ 0.9755 0.9750 0.9756
0.95 I6 0.9518 0.9513 0.9520
- 33.41 - 32.39 ~ 34.49 -31.74
T/K
T/K
T/K
TiK
T/K
CAPACITY molar
pIMPa
9.73 9.46 9.51 = 324.32 9.96 10.50 9.91 = 324.38 3.80 3.88 3.87 2.88 2.98 2.97 2.53 2.52 = 350.06
piMPa 23.04 9.70 12.20 p.!MPa - 13.01 13.89 ~ 15.61 p.iMPa -2.98 1.21 0.52 -6.14 -0.87 -1.75 0.44 0.04 piMPa
12.08 18.91 12.05 17.40 11.20 -25.29 7.53 20.57 6.57 -27.05 7.25 6.75 4.26 1.15 4.25 0.78 4.28 2.38 3.27 2.64 _3 .--7’ 0.15
=
350.27
p.‘MPa
2.70 2.68 2.72 2.67
4.67 3.66 5.76 3.01
= 17.24 0.5009 1.0010 1.0010 1.0010 2.0153 2.0153 2.0153 2.9706 2.9706 2.9706
= 17.58 0.0996 0.0996
= 17.20 0.0996 0.0996 0.0996 = 17.27 1.0010 2.0153 2.0153 2.0153 2.9706 2.9706 2.9706
= 17.79 0.5009 I.0010 I.0010 I .OOlO 2.0153 2.0153 2.0153 2.9706 2.9706 2.9706 2.9706 17.75 2.0153 2.0153 2.0153 2.9706
1039
LiCl(aq)
heat capacity
9.11 -8.44 9.32 2.41 8.96 - 15.95 5.78 -2.06 5.84 0.89 5.82 -0.38 3.67 0.10 3.68 0.94 3.59 -3.60 2.92 0.22 2.90 -0.45 = 307.78
OF
C,.,
t’=
or LiCl(aq)
1.01 I d
0.9868 0.9746 0.9746 0.9747 0.9520 0.9522 0.9522 0.9327 0.9328 0.9328
0.9753 0.9526 0.9526 0.9527 0.9114 0.9115 0.9116 0.8771 0.8772 0.8772
_ 33.26 -28.70 -28.87 -28.23 - 22.08 -21.80 -21.63 - 17.37 -17.15 - 17.19
2.92 2.51 2.52 2.51 2.25 2.25 2.24 2.13 2.13 2.13
0.56 0.99 1.17 0.53 0.14 -0.14 -0.32 -0.94 1.16 I.1 I
0.9950 0.9947
_ 32.76 -44.1 I
5.65 5.8X
-X.56 11.80
0.9946 0.9950 0.9956
-48.12 - 33.24 -8.79
6.43 6.13 5.63
5.99 ~ x.x9 ’
0.9528 0.9121 0.9122 0.9121 0.8781 0.8785 0.8785
-28.06 -20.53 -20.30 - 20.44 - 15.74 - 15.19 -- 15.24
2.55 2.25 2.24 7.24 2.12 2.1 I 7 II
1.37 0.78 0.55 0.69 0.49 - 0.05 -0.01
0.9751 0.9521 0.9523 0.9522 0.9137 0.9138 0.9138 0.8778 0.8797 0.8798 0.8796
-34.51 -31.01 -30.10 - 30.87 - 17.05 - 16.75 - 16.71 - 16.31 - 13.37 - 13.21 - 13.48
3.1x 2.68 2.67 2.68 ’ ‘I -.-2.21 2 71 2.16 2.10 2.10 2.10
- I .6X ? 3’ -._.. 1.41 2.17 ~-2.56 - 2.86 - 2.90 2.65 -0.30 -0.45 -0.1x
-
2.27 2.27 2.24 2 13
0.82 1.07 - 0.76 1.72
/ = 1.010” 0.9Y74 0.9971
/‘=
1.050”
0.9972 0.9975 0.9981 / = l.OSO* 0.9757 0.9545 0.9546 0.9545 0.9363 0.9366 0.9366
f’-
1.067’
