Department of Chemistry, Baker Laboratory, Cornell University, Ithaca, New York 14853-1301, USA.
J Phys Chem B. 2012 Aug 9;116(31):9492-9. doi: 10.1021/jp3051802. Epub 2012 Aug 1.
The second osmotic virial coefficient is in principle obtained from the second-order term in the expansion of the osmotic pressure Π or solute activity z(2) in powers of the solute density ρ(2) at fixed solvent activity z(1) and temperature T. It is remarked that the second-order terms in the analogous expansions at fixed pressure p or at liquid-vapor coexistence instead of at fixed z(1) also provide measures of the effective, solvent-mediated solute-solute interactions, but these are different measures. It is shown here how the function z(2)(ρ(2), z(1), T) required to obtain the second osmotic virial coefficient B from an expansion in ρ(2) may be obtained from an equation of state of the form p = p(ρ(1), ρ(2), T) with ρ(1) the solvent density, and also how the analogous coefficient B' in the fixed-p expansion may be so obtained. The magnitude of the difference B - B' is often much smaller than that of B and B' separately, so B' is sometimes an acceptable approximation to B. That is not true of the analogous coefficient in the expansion at liquid-vapor coexistence. These calculations are illustrated with the van der Waals two-component equation of state and applied to solutions of propane in water as an example.
第二渗透压维里系数原则上可从渗透压 Π 或溶质活度 z(2)的二阶项在固定溶剂活度 z(1)和温度 T 下的 ρ(2)幂次展开式中获得。值得注意的是，在固定压力 p 或在液-气相共存而不是在固定 z(1)下进行类似展开的二阶项也提供了有效溶剂介导的溶质-溶质相互作用的度量，但这些是不同的度量。本文展示了如何从 ρ(2)展开式中获得第二渗透压维里系数 B 所需的函数 z(2)(ρ(2), z(1), T)，并展示了如何从形式为 p = p(ρ(1), ρ(2), T)的状态方程中获得该函数，其中 ρ(1)是溶剂密度，以及如何从固定压力 p 展开式中获得类似的系数 B'。B-B'的大小通常比 B 和 B'分别的大小小得多，因此 B'有时是 B 的可接受的近似值。在液-气相共存时的展开式中的类似系数则不然。这些计算以范德华两组件状态方程为例进行了说明，并应用于丙烷在水中的溶液。
