On Abraham's Linear Equations in Thermodynamics of Solution of Gaseous Solutes in Water and Nonaqueous Solvents

Abstract

Regarding the standard entropy and enthalpy of solution of gaseous solutes in solvents, δS°_s and δH°_s, Abraham's linear equations are examined to clarify the significance of th e solute parameter R_HS, and the solvent parameters. On the basis of a previous work on ionic hydration, J. Phys. Soc. Jpn.55, 1021(1986), an effective solute radius re=2r_sw(δS°_{s, m}/δS°_cw)^1/2 is introduced after discussing the correlation between δS°_sx. and the square of the van der Waals b radius rb. Here the subscripts m and x of δS°_s denote the scale of molality and of mole fraction, δS°_cx is the standard entropy of condensation of water vapor, -118.8, J.mol-1.K-1 at 298 K, and r_sw is the Stokes radius of water, 1.07×10^-8cm at 298 K. It is found out that r_e² just equals 2 R_HS. The effective area r_e2 can be extensively used in nonaqueous solvents. Referring to solutes and solvents treated by Abraham, δS°_{s, x}, δH°_s, and the standard Gibbs energy of solution δG°_sx can be expressed as linear, equations of r_e², with coefficients B_S and B_H and constant terms A_S and A_H characteristic of solvents. Effec tive solute radii r_e.o at δG°_{s, x}=0 are calculated for 28 solvents by using individual values of A_H, A_S, B_H, and B_S. For water alone, there is no real value of re.o. For 27 nonaqueous solven ts, the averaged value of r_e.o is (2.56±0.20)×10^-8 cm, by which an averaged nonaqueous solvent is discussed. An excess amount of δG°_{s, x}, for water from that for the averaged nonaqueous solvent is attributed to the hydrophobic hydration of solutes.