0.9874 0.9755 0.9757 0.9755 0.9567 0.9569 0.9569 0.9369 0.9387 0.9388 0.9387 f’=
I.081 J
0.9558 0.9557 0.9565 0.9383
0.9122 0.9120 0.9129 0.8784
20.45 20.70 18.87 15.39
1040
D. E. WHITE.
J. A. GATES. TABLE
T/K 0.0502 0.0502 0.0502 0.0996 0.0996 0.0996 0.2504 0.2504 0.2504 0.5009 0.5009
0.9980 0.9982 0.9983 0.9968 0.9968 0.9963 0.9925 0.9921 0.9919 0.9846 0.9847
0.9966 0.9968 0.9969 0.9942 0.9942 0.9936 0.9859 0.9855 0.9853 0.9718 0.9719
- 109.19 -91.65 - 83.34 - 69.42 - 69.42 -95.04 - 60.67 -67.73 - 72.38 - 64.02 -62.91
0.0502 0.0502 0.0502 0.0502
0.9980 0.9980 0.9987 0.9967
0.9967 0.9967 0.9974 0.9953
-99.97 -97.38 -40.98 -214.64
0:5009 0.5009
0.9804 0.9804
0.9675 0.9675
- 103.37 - 103.37
0.0502 0.0502 0.0502
0.9978 0.9975 0.9979
0.9964 0.9960 0.9965
- 129.55 - 158.43 -116.51
0.0996 0.0996 0.0996 0.2504 0.2504
0.9956 0.9949 0.9957 0.9895 0.9892
0.9929 0.9922 0.9930 0.9829 0.9826
- 126.17 - 157.43 - 121.97 - 115.46 -120.11
1.0010 1.0010 1.0010 2.0153 2.0153
0.9647 0.9647 0.9645 0.9400 0.9402
0.9405 0.9405 0.9402 0.8959 0.8961
-84.81 -84.67 -85.91 -59.19 -58.76
0.0502
0.9974 0.9974 0.9967 0.9942 0.9945 0.9942 0.9865 0.9865 0.9867 0.9159 0.9762
0.9956 0.9956 0.9947 0.9906 0.9908 0.9906 0.9776 0.9777 0.9179 0.9592 0.9596
-206.17 -206.17 - 284.56 -239.14 -226.71 -239.14 -217.22 -216.39 -213.11 - 185.26 - 181.17
T/K
18.97 18.62 18.45 10.63 10.63 11.14 5.85 5.99 6.09 4.41 4.39 = 401.07 18.31 18.26 17.13 20.61
T/K
T/K
T/K
T/K
T/K
0.0502 0.0996 0.0996 0.0996 0.2504 0.2504 0.2504 0.5009 0.5009
= 405.15
= 450.10 5.68 5.68 = 450.04 23.74 24.32 23.48 = 450.15
p/MPa 15.10 -2.44 - 10.75 - 18.87 - 18.87 6.75 - 16.65 -9.58 -4.94 -2.31 -3.43 p/MPa 9.56 6.96 v ” p/MPa 1.83 1.83 p/MPa -2.70 26.18 ~ 15.75
AND
I ~wtrtinurd
= 17.75 0.5009 1.0010 1.0010 1.0010 2.0153 2.0153 2.0153 2.9706 2.9706 2.9706 = 17.48 2.9706 2.9706 2.9706 = 17.65 0.0502 0.0502 = 17.51 0.0996 0.0996
p/MPa
= 17.41
0.28 31.54 -3.92 I.1 1 5.76
0.2504 0.5009 0.5009 0.5009 1.0010
= 449.89
p/MPa
= 17.34
4.36 4.35 4.38 3.39 3.39
1.37 1.22 2.46 1.20 0.76
13.91 14.54 13.83 7.83 7.92
= 500.97 30.77 30.77 32.34 19.06 18.81 19.06 11.06 11.05 10.98 7.94 7.86
p/MPa -45.78 -45.78 32.60 1.64 - 10.79 1.64 4.51 3.68 0.40 - 1.63 -- 5.71
R. H. WOOD
2.0153 2.9706 2.9706 2.9706 = 17.41 0.5009 1.0010 1.0010 1.0010 2.0153 2.0153 2.0153 2.9706 2.9706 2.9706
,f’= 1.096’ 0.9845 0.9718 0.9717 0.9718 0.9500 0.9495 0.9505 0.9336 0.9337 0.9333 f’=
4.44 3.44 3.45 3.44 2.78 2.81 2.76 2.47 2.46 2.48
