101
Ind. Eng. Chem. Fundam. 1984, 2 3 , 101-104
Entropy of Vaporization from the Log ( T / p ) vs. Log p Relationship J. Gordon H m r Analytlcel Ctwt&by Dspertment, The Connecticut Agricuttural Experiment Station, New Haven, Connecticut 06504
The entropy of vaporlzatlon of a compound at the temperature where log ( T l p ) = 0.5 is directly related to the C term of the power series, log p = A [log ( T / p ) I 3 B [log ( T / p ) l 2 C[log ( T l p ) ] D, that describes the temperature-presswe relationship of the compound, by AS, = 268.82C 320.25. This relationshop of AS, to C is generally valki regardless of the degree of association of the compound in the liquid state.
+
+
To distinguish between normal and associated liquids, Hildebrand (1915) showed that the entropy of vaporization
+
+
is more nearly constant for different normal liquids a t temperatures where these liquids give the same vapor
Table I. Data Basis for Eq 5 Compound with Literature Values
-~ compound
AS"
method of Pitzer e t al.
method of Thomas
Tatc=0.5
Cofeq2
lit.
eq 5
(1955)
(1959)
223.0 212.5 248.4 286.9 278.5 281.3 275.7 314.9 296.1 340.7 132.2 227.8 291.5 220.4 233.5 297.9 294.7 203.7 223.9 302.3 257.2 345.6 338.4 254.5 292.9 307.7 318.5 226.7 331.8 302.0 312.4 309.2 286.5 272.3 314.9 381.7 219.8 19.98 558.2 325.3
-1.0925 -1.093 3 - 1.0 93 1 -1.0916 -1.0925 -1.0929 1.0939 -1.0910 -1.0952 -1.0904 -1.0908 -1.0908 -1.0908 -1.0909 -1.086 8 -1.0907 -1.091 5 -1.0888 -1.0884 -1.0904 -1.0883 -1.0886 -1.0877 -1.0874 -1.0738 -1.0705 -1.0867 -1.0912 -1.0887 -1.0900 -1.0899 -1.0904 -1.0904 -1.0908 -1.0908 -1.0903 -1.0805 -1.0788 -1.0971 -1.0752
26.45 26.55 26.51 26.77 26.56 26.50 26.20 26.98 25.95 27.05 27.13 27.06 26.99 27.05 28.43 27.08 26.50 27.59 27.75 27.13 27.45 27.68 27.96 27.87 31.38 32.47 27.88 27.02 27.62 27.25 27.10 27.17 27.10 27.07 27.03 27.20 29.88 30.04 24.97 31.44
26.56 26.35 26.40 26.81 26.56 26.46 26.19 26.97 25.84 27.13 27.02 27.02 27.02 26.99 28.10 27.05 26.83 27.56 27.67 27.13 27.69 27.61 27.85 27.94 31.59 32.48 28.12 26.91 27.59 27.24 27.26 27.13 27.13 27.02 27.02 27.16 29.79 30.25 25.33 31.21
26.14 26.69 26.4% 26.91 27.26 26.49 26.53 26.83 26.15 27.27 27.65 27.33
33.34
26.97 26.50 26.61 27.09 26.80 26.86 26.48 26.26 26.19 27.56 27.02 27.23 27.34 27.09 28.31 27.41 26.81 27.72 27.38 27.43 27.93 28.02 28.30 28.29 31.38 33.19 28.38 27.31 27.92 26.94 27.42 27.46 27.40 27.27 27.34 27.58 29.77 30.63 25.89 31.69
0.75
0.38
lit. ref _ _ _ I
butane isobutane
isopentane hexane 2-meth ylpentane
3-methylpentane 2,3-dimethylbutane heptane 2,2,3-trimethylbutane octane ethylene cis 2-butene 2,3-dimethyl-2-butene 1,3-butadiene 1-butyne benzene carbon tetrachloride methyl chloride perflu oro-n-butane fluorobenzene diethyl ether mesityl oxide isomesityl oxide furan methanol ethanol nitromethane trimethylamine pyridine thiophene 2-thiapentane diethyl sulfide 1-propanethiol 2-propanethiol 1-butanethiol benzenethiol sulfur dioxide ammonia mercury water standard error of estimate
