The complete solution to the mean-spherical approximation is given for an arbitrary mixture of ions in a dipolar solvent. The calculation is done for an overall neutral collection of charged hard spheres (ions) and dipoles (solvent) that bear a central point dipole. Previous solutions to this problem were not consistent because they did not include the solvent particles as a (neutral) solute in the mixture. The present solution accounts for this peculiar counterintuitive feature, fully and consistently. Complete expressions for the chemical potentials of the ions and solvent are provided for the first time. To illustrate, a binary 1-1 asymmetric electrolyte solution in a water-like dipolar solvent is considered, and some numerical results are examined. In particular, it is verified that a set of thermodynamic consistency relations are accurately fulfilled.

中文翻译：

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偶极溶剂中任意离子混合物的平均球面近似 (MSA) 的完整解

对于偶极溶剂中的任意离子混合物，给出了平均球近似的完整解。该计算是针对带有中心点偶极子的带电硬球（离子）和偶极子（溶剂）的整体中性集合完成的。这个问题的先前解决方案并不一致，因为它们不包括溶剂颗粒作为混合物中的（中性）溶质。本解决方案充分且一致地解释了这种特殊的违反直觉的特征。首次提供了离子和溶剂化学势的完整表达式。为了说明这一点，考虑了类水偶极溶剂中的二元 1-1 不对称电解质溶液，并检查了一些数值结果。特别是，