-0.95 -0.94 -0.42 -0.80 -0.03 1.04 - 1.30 -0.51 -0.73 -0.13
0.8744 0.8748 0.8746
-21.98 -21.36 -21.71
2.40 2.39 2.39
-2.09 -2.71 -2.36
1.081 d
0.9976 0.9977 .f=
- 65.39 -51.87 - 52.39 - 52.01 - 36.22 -37.30 - 34.96 -24.83 - 24.61 -25.21
l.064d
0.9333 0.9337 0.9335 f‘=
0.9716 0.9475 0.9474 0.9475 0.9054 0.9049 0.9059 0.8727 0.8728 0.8724
0.9962 0.9963
- 140.80 - 132.41
23.98 23.81
8.49 0.09
0.9930 0.9929
- 121.09 - 128.14
13.88 14.02
-4.69 2.36
0.9824 0.9678 0.9668 0.9672 0.9407
-
123.46 100.63 109.33 105.87 -83.63
7.99 5.61 5.78 5.71 4.33
9.11 -0.95 1.74 4.28 -0.03
- 58.30 -40.79 - 39.86 -42.00
3.38 2.90 2.88 2.93
0.30 1.18 0.25 2.40
186.90 149.60 148.17 147.15 108.16 107.09 107.49 - 77.98 -78.91 -78.97
7.98 6.01 5.98 5.96 4.60 4.58 4.59 3.83 3.85 3.85
0.01 ~ 3.40 -4.83 -5.85 -0.02 - 1.09 -0.69 0.90 1.84 I .89
l.080d
0.9957 0.9956 ,f‘= l.072d 0.9890 0.9805 0.9796 0.9800 0.9647 ,f=
1.079’
0.9404 0.9233 0.9239 0.9226 ,f‘=
0.8963 0.8633 0.8639 0.8625
1.226“
0.9757 0.9582 0.9585 0.9587 0.9312 0.9316 0.9314 0.9148 0.9144 0.9143
0.9590 0.9277 0.9280 0.9282 0.8771 0.8775 0.8774 0.8429 0.8423 0.8423
-
HEAT
CAPACITY TABLE
5 c;
a
m molkg-‘P,
PS
c P.4 J-K-‘,mol-’
0.0502 0.0502 0.0502 0.0996 0.0996 0.0996 0.2504 0.2504 0.2504 0.5009 0.5009
0.9942 0.9940 0.9933 0.9896 0.9891 0.9887 0.9778 0.9784 0.9778 0.9614 0.9618
0.9913 0.9911 0.9903 0.9843 0.9836 0.9831 0.9657 0.9666 0.9658 0.9395 0.9400
T/K -653.00 -673.51 -761.95 - 582.85 -613.88 -641.68 -480.34 -463.83 -479.26 -405.97 -400.53
= 551.84 57.19 57.60 59.37 34.84 35.46 36.01 19.98 19.65 19.96 14.28 14.17
0.9905 0.9916 0.9915 0.9844 0.9847 0.9847 0.9684 0.9679 0.9679 0.9462 0.9454
0.9859 0.9875 0.9873 0.9766 0.9769 0.9769 0.9516 0.9509 0.9510 0.9165 0.9154
T/K - 1315.47 - 1141.01 - 1160.46 - 1065.56 -1046.09 -1046.09 -842.29 -857.53 -855.73 - 704.06 -716.21
= 577.92
0.0502 0.0502 0.0502 0.0996 0.0996 0.0996 0.2504 0.2504 0.2504 0.5009 0.5009
T/K
= 602.72
0.0502 0.0502 0.0502 0.0996 0.0996 0.0996 0.2504 0.2504 0.2504 0.5009 0.5009
0.9871 0.9873 0.9871 0.9771 0.9772 0.9780 0.9522 0.9499 0.9507 0.9204 0.9199
0.9803 0.9805 0.9802 0.9648 0.9649 0.9661 0.9260 0.9227 0.9237 0.8756 0.8748
-2268.93 -2244.82 -2281.92 -2024.77 -2018.22 -1942.41 -1661.84 - 1748.45 -1721.20 -1369.53 -1380.03
66
81.77 78.28 78.67 50.30 49.91 49.91 29.65 29.95 29.92 21.56 21.80
122.88 122.40 123.14 80.78 80.65 79.14 50.77 52.50 51.96 37.43 37.64
1041
LiCl(aq)
l-continued
A’