0.14
__.
26.97
___
26.79 26.17 27.90 27.92 27.07 27.51 26.84 29.42
--_
33.37 33.96 29.31 26.73 27.30
--.--
27.54 27.83
___
_-_ _-_ 29.6 5
___
--_
a b C
d ,e d, f
f
d,f,g h e,h e, i j
k 1
m n e,o,p (7, r S
t U U W
W X
P,Y P z
M
b b,cc,dd ee
ff gg hh
ii ff
JJ S S
S S
Aston and Messerly (1940). Aston e t al. (1940). Schumann e t al. (1942). Lemons and Felsing (1943). Osborne and Ginnings (1947). f Waddington et al. (194913). g Ambrose e t al. (1960). Waddington e t al. (1947). Barrow (1951). Clusius and Konnertz (1949). Scott et al. (1944). Scott et al. (1955). Scott e t al. (1945). Alston e t al. (1950). O Smits and Cannegieter (1934). Fiock e t al. (1931). 4 Pitzer (1941). ' Mathews (1926). Weast (1980-81). Brown and Mears (1958). Scott et al. (1956a). " Leduc (1917). Stross e t al. (1947). Guthrie e t al. (1952). Bartoszwiczowna (1931). * McCullough e t al. (1954b). Aston e t al. (1944). b b Andon e t al. (1957). c c McCullough e t al. (1957). d d Biddiscombe et,al. (1954). e e Waddington et,al. (1949a). f f Scott e t al. (1957). g g Scott e t al. (1952). h h Pennington et al. (1956). * I McCullough e t al. (1954a). Scott e t al. (1956b). e
JJ
0198-4313/84/1023-0101$01.50/00 1984 American Chemical Society
102
Ind. Eng. Chem. Fundam., Vol. 23, No. 1, 1984
Table 11. Entropies Calculated with Eq 5
~ _ - I I _ _ _ _ ~ - _ - ~ - - _ - _ - _ _ - _ - - - _ _
AS"
compound n-pentane 2,2-dimethylbutane cyclopropane cyclopen tane cyclohexane methylcyclohexane propene toluene e th ylbenzen e 0-xylene m-xylene p-xylene n-butylbenzene naphthalene phosgene fluoroform methyl bromide trifluorochloroeth ylene ethyl chloride bromobenzene dimethyl ether ethylene oxide acetone methyl ethyl ketone dimethyl formal dimethyl acetal diethyl formal acetaldehyde butyraldehyde n-propyl alcohol sec-butyl alcohol tert-butyl alcohol acetic anhydride ethyl acetate methyl propionate n-propyl formate propioni trile me thylamine dime thy lamine piperidine a-picoline Y -pic0line methyl mercaptan tetramethylsilane
T a t c = 0.5
Cofeq 2
lit.
269.1 196.5 268.3 297.3 315.3 181.1 325.8 349.9 357.7 355.7 351.8 394.7 426.6 232.3 153.9 228.1 200.0 236.1 367.9 203.3 236.0 277.9 296.7 264.6 284.4 305.9 246.1 294.8 319.3 328.2 312.2 358.7 298.9 300.6 301.2 314.0 224.2 235.8 322.6 345.9 359.7 231.0 247.2
-1.0915 -1.0948 -1.0922 -1.0923 -1.0927 -1.0936 -1.0911 -1.0910 -1.091 7 -1.0915 -1,091 3 -1.091 7 -1.0911 -1.0930 -1.0897 -1.0833 -1.0895 -1.0878 -1.0897 -1.0933 -1.0878 -1.0866 -1.0852 --1.OS9 3 -1.087 5 -1.0888 -1 .OS95 -1.0841 -1.0881 -1.07 03 -1.0704 -1.0693 -1.081 9 -1.0837 -1.0846 -1.0865 -1.0909 -1.0801 -1.0812 -1.0896 -1.0836 -1.0856 -1.0882 -1.0935
26.91 26.10 26.26 27.26 26.58 26.17 26.73 26.89 26.98 27.18 26.49 26.8 2 27.04 26.36 27.29 28.82 26.99 27.56 27.16 26.66 27.66 27.89 28.70 27.76 27.94 27.51 27.63 28.39 27.71 32.77 32.67 33.10 29.99 28.85 28.73 28.26 26.79 29.79 29.17 27.30 28.29 28.29 27.35 26.01
standard error of estimate
method of Pitzer etal.
