Descriptors for solutes from the solubility of solids: trans-stilbene as an example

Abstract

Solubilities of trans-stilbene in 17 nonaqueous solvents are reported. These may be combined with literature values for the solubility in water and for the vapour pressure of stilbene to give 17 values of water–solvent partitions, P, and 17 values of gas–solvent partitions, L. Coefficients in the general solvation equations (i) and (ii) are known for all 34 of these systems, together with two additional equations for gas–water partitions. In equations (i) and (ii), the independent variables are solute descriptors as follows: R₂ is an excess molar refraction, π₂^H is the dipolarity/polarizability, Σα₂^H and Σβ₂^H are the overall hydrogen-bond acidity and basicity, Vx is the McGowan characteristic volume, and log L¹⁶ is a descriptor where L¹⁶ is the solute L-coefficient on hexadecane at 298 K.

     log SP = c + rR₂ + sπ₂^H + aΣα₂^H + bΣβ₂^H + vVx     (i)

     log SP = c + rR₂ + sπ₂^H + aΣα₂^H + bΣβ₂^H + l log L¹⁶     (ii)

We estimate R₂ as 1.45 and calculate Vx as 1.563, and then solve the total set of 36 equations to yield π₂^H = 1.04, Σα₂^H = 0.00, Σβ₂^H = 0.34 and log L¹⁶ = 7.525 units. These descriptors reproduce the 36 observed log P and log L values with a standard deviation of only 0.086 log units. This represents an entirely new method for determining solvation descriptors and is also a quite novel method for the correlation and estimation of solubilities.