p/MPa 22.18 42.69 2148 33.51 e -8.77 -25.28 -9.86 -0.01 -5.45 p/MPa ’ - 14.46 4.99 11.76 -7.72 - 7.72 -31.71 - 16.41 - 18.26 -8.90 3.26 p/MPa 16.83 -7.28 29.82 -21.82 -28.37 e - 39.64 46.97 19.72 - 19.53 -9.03
OF
m ~ mol.kg’ = 17.46 0.5009 1.0010 1.0010 1.0010 2.0153 2.0153 2.0153 2.9706 2.9706 2.9706
-PS P, .f=
c P. 0 J,K-‘.mol-’
u
A’
1.283“
0.9614 0.9356 0.9354 0.9354 0.8992 0.8997 0.9003 0.8782 0.8778 0.8789
= 17.41 0.5009 1.0010 1.0010 1.0010 2.0153 2.0153 2.0153 2.9706 2.9706 2.9706
.f =
= 17.55
/‘=
0.5009 1.0010 1.0010 1.0010 2.0153 2.0153 2.0153 2.9706 2.9706 2.9706
5 c;
1.353 0.9463 0.9116 0.9120 0.9113 0.8686 0.8682 0.8686 0.8431 0.8427 0.8426
0.9395 0.8969 0.8966 0.8967 0.8340 0.8346 0.8353 0.7940 0.7936 0.7949
-405.19 -325.33 - 326.96 -326.64 -235.64 - 234.01 - 232.09 - 178.76 - 179.63 -177.11
14.27 10.59 10.62 10.62 7.78 7.75 7.71 6.34 6.36 6.31
-0.79 8.10 9.73 9.40 4.75 3.12 1.20 -5.15 - 4.28 -6.80
d 0.9166 0.8607 0.8613 0.8604 0.7876 0.7870 0.7876 0.7414 0.7408 0.7407
-702.11 - 564.84 -561.58 - 566.66 -396.37 - 397.95 -396.18 - 306.20 -307.37 - 307.53
21.52 - 10.85 16.14 19.04 16.07 15.78 16.18 20.86 I 1.48 4.28 Il.51 5.85 I 1.48 4.09 9.29 -- 7.32 9.31 -6.15 9.32 - 5.99
0.8726 0.8023 0.8025 0.8031 0.7117 0.7123 0.7128 0.6614 0.6614 0.6604
-1409.84 -1060.09 -1058.95 -1054.41 - 732.04 - 729.78 -728.15 -557.27 - 557.27 - 559.83
1.435*
0.9183 0.8750 0.8751 0.8756 0.8209 0.8214 0.8217 0.7929 0.7929 0.7921
38.24 27.53 27.51 27.41 19.14 19.09 19.06 15.09 15.09 15.15
20.79 4.17 3.03 - 1.52 -0.53 ~~ 2.79 -4.42 0.22 0.22 2.78
’ The apparent molar heat capacity C,, was calculated from equations (1) and (2). h 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 absolute errors estimated from the experimental sensitivity at each temperature. The absolute error estimates varied from +O.OOOl to +0.0005. ‘ A is the value of [C, +(calc.) - C,, ,+}/(J K - t mol - ‘), The calculated value is from a cubic-spline interpolation of the knots in table 2. d The value of the heat-loss correction factorjwas calculated using the heat capacity of 3.005 mol. kg 1 NaCl as a standard.‘3.15’ The measured values of APjP for 3.005 mol. kg-’ NaCl at the experimental pressure were -0.04828 at 306.56 K, -0.04830 at 307.78 K, -0.04733 at 324.32 K. -0.04734 at 324.38 K, -0.04893 at 350.06 K, ~-0.04833 at 350.27 K, -0.05897 at 405.15 K, -0.05961 at 401.07 K, -0.07411 at 450.10 K. -0.07488 at 450.04 K, -0.07481 at 450.15 K, -0.07426 at 449.89 K. -0.08671 at 500.97 K. -0.12465 at 551.84 K, -0.16077 at 577.92 K. and -0.21096 at 602.72 K.