method of Thomas
ea 5
11955)
(1959)
26.86 25.95 26.64 26.62 26.51 26.27 26.94 26.97 26.78 26.83 26.89 26.78 26.94 26.42 27.32 29.04 27.37 27.83 27.32 26.35 27.83 28.1 5 28.53 27.42 27.91 27.56 27.37 28.82 27.75 32.53 3 2.51 32.80 29.41 28.93 28.69 28.18 26.99 29.90 29.60 27.34 28.96 28.42 27.72 26.30
26.81
27.83 26.32
26.99 26.20 26.52 26.84 26.81 26.07 26.96 27.06 27.21 27.19 27.21 27.07 27.07 27.10 27.73 29.15 27.65 27.71 26.97 27.07 27.98 28.40 28.43 28.26 28.49 27.86 27.59 28.90 27.94 34.00 34.88 35.06 29.68 29.12 28.58 28.45 27.53 30.71 30.54 27.37 27.91 27.74 27.84 26.59
0.60
0.65
0.26
__.
26.22 26.67 26.36 25.97 26.55 26.98 27.23 26.31 26.25 27.11 27.64 26.90 27.81 29.65 27.53 27.95 27.58 26.95 27.83 28.44 28.37 28.41
-__
__-
___
-__
___
33.49 30.99 31.70 29.64 28.24 28.24 27.66 27.93 29.88 28.79
-__
___
___
lit. ref a, b,c, d, e
f
g
h t i
f j
f,k 1, m
k k k
f
n 0
P 4 r s
n t U
u, w u,x Y
Y Y
n,2 Y,Z
aa
bb cc
n dd dd dd
ee
ff gg
n hh,ii hh,jj
n kk
Pitzer (1941). Messerly and Kennedy (1940). Scott e t al. (1951). Sage e t al. (1939). e Bennewitz and Rossner (1938). Osbprne and Ginnings (1947). Ruehrwein and Powell (1946 . Douslin and Huffman (1946). Aston e t al. (1943). I Powell and Giauque (1939). Pitzer and Scott (1943). )Scott and Brickwedde (1945). Mathews (1926). Fishtine (1963). O Davies (1946). P Valentine e t al. (1962). 4 Egan and Kemp (1938). Oliver e t al. (1951). Gordon and Giauque (1948). Kennedy et al. (1941). Giauque and Gordon (1949). " Grimm and Patrick (1923). UJ Pennington and Kobe (1957). Nickerson et al. (1961). Nicolini (1951). Smith and Bonner (1951). Bartoszwiczowna (1931). b b Berman and McKetta (1962). c c Beynon and McKetta (1963). d d International Critical Tables (1933). e e Weber and Kilpatrick (1962). f f Aston e t al. (1937). gg Aston et al. (1939). h h Andon et al. (1957). Hopke and Sears (1951). Biddiscombe e t al. (1954). " Aston et al. (1941). a
concentrations than at temperatures giving the same vapor pressure as required by the Trouton relation. He defined a vapor concentration constant, c, as c =
log ( T / p )
(1)
with c arbitrarily assigned a value of 0.5. Hildebrand and Scott (1950) proposed linear plots of log ( T l p ) against log p to obtain T or p at a given vapor concentration. Hanna (1981) showed that results of greater precision for real liquids can be realized by means of a power series, eq 2, to define the temperature-pressure relationship than can be obtained based on the assumption
of constant slopes for linear plots. log p = AUog ( T / p ) I 3+ BUog ( T / p ) I 2+ C[log ( T / p ) l + D (2) The D term of this expression is directly related to the normal boiling point (Hanna, 1981). The C term is now shown to correspond directly to the entropies of vaporization for both normal and associated liquids under Hildebrand's conditions. The entropies of vaporization in Table I calculated at T,where c = 0.5, show variations from the constancy predicted by Hildebrand's rule for normal liquids and
23, No. 1, 1984 103
Ind. Eng. Chem. Fundam., Vol.
