LETTER TO THE EDITOR
Vapor Pressures of Liquids as a Function of Temperature. Two-Parameter Equation Based on Kinetic Theory of Fluids Sir: There are two typographical errors in the vapor pressure equation of Abrams et al. (1974). Equation 4 of that paper should read: (4') and eq 6 should read:
E=
(s
- 3)(s - 1)
(61)
2 (EoIR)*
then found from a one-dimensional search, the fit of the data is significantly impaired; in a typical case the average error is trided. The usefulness of the vapor pressure equation for extrapolation to low temperatures was tested by predicting vapor pressures of n-hexane and n-eicosane near their triple points. Using the parameters reported in Table Ia, determined from data above 10 mmHg, vapor pressures down to I X mmHg were predicted to within about 10%.
Table Ia. Vapor Pressure Parameters for Some Representative Liquids s
EoIR, K
68.26 211.48
7.68 14.07
5575 15062
0.2 0.4
0.6 1.0
10-1500 10-1500b
69.78
8.41
6844
0.7
1.4
16-760'
69.73 63.00 71.81 76.44 64.78 48.39 131.12
8.48 8.64 13.47 8.26 7.52 7.05 10.11
7036 6763 10768 7055 5425 5637 10506
0.1 0.0(5) 1.3 0.7 0.2 0.1 0.4
0.1 0.1 2.6 2.7 0.5 0.2 1.0
153-1000' 69-746' 6-757c 5-773'
81.81 60.22 10.5lQ 78.49 78.48 78.48 78.48 78.47 78.47 78.47 78.47
8.27 7.13 7.05 8.18 8.02 7.99 7.95 7.69 7.78 7.84 7.48
7670 5568 6869 6303 6060 6074 6083 5684 5921 5787 5689
0.2 0.0(4) 0.2 0.3 0.3 0.2 0.3 0.3 0.3 0.3 0.3
0.4 0.1 0.4 0.5 0.6 0.6 0.6 0.6 0.7 0.6 0.8
48-780' 77-780' 5-15006 10-15006 10-15006 10-1500 10-1500 10-1 500 1O-150Ob 10-1500 10-1500
78.46
7.36
5537
0.3
0.8
10-1500
Liquid
V,, ~3/m0l
n -Hexane n-Eicosane Methyl isobutyl ketone Ethyl propyl ketone Propyl acetate 1-Hexanol 1-Chlorohexane 1-Hexene Benzene n -0ctyl benzene 1,2,4-Trimethyl benzene Cyclohexane Water n-Heptane 2-Methylhexane 3-Methylhexane 3-Ethylpentane 2,2-Dimethylpentane 2,3-Dimethylpentane 2,4-Dimethylpentane 3,3-Dimethylpentane 2,2,3-Trimethylbutane
Av error, %
Max error, %
Range, Torr
10-1500
40-1500b 10-15006
a Calculated as suggested by Bondi using van der Waals radii of 1.2 8, for hydrogen and 1.4 8, for oxygen with a covalent bond distance of 0.9588,. Zwolinski et al. (1971). Hala et al. (1973).
As stated in the earlier paper, eq 1correlates vapor pressures from 10 to 1500 Torr generally within about 0.546, utilizing only two adjustable parameters, s and Eo. However, the parameters listed in Tables I and I1 of the earlier paper are slightly in error and should be disregarded. Table Ia, shown here, has been prepared for 22 of these same liquids. (Insufficient precise data precluded refitting the remainder of the entries in the prior tables.) As previously, the van der Waals volume, V,, was estimated from Bondi's (1968) group-contribution method. The constant a in eq 2 was fixed for all species, as before, a t 0.0966. The parameters s and Eo are found to be correlated. However, the best-fit values reported are well defined. If either s or Eo is pre-set a t 1%off the optimum value, and the other is 392
Ind. Eng.
Chem., Fundam., Vol.
16, No. 3, 1977
L i t e r a t u r e Cited Abrams, D. S.,Massaldi. H. A,, Prausnitz,J. M., hd. Eng. Cbem., Fundam., 13, 259 (1974). Bondi, A., "Physical Properties of Molecular Crystals, Liquids, and Glasses", p 453, Wiley, New York, N.Y., 1968. Hala, E., Boublik. T., Vostech, F., "The Vapor Pressures of Pure Substances", Elsevier, New York, N.Y., 1973. Zwolinski, B. J., Wilhoit, R. C., "Handbook of Vapor Pressures and Heats of Vaporization of Hydrocarbons and Related Compounds", American Petroleum Institute Research Project 44, Texas A&M University, College Station, Texas, 1971.
Chemical Engineering Department University of California Berkeley, California 94720
A. B. Macknick J. Winnick J. M. Prausnitz*
Received for review April 22, 1977 Accepted May 10,1977