1042
D. E. WHITE,
J. A. GATES.
AND
R. H. WOOD
apparent molar heat capacities were fitted by the multi-dimensional cubic-splint method described previously. ‘3.19’ The experimental pressure varied between 17.2 and 17.8 MPa. These small variations in pressure have been ignored in the representation of the results. This isobaric assumption introduces an increase of less than 10 per cent in the estimated uncertainties. The knot positions and fitted 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,.,/(J K - ’ . mol- ‘) as a function of (m/m”)1i2 with mu = 1 mol. kg-‘, labeled A,, have been included in table 2. These have been calculated using Haar, Gallagher, and Kelps equation of state for water’r7’ with Uematsu and Franck’s equation for the dielectric properties of water.‘*” As with the C,,, surfaces presented previously,‘3-6’ the LiCl surface required three m ‘I2 knots placed at 0, 0.4, and 1.75 mol. kg- ’ and six temperature TABLE
2. LiCl
knot
positions,
knot
values,
T/K:
298.15
350.00
A,:
35.15
47.88
-50.58 - 39.33 - 19.70
-61.41 -45.54 -13.15
and DebyeHuckel
slopes A, for calculating
425.00
C,,,
of LiCl(aq)
550.00
575.00
603.00
559.45
1116.19
3730.03
-735.13 - 520.08 - 114.42
- 1305.77 ~ 889.47 - 286.08
- 2944.50 ~ 1891.58 - 545.51
p = 17.5 MPa
(m/(mol
kg
81.24
l))‘/*
C,,S/(J.kgm’,molF’)
0 0.4000 1.7500
- 128.72 -99.40 - 30.40
’ This fit is a representation of 216 points. The sum of the squares of the residuals a standard error of the fit of 12.3 J. Km ’ mol- I. The minimum sum of the squares
TABLE m/(mol.
3. Apparent kg-‘)
molar 0
heat capacity 0.100
of LiCl
0.250
from 0.500
298.15
to 598.15 1.ooo
K at 17.50 MPa Loo0
3.000
~ 23.28 - 22.52 -21.09 - 19.95 ~ 19.27 - 19.25 ~ 20.08 - 21.82 -24.31 - 33.43 -44.74 -57.31 - 75.32 - 104.49 - 150.59 -219.36 - 347.90 -665.70
- 19.88 - 18.88 - 16.96 -. 15.30 - 14.08 ~ 13.47 - 13.64 ~ 14.66 - 16.40 -22.89 ~ 30.65 - 38.46 ~ 50.54 - 72.80 --Ill.16 -171.52 ~~277.60 ~ 503.53
C,,+,/(J.K~‘.molJ’)
T/K 298.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15 398.15 423.15 448.15 473.15 498.15 523.15 548.15 573.15 598.15
C,,,
is 30000 resulting in for this set is 17700.
- 50.58 - 50.86 -51.58 - 52.82 - 54.93 - 58.26 -63.14 - 69.68 - 77.60 - 101.39 - 126.90 - 153.20 - 199.42 - 290.96 -453.19 -711.50 - 1234.89 -2617.30
-41.31 -41.29 -41.40 -42.00 -43.39 -45.90 - 49.84 -55.31 - 62.03 - 82.22 - 103.37 - 123.87 - 158.39 -226.71 - 348.58 -543.77 -919.96 - 1841.73
-37.14 - 37.01 ~ 36.90 - 37.20 - 38.22 -40.22 -43.48 -48.1 I - 53.88 -71.80 -91.73 - 112.41 - 144.84 -203.79 - 304.09 -460.52 ~ 764.33 -1531.93
-33.13 - 32.87 - 32.48 - 32.46 - 33.07 ~ 34.54 -37.14 -40.94 - 45.80 -61.39 -79.71 - 99.75 - 129.46 - 179.56 - 260.77 -383.82 -624.33 -1250.50
~ 28.46 - 28.01 - 27.20 -26.72 -26.78 - 27.59 - 29.37 - 32.20 - 35.98 - 48.66 -64.30 ~ 82.05 - 107.28 - 147.30 - 209.40 - 300.90 -479.20 -951.11
HEAT
CAPACITY
OF
1043
LiCI(aq)
knots placed at 298.15, 350.00, 425,00, 500.00, 575.00, and 603.00 K. The surface was extended to 298.15 K using the measurements of Fortier, Leduc, and Desnoyers’21) corrected to 17.5 MPa using the pressure dependence of C,., of NaCl(aq).‘22’ There were a total of 217 points, of which 7 were eliminated (see table 1) because they were not in reasonable agreement with the other results. The fit of the remaining 210 points (and 6 additional points at 298.15 K)“” to the cubic-spline surface resulted in a sum of the squares of the residuals of 30000 and a standard error of 12.3 J. K- ’ . 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 = 30000) with the sum of the squares of the residuals for a surface which passed through the average of each duplicate set of results (s = 17700). 4. Discussion There are no other high-temperature heat capacities available in the literature for LiCl(aq). The heat capacities presented herein complete a series for the alkali-metal halides (LiCl, NaCl, KCl. and NaBr). At lower temperatures, between 298 and 373 K at 17.5 MPa, there may be real differences between the shapes of the C,,, surfaces. At infinite dilution the LiCl and NaBr surfaces do not have the maximum in Cc,, observed for both the NaCl and KC1 surfaces as a function of temperature but as the molalities increase maxima occur in C,,, for all of these aqueous salts. At low pressures, maxima are typically found for C’z, of aqueous l-l electrolytes between 300 and 400 K.