Table 111. Entropies from Eq 5 Compared with Those from Other Calculation Methods
AS,
compound nonane decane undecane dodecane tridecane tetradecane pentadecane hexadecane heptadecane octadecane 1-hexene 1,5-hexadiene a-pinene ProPYne n-propylbenzene styrene methyl iodide 2-propyl bromide epichlorohydrin dioxane anisol diethyl ketone acetophenone benzaldehyde propionic anhydride formic acid acetic acid propionic acid isobutyric acid benzoic acid salicylic acid chloroacetic acid ethyl propionate allyl alcohol ethylene glycol cyclohexanol 2-ch lor oe than 01 phenol o-cresol m-cresol p-cresol acetonitrile bu tyron itrile benzoni trile phenyl isocyanate allyl isothiocyanate dibutyl sulfide propylamine pyrrolidine aniline N-methylaniline nitrobenzene formamide acetamide pr opi onam ide ethyl methyl carbamate propyl carbamate oxygen chlorine bromine hydrogen chloride
T a t c = 0.5 364.7 387.2 406.3 428.1 446.9 474.0 481.5 497.5 51 2.7 526.9 281.8 277.2 365.7 205.3 371.5 359.0 261.8 289.2 336.6 318.5 370.4 318.3 414.9 294.8 386.4 31 7.0 343.7 362.2 375.2 467.1 473.7 410.5 319.0 323.5 420.5 383.2 350.7 400.4 406.9 418.5 418.8 299.4 333.5 403.5 378.7 366.8 397.6 270.6 307.0 398.6 409.7 421.3 438.9 441.0 437.8 390.5 418.7 75.8 194.3 280.0 150.3
C of eq 2
-1.0898 -1.0887 -1.0886 -1.0880 -1.0875 -1.0870 -1.0865 -1.0860 -1.0870 -1.0856 -1.091 9 -1.0941 -1.0938 -1.0856 -1.0917 -1.0910 -1.0933 -1.091 2 -1.0846 -1.0886 -1.0871 -1.0819 -1.0873 -1.0885 -1.0805 -1.0906 -1.0775 -1.0774 -1.0781 -1.080 2 -1.0733 -1.0747 -1.0844 -1.0730 -1.0703 -1.0777 -1.0784 -1.0800 -1.0836 -1.0838 -1.0812 -1.0898 -1.0890 -1.0875 -1.0894 -1.0851 -1.0842 -1.0875 -1.0852 -1.0856 -1.0830 -1.0901 -1.0619 -1.0797 -1.0672 -1.0770 -1.070 2 -1.0883 -1.0907 -1.0859 -1.0846
confirm the greater ASv values for associated liquids pointed out by Hildebrand (1915). Literature values for heats of vaporization at different temperatures for compounds in Table I fit the linear relationshop described by log ( w . d ~ v 2 )= w 1% [(Tc- T , ) / ( T c- T,)1 + Y (3) Linear regression to relate the C terms of eq 2 and the
eq 5 27.29 27.59 27.61 27.77 27.91 28.04 28.18 28.31 28.04 28.41 26.73 26.13 26.21 28.42 26.78 26.97 26.35 26.91 28.69 27.61 28.02 29.41 27.96 27.64 29.79 27.07 30.60 30.62 30.44 29.87 31.73 31.35 28.74 31.80 32.53 30.54 30.35 29.92 28.96 28.90 29.60 27.29 27.51 27.91 27.40 28.55 28.80 27.91 28.53 28.42 29.12 27.21 34.79 30.01 33.37 30.73 32.56 27.69 27.05 28.34 28.69
method of Pitzer e t al. (1955) 27.43 27.60 27.87 27.72 27.72 27.14 28.03 28.03 28.1 5 28.28 26.76 26.29
___
28.45 27.12
___
25.25 27.57
--_
28.15 27.92 28.86
_-_ _-_ ___ _-_
30.33 31.08 31.76
_._ .__ -.-
28.11 32.49
--_ -.-
___
30.32 29.3 2 29.32 30.46 27.52 28.51 27.44
___
-__
___
28.09
-__
28.60 29.01
-.-_--___ __. -__
28.05 27.02 29.43 29.69
method of Othmer et al. (1957)
method of Thomas (1959)
27.11 26.79 26.81 26.60 26.27 24.97 25.21 24.60 23.66 22.79 26.61 26.24 26.18
27.83 27.65 28.25 28.49 28.65 28.83 29.03 29.20 28.12 28.86 27.02 26.80 26.78 28.81 27.24 26.90 26.95 26.92 28.52 28.2 2 28.26 28.1 7 28.13 28.32 29.47 26.85 28.10 30.06 31.21 32.35 35.57 31.37 29.00 33.15 34.22 30.35 30.54 30.70 29.88 30.58 30.80 27.50 27.62 27.57 27.06 28.43 29.31 28.40 29.15 28.74 28.22 27.71 36.16 31.85 33.14 30.60 32.66 27.10 27.63 27.81 28.31
-__
___ ___ ___
26.48 28.30 27.30 27.68
_._
26.48 27.67 28.83 26.95 27.10 29.58 30.10 30.44 31.56 30.22 28.32 31.02 32.35 29.68 30.26 28.70 28.32 28.80 28.75 27.65 27.19 26.75 26.68 27.32 28.11 27.06 28.73 28.19 27.49 26.02 34.03 29.00 31.76 29.96 31.65
--_ --_ -.--_
corresponding entropies of vaporization at T, where c = 0.5, for the compounds in Table I gives eq 4 and a correlation coefficient of 0.996. ASv = 268.82C + 320.25 (4) Entropies of vaporization calculated with eq 4 are listed in Table I with the literature values and values calculated by the methods of Pitzer et al. (1955) and Thomas (1959).
