混合电解质溶液热力学——从渗透系数计算溶质活度系数的新型公式和计算方法

The new equations and computating methods for calculating activity coefficients of solutes from the practical osmotic coefficients in mixed electrolyte solutions

从热力学基本关系式出发,应用变量替换,导出从混合电解质溶液的渗透系数计算溶质活度系数的通用热力学方程。分别讨论了在以离子强度I和组分离子强度分数y为变量,或以总离子浓度m和组分离子浓度分数y为变量时方程的各种实用形式。以m和y为变量的方程与C. Pan的方程相同,但不需要两电解质具有相同电价形式的限制。从电解质溶液的理论分析导出渗透系数φ的合适的函数式,使φ的曲面拟合能在较大的浓度区间上进行且有较高的精度。将拟合的φ曲面函数式代入本文的方程能非常简单地求出溶质的活度系数,解决了I=0端点的广义积分问题。四个体系的计算结果与Pitzer方程的结果吻合,本文的公式和计算方法还适用于溶质为非挥发性的非电解质体系。

The new equations for calculating the mean activity coefficients of solutes from the osmotic coefficients in mixed electrolyte solutions were derived from strict thermodynamic relations. For the ternary system of solvent (s)-electrolyte (1)-electrolyte(2), at fixeP y2, the equation is where γ1 ahe the mean activity coefficients of electrolytes in mixture; φ is the practical osmotic coefficient of solution; v; is the number of ions of electrolyte i, and vi = 1 for nonelectrolyte; m and yi(i = 1,2) are defined aswhere k1 and k2 are constants, Setting ki =vi (i = 1,2), the m and yi(1 = 1,2) denote the total ionic concentration and the fractions of the ionic concentraton. In this case, eq.(1) is converted to the same form of C. Pan's eq., but the limited condition, v1=v2, in deriving his equation is not required in thepresent paper. As ki =vi(vi(+) vi(- )/2(i = 1,2) are chosen, the m and yi(1=1,2)denote the ionic strength and the fractions of the ionic strength.From the theory of electrolyte solution, the suitable expression of φ with m (or I) and y2 was given. After the experimental data of 0 were fitted to the expression; the terms of integration and differentaion of eq.(1) were easily computed by the expression of φ, and then lnγi(i = 1,2) were obtained by eq. (1). The calculating method proposed in the paper solved the known difficult problem of calculation of infinite integration with ionic strength being equal to zero, which had teen solved by the tedious graphical methods for many years. The activity coefficients of solutes were computated for the aqueous systems of NaCl-KCl, NaCl-LiCl, NaCl-CsCl and NaCl-MnCl2, and the results agreed with those calculated using Pitzers equation. The method in the paper may also be applicable to the system containing nonvolatile nonelectrolytes.