(23-2s’ It is quite possible that more accurate experiments will show that there are maxima in C’z, for LiCl(aq) and NaBr(aq) in this temperature range since the present results show only very small decreases in C& from 298 to 340 K. It is also possible that these salts would have maxima if either the temperature or the pressure were lowered. A comparison of the molality dependence given in table 4 shows that the TABLE
4. Values
T,‘K 298. I5 373.15 473.15 573.15 598.15
of {(C’,+(3.0
kg- ’ )
m/(mol 0 0.5 0 0.5 0 0.5 0 0.5 0 0.5
mol.
kg-I)-C,,+(m,)}/(J. 17.1 MPa
K--’
‘mol-‘1
for
some
I-1
salts
at about
LiCl
NaCl
KCI
NaBr
21 13 61 29 149 19 951 347 2110 141
89 53 55 36 148 82 x00 330 1850 690
55 38 57 31 I46 6X 770 321 2030 701
72 53 6X 35 149 X6 1160 426 2170 781
1044
D. E. WHITE. J. A. GATES, AND R. H. WOOD
differences in values of (C,,,(m,) -Cp,+(m,)) for the four salts increases with temperature but the fractional differences decrease. The differences at the higher temperatures are only slightly larger than our estimates of the experimental errors. In previous papers’5*6’ we have noted the similarity of Cz, for aqueous NaCI, KCI, and NaBr. As expected, the present results for C;, of LiCl are similar to those for the other three salts at the higher temperatures. There still are real differences between these 1- 1 salts but the fractional differences between both Czd and {C~+(Q) - CF,(m,)} decrease with increasing temperature. These similarities should be very useful in estimating the properties of other 1-l salts at high temperatures. Helgeson, Kirkham, and Flowers(23’ and recently Tanger and Helgeson’24’ have published predictive equations for the standard partial molar properties of electrolytes. A comparison of Helgeson, Kirkham, and Flower’s surface with the extrapolation of our heat-capacity surface to m = 0 shows excellent agreement below 573.15 K. Above 573.15 K the predicted values tend to be too negative although the qualitative shape of the curve is correct. Tanger and Helgeson’24’ have improved upon Helgeson et al.‘23’ using many of the recent higher-temperature values (including the present results). The agreement of this improved surface and our results is excellent. A more thorough discussion is included in Tanger and Helgeson’s paper. In view of the similarities in the molality dependence of C,,, it seemed very unusual that the relative apparent molar enthalpy of LiCl(aq) measured earlier in this laboratory’26’ is so different from that of other l-l salts. At high molalities L, of LiCl decreases between 373 and 423 K rather than increasing like the other salts. Holmes and Mesmer’27’ found that the L, measurements above 373.15 K were not consistent with their high-temperature isopiestic measurements on LiCl(aq) and that a steadily increasing L, with temperature was necessary to fit their results. If we neglect the large pressure difference between the L, and C,, measurements (< 2 MPa compared with 17.5 MPa) we can calculate {ALb(T2)-AL,+,(T1)} where AL, = {L,(3.0 mol. kg-‘) - L,(O.5 mol. kg- I)>. The two sets of results give good agreement for LiCl between 298.15 and 373.15 K and no agreement above 373.15 K. In contrast, a check calculation using results for NaCl gave good agreement at all temperatures. We conclude that the enthalpy of dilution results of Mayrath and Wood’26’ are in error at 423 and 473 K. Since other results run at the same time have proved reliable we suspect an error in the preparation of the LiCl solutions used above 373 K. 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. The authors thank Mark A. Ryan, David M. Tillet, and Anne L. Doberstein for help with the experimental measurements. REFERENCES 1. Smith-Magowan. 2. Smith-Magowan,
1981, 13, 1047. D.; Wood, R. H. J. Chem. Thermodynamics D.: Wood, R. H.: Tillett, D. M. J. Chem. Eng. Data 1982, 27, 235.