Ind. Eng. Chem. Fundam., Vol. 23, No. 1, 1984
104
The data in Table I1 are for compounds for which the heats of vaporization were available at only one temperature for each compound. The scheme recommended by Janz (1958), eq 6, was used to calculate the heat of vaporization at T where c = 0.5. log (mvi/AHVJ = n log [(T, - T i ) / ( T ,- Tz)1 (5) The n term was evaluated based on the correlation with the ratio Tb/TcFroposed by Fishtine as reported by Reid et al. (1966). Again, comparison values for AS, calculated according to Pitzer et al. (1955), where possible, and Thomas (1959) are shown. Table I11 contains compounds for which heats of vaporization at specific temperatures were not found. The AS, values from eq 5 are compared with values obtained by the methods of Pitzer et al. (1955), Othmer et al. (1957), and Thomas (1959).
Conclusion Associations in the liquid states and other characteristics contributing to variabilities of entropies of vaporizations among different compounds are reflected in the temperature-pressure relationships described by eq 2. These relationships then are useful as bases for predictions of entropies and heats of vaporization for many different types of compounds. Nomenclature log = logarithm, base 10 p = vapor pressure, mmHg
T = temperature, K Tb = normal boiling point, K T, = critical temperature, K AS, = entropy of vaporization, cal mol-' deg-' AH,,= heat of vaporization, cal mo1-l Literature Cited Ambrose, D.; Cox, J. D.; Townsend, R. Trans. Faraday SOC. 1980, 56,
.
1459
Andon, R. J. L.; Cox, J. D.; Herrington, E. F. G.; Martin, J. F. Trans. Faraday SOC. 1957, 5 3 , 1074. Aston, J. G.; Eidinoff, J. L.; Forster, W. S . J. Am. Chem. SOC. 1939, 6 1 , 1539. Aston, J. G.; Kennedy, R. M.; Messerly, G. H. J. Am. Chem. SOC.1941, 63, 2343. Aston, J. G.; Kennedy, R. M.; Schumann, S. C. J. Am. Chem. SOC. 1940, 6 2 , 2059. Aston. J. G.; Mastrangelo, S. V. R.; Moessen, G. W. J. Am. Chem. SOC. 1950, 7 2 , 5287. Aston. J. G.; Messeriy, G. H. J. Am. Chem. SOC. 1940, 62, 1917. Aston, J. G.; Sagenkahn, M. L.; Szasz, G. J.; Moessen, G. W.; Zuhr, H. F. J . Am. Chem. SOC.1944, 66, 1171. Aston, J. G.; Siiler, C. W.; Messeriy. G. H. J . Am. Chem. SOC. 1937, 5 9 , 1743. Aston, J. G.; Szasz, G. J.; Finke, H. L. J. Am. Chem. SOC.1943, 6 5 , 1035. Barrow, G. M. J. Am. Chem. SOC. 1951, 7 3 , 1824. Bartoszwiczowna, E. Rocz. Chem. 1931, 1 1 , 90. Bennewitz, K.; Rossner, W. Z . Phys. Chem. 1938, 8 3 9 , 126. Berman, N. S.; McKetta, J. J. J. Phys. Chem. 1962. 66, 1444. Beynon, E. T., Jr.; McKetta, J. J. J. Phys. Chem. 1983, 6 7 , 2761. Biddiscombe, D. P.; Coulson, E. A.; Handley, R.; Herrington, E. F. G. J . Chem. SOC. 1954, 1957. Brown, J. A.; Mears, W. H. J. Phys. Chem. 1958, 6 2 , 960. Clusius, K.; Konnertz, F. Z . Naturforsch. 1949, 4 a , 117. Davies, C. N. J. Chem. Phys. 1946, 14, 48. Douslin, D. R.; Huffman, H. M. J. Am. Chem. SOC. 1948, 6 8 , 173, 1704. Egan, C. J.; Kemp, J. D., J. Am. Chem. Soc.1938, 6 0 , 2097. Flock, E. F.; Ginnings, D. C.; Holton, W. B. J. Res. Natl. Bur. Stand. 1931, 6, 881. Fishtine, S. H. Ind. Eng. Chem. 1983, 55.47. Giauque, W. F.; Gordon, J. J . Am. Chem. SOC.1949, 71, 2176. Gordon, J.; Giaugue, W. F. J. Am. Chem. SOC. 1940, 7 0 , 1506. Grimm, F. W.; Patrick, W. A. J. Am. Chem. SOC. 1923, 4 5 , 2794.
