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J . Phys. Chem. 1989, 93, 5272-5279
Second Virial Coefficients of Aqueous Alcohols at Elevated Temperatures: A Calorimetric Studyt Donald G . Archer Electrolyte Data Center, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 (Receioed: September 26, 1988; In Final Form: February 6, 1989)
Enthalpies of dilution of cyclohexanol (aq) to 448 K and of myo-inositol (aq) and of cyclohexanol + myo-inositol (aq) to 398 K are reported. These results, along with enthalpies of dilution for 1-butanol (aq) to 448 K and for 2-methyl-2-propanol (aq) to 423 K, were combined with freezing point depression measurements and ambient-temperature enthalpy of dilution and heat capacity measurements in order to provide the excess Gibbs energy for the aqueous solutes from 273 to 523 K. These excess Gibbs energies were then used to provide parameters for an additivity scheme that permits an approximation of the excess Gibbs energy, and thus the solute and solvent activity coefficients, for dilute aqueous alcohols for which high-temperature data do not exist. These excess Gibbs energies were also used to estimate the aqueous-solution second virial coefficients of the alcohols and of cyclohexane (as), 1-butane (aq), and 2-methylpropane (aq) in the McMillan-Mayer convention. These virial coefficients for the aqueous hydrocarbons, when compared to gas-phase virial coefficients for the hydrocarbons, suggest that the effect of low-temperature (298 K) water is to lessen the pairwise attraction of aqueous hydrocarbon over that found in the gas phase at the same temperatur,e and that this lessening of the pairwise attraction diminishes at higher temperatures.
Introduction Thermodynamic properties, such as solute activity coefficients, are important in determining the feasibility of reaction schemes and the extent of reactions in solution. Measurement of thermodynamic properties for all possible constituents of all possible reactions is, of course, impossible. Therefore, it is important to obtain good thermodynamic results for a few model compounds, from which the estimation or approximation of values for other similar compounds is possible. Savage and Wood’ proposed a simple additivity scheme that allowed values of the sign and magnitude of the enthalpy of the pairwise interaction of various functional groups in aqueous solution to be calculated for 298.15 K. The Savage-Wood principle was subsequently expanded to excess Gibbs and to a wider range of functional group^.^-^ Recently, Blandamer and coauthor^^^^ have applied the Savage-Wood additivity scheme to problems in kinetics and electrolyte solutions. The Savage-Wood functional group interaction energies allow calculation of approximate values of the Gibbs energy of pairwise interaction, and thus approximation of the solute and water activity coefficients, for dilute aqueous solutions of small nonelectrolyte solutes, or aqueous solutions of mixtures of these solutes, for 298.15 K in the absence of experimental data. If this additivity relation is valid at higher temperatures, then measurement of excess thermodynamic properties for a few, carefully selected, model alcohols would allow an approximation of the excess Gibbs energy of dilute solutions of other alcohols, and mixtures of dilute aqueous alcohols, a t elevated temperatures. Due to the scarcity of any excess thermodynamic results for aqueous alcohols at elevated temperatures, the success of such an approximation scheme would be of some significance. The present contribution is concerned with the pairwise interaction of solutes containing within their molecular structure some functionality that might be considered ‘hydrophobic”. Aqueous solutions of hydrophobic solutes have long been the subject of curiosity for scientists. An enormous body of research, both theoretical and empirical, concerning solutions of such solutes has accumulated over the decades. However, most of this work has been exclusively devoted to the behavior of these solutions at 298.1 5 K or for a small temperature interval centered about room temperature. Limiting the scope of observation to such a ‘Certain commercial materials are identified in this paper in order to adequately specify the experimental procedure. Such identification does not imply recommendation or endorsement by either the US.Government or the National Institute of Standards and Technology, nor does it imply that the equipment or materials identified are necessarily the best available for the purpose
narrow temperature region might provide only a narrow view of the physical effects that create the solution behavior observed at room temperature. Recent improvements in the sensitivity levels of high-temperature, mass-flow calorimeters now permit measurement of enthalpies of dilution of aqueous solutions at low concentrations and Thermodynamic relationships allow high temperature^.^-'^ calculation of certain other thermodynamic properties from these measurements. In the present paper, enthalpies of dilution of binary and ternary aqueous solutions of cyclohexanol and inositol at temperatures somewhat higher than room temperature are presented. These results, when combined with existing freezing point depression measurements for these systems, within the Savage-Wood additivity scheme, provide a method for estimating the activity coefficients of other alcohol solutes, for which data do not exist, in aqueous solution at elevated temperatures. Cyclohexanol and inositol were chosen because they provide for large numbers of the functional groups required for the Savage-Wood additivity scheme for aqueous alcohols. In addition, recent calorimetric results for l-butanol (aq) to 448 K and for 2-methyl2-propanol (aq) to 423 K have been collected and used to provide calculated values of their excess Gibbs energy. The butanol results were compared with the values calculated from the additivity scheme at high temperature. The present results have also been used to estimate virial coefficients for aqueous hydrocarbons. A comparison of these aqueous-solution virial coefficients with gas-phase virial coefficients is used to examine the effect of temperature on pairwise solute association in aqueous solutions. (1) Savage, J. J.; Wood, R. H. J. Solution Chem. 1976, 5, 733. (2) Okamoto, B. Y.; Wood, R. H.; Thompson, P. T. J . Chem. Soc., Faraday Trans. 1 1978, 7 4 , 1990. (3) Spitzer, J . J.: Tasker, 1. R.; Wood, R. H. J . Solution Chem. 1984, 13, 221. (4) Tasker, I. R.; Wood, R. H. J , Solution Chem. 1982, 11, 295, 469, 481, 729. ( 5 ) Blackburn, G . M.;Lilley, T. H.; Walmsley, E. J. Chem. SOC., Faraday Trans. 1 1980, 76, 915; 1982, 78, 1641; 1985, 81, 2191.
( 6 ) Suri, S. K.; Spitzer, J . J.; Wood, R. H.; Abel, E. G.; Thompson, P.T. J . Solution Chem. 1985, 14, 7 8 1. ( 7 ) Blokzijl, W.; Jager, J.; Engberts, J. B. F. N.; Blandamer, M. J. J . Am. Chem. Soc. 1986, 108, 6411. (8) Blandamer, M. J.; Burgess, J.; Cottrell, M. R.; Hakin, A. W. J . Chem. Soc., Faraday Trans. 1 1987, 83, 3039. (9) Mayrath, J . E.; Wood, R. H. J . Chem. Thermodyn. 1982, 1 4 , 15. (IO) Busey, R. H.; Holmes. H. F.; Mesmer, R. E. J, Chem. Thermodyn. 1984, 16, 343. ( 1 I ) Archer, D. G.; Albert, H. J.; White, D. E.; Wood, R. H. J . Colloid lnterface Sci. 1984, 100, 84.
This article not subject to U.S. Copyright. Published 1989 by the American Chemical Society
The Journal of Physical Chemistry, Vol. 93, No. 13, 1989 5213
Second Virial Coefficients of Aqueous Alcohols
Experimental Section Cyclohexanol (Fisher Certified) was analyzed for water content by Karl-Fisher titration. Water content was found to be