HEAT CAPACITY
OF LiCl(aq)
1045
3. Gates. J. A.: Tillett. D. M.: White. D. E.: Wood. R. H. J. Chem. Thermodvnamics 1987. 19. 131. 4. White. D. E.: Doberstein. A. L.; Gates. J. A.; Tillett, D. M.; Wood, R. H. j. Chem. Theimodvnamics 1987, 19, 251.
5. White, D. E.: Gates, J. A.; Wood. R. H. J. Chem. Thermo&namics 1987, 19. 493. 6. White. D. E.; Ryan, M. A.; Armstrong, M. V. C.; Gates, J. A.; Wood. R. H. J. Chem. Thermodynamics 1987, 19, 1023. 7. Wood, R. H.; Quint, J. R.; Grolier, J.-P. J. Phys. Chem. 1981, 85, 3944. 8. Wood, R. H.; Quint, J. R. J. Chem. Thermod.vnamics 1982, 14, 1069. 9. Wheeler, J. C. Ber. Bunsenges. Physik. Chem. 1972, 76, 308. IO. Gates, J. A.: Wood, R. H.; Quint, J. R. J. Phvs. Chem. 1982, 86. 4948. II. Helgeson, H. C.; Kirkham, D. H. Abstracts c>fpapers, 174th meeting. American Chemical Society: New Orleans, LA: March 1977. 12. Cobble, J. W.; Murray, R. C., Jr. Discuss. Furaday Sot. 1977, 64, 144. 13. Chang, R. F.; Morrison, G.; Levelt-Sengers, J. M. H. J. Phys. Chem. 19&(, 88, 3389. 14. Vaslow, F. J. Phys. Chem. 1966, 70, 2286. 15. White, D. E.; Wood, R. H. J. Solution Chom. 1982, I I. 223. 16. Gates, J. A.; Wood, R. H. J. Chem. Eng. Data 1985, 30. 44. 17. Haar. L.; Gallagher, J. S.; Kell. G. S. NBS/NRC Steam Tables. Hemisphere Publishing Corp.: Washington, DC. 1984. 18. Fortier, J.-L.; Benson, G. C.; Picker, P. J. Chem. Thermodynamics 1976, 8, 289. 19. Gates, J. A. Ph.D. dissertation, University of Delaware. January 1985. 20. Uematsu, M.; Franck, E. U. J. Phys. Chem. Ref. Dafa 1980,9, 1291. 21. Fortier, J.-L.; Leduc, P.-A.; Desnoyers, J. E. J. So&ion Chem. 1974, 3. 323. 22. Rogers, P. S. Z.; Pitzer, K. S. J. Phys. Chem. Ref. Data 1982, Il. 15. 23. Helneson. H. C.: Kirkham. D. H.: Flowers. G. C. Am. J. Sci. 1981., 281. 1249 24. Tanger, J. C., IV; Helgeson, H. C. Am. J. Sri., in press, 25. Saluja, P. P. S.; Pitzer, K. S.; Phutela, R. C. Can. J. Chem. 1986, 64, 1328. 26. Mayrath, J. E.; Wood, R. H. J. Chem. Thermodynamics 1982, 14, 15. 17. Holmes. H. F.; Mesmer. R. F. J. Phys. Chem. 1983, 87. 1242.