Guthrie, G. B.; Scott, D. W.; Hubbard, W. N.; Katz, C.; McCuliough. J. P.; Boss, M. E.; Williamson, K. D.; Waddington, G. J. Am. Chem. SOC. 1952, 74, 4662. Hanna, J. G. Ind. Eng. Chem. Fundam. 1981, 20, 376. Hildebrand, J. H. J. Am. Chem. SOC. 1915, 3 7 , 970. Hlldebrand, J. H.; Scott, R. L. "Solubility of Non-Electrolytes", 3rd ed.; Rheinhold: New York, 1950. Hopke, E. R.; Sears, G. W. J. Chem. Phys. 1951, 19, 1345. "Internationai Critical Tables"; McGraw-HM. New York, 1933. Janz, G. J. "Estimation of Thermodynamic Properties of Organic Compounds"; Academic Press; New York, 1958. Kennedy, R. M.; Sagenkahn, M.; Aston, J. G. J. Am. Chem. SOC.1941, 6 3 , 2267. Leduc, A. Comp. Rend. 1917, 164, 495. Lemons, J. F.; Feising, W. A. J. Am. Chem. SOC. 1943, 65, 46. Mathews, J. H. J. Am. Chem. SOC. 1928, 48, 562. McCullough, J. P.; Douslin, D. R.; Messeriy, J. F.; Hosseniopp, I. A,; Klncheioe. T. C.; Waddington, G. J. Am. Chem. SOC. 1957, 79, 4289. McCullough, J. P.; Finke, H. L.; Scott, D. W.; Gross, M. E.; Messerly, J. F.; Pennington, R. E.; Waddington, G. J. Am. Chem. SOC.1954a, 76, 4796. McCullough, J. P.; Scott, D. W.; Pennington, R. E.; Hossenlopp, I.A.; Waddington, G. J. Am. Chem. SOC. 1954b, 7 6 , 7791. Messerly, G. H.; Kennedy, R. M. J. Am. Chem. SOC. 1940, 62, 2968. Nickerson, J. K.; Kobe, K. A.; McKetta, J. J. J. Phys. Chem. 1981, 6 5 , 1037. Nicolini, E. Ann. Chim. 1951, 6 , 582. Oliver, G. D.; Bisard, J. W.; Cunningham, C. W. J. Am. Chem. SOC.1951, 73, 5179. Osborne, N. S.; Ginnings, D. C. J. Res. Natl. Bur. Stand. 1947, 39, 453. Othmer, D. F.; Maurer, P. W.; Molinay, C. J.; Kowaiski, R. Ind. Eng. Chem. 1957, 49, 125. Pennington, R. E.; Kobe, K. A. J. Am. Chem. SOC. 1957. 79, 300. Pennington. R. E.; Scott, D. W.; Finke, H. L.; McCullough, J. P.; Messerly, J. F.; Hossenlopp, I. A.; Waddington, G. J. Am. Chem. SOC. 1958, 78, 3266. Pitzer, K. S . J. Am. Chem. SOC. 1941, 6 3 , 2413. Pitzer, K. S.; Llpman, D. 2.; Curl. R. F., Jr.; Huggins, C. M.; Petersen, D. E. J. Am. Chem. SOC. 1955, 77, 3433. Pker, K. S.; Scott, D. W. J. Am. Chem. SOC.1943, 65, 803. Powell, T. M.; &que, W. F. J. Am. Chem. Soc. 1939, 6 1 , 2366. Reld, R. C.; Sherwood, T. K. "The Properties of Gases and Liquids-Their Estimation and Correlation", 2nd ed.; McGraw-Hill: New York, 1966. Ruehrwein, R. A.; Powell, T. M. J. Am. Chem. Soc.1948, 68, 1063. Sage, R. H.; Evans, H. D.: Lacey, W. N. Ind. €178. Chem. 1939, 3 1 , 783. Schumann, S. C.; Aston, J. G.; Sagenkahn, M. J. Am. Chem. SOC. 1942, 6 4 , 1039. Scott, 0. W.; Finke, H. L.; Hubbard, W. N.; McCullough, J. P.; Oliver, G. D.; Gross, M. E.; Katz, C.; Williamson, K. D.; Waddington, G.; Huffman, H. M. J. Am. Chem. SOC.1952, 74, 4656. Scott, D. W.; Finke, H. L.; McCullough, J. P.; Gross, M. E. Messerly, J. F.; Pennlngton, R. E.; Waddington, G. J. Am. Chem. SOC. 1955, 77, 4993. Scott, D. W.; Finke, H. L.; McCullough, J. P.; Messerly, G. H.; Pennlngton, R. E.; Hosseniopp, I. A.; Waddington, G. J. Am. Chem. SOC. 1957, 7 9 , 1062. Scott, D. W.; McCullough, J. P.; Good,W. D.; Messeriy, G. H.; Pennington, R. E.; Kincheloe, T. C.; Hossenlopp, I. A.; Dousiin, D. R.; Waddington, G. J. Am. Chem. SOC. 1958a, 78, 5457. Scott, D. W.; McCullough, J. P.; Hubbard, W. N.; Messerly, G. H.; Hossenlopp, I.A.; Frow, F. R.; Waddington, G. J. Am. Chem. Soc. 1958b. 7 8 , 5463. Scott, D. W.; McCullough, J. P.; Williamson, K. D.; Waddlngton, G. J. Am. Chem. SOC. 1951, 73, 1707. Scott, R. G.; Brickwedde, F. G. J. Res. Natl. Bur. Stand. 1945, 35, 501. Scott, R. B.; Ferguson, W. J.; Brickwedde, F. G. J. Res. Natl. Bur. Stand. 1944, 3 3 , 1. Scott, R. B.; Meyers, C. H.; Rands, R. D., Jr.; Brickwedde, F. G.; Bekkedahl, N. J. Res. Natl. Bur. Stand. 1945, 35, 39. Smith, T. E.; Bonner, R. F. Ind. Eng. Chem. 1951, 43, 1169. Smits, A.; Cannegleter, D. Z . Phys. Chem. 1934, A168, 391. Strnss, F. H.; Monger, J. M.; Finch, H. deV. J. Am. Chem. SOC.1947, 6 9 , 1627. Thomas, L. H. J. Chem. SOC. 1959, 2132. Valentine, R. H.; Brodaie, G. E.; Giauque, W. F. J. Phys. Chem. 1982, 66, 392. Waddington, G.; Knowiton, J. W.; Scott, D. W.; Ollver, 0. D.; Todd, S. S.; Hubbard, W. N.; Smith, J. C.; Huffman, H. M. J. Am. Chem. SOC. 1949a, 7 1 , 757. Waddington, G.; Smith, J. C.; Scott, D. W.; Huffman, H. M. J. Am. Chem. SOC. 194@b,77, 3902. Waddington, G.; Todd, S. S.; Huffman, H. M. J. Am. Chem. SOC. 1947, 6 9 , 27. Weast, R. C., Ed. "Handbook of Chemistry and Physlcs", 61st, ed.; CRC Press: Boca Raton, FL; 1980-1961. Weber, L. A.; Kilpatrick. J. E. J. Chem. Phys. 1982, 3 6 , 829.
Received for review August 31, 1982 Accepted October 7 , 1983
