Solid–liquid phase equilibria of the quaternary system (Li + K + Mg + SO₄ + H₂O) at 288.15 K were investigated with the isothermal dissolution method. The diagrams of solubilities, densities and refractive indices were plotted, respectively. The solubilities diagram of the quaternary system includes three invariant points cosaturated with three salts and five crystallization zones. Two kinds of double salts K₂SO₄·MgSO₄·6H₂O and Li₂SO₄·K₂SO₄ were found, and no solid solution was formed. Pitzer theory for aqueous electrolyte solution and its extended Harvie-Møller-Weare (HMW) model was used to calculate the solubilities of the quaternary system. A comparison between the calculated and the experimental results shows that the predicted solubilities obtained with the extended HMW model agree well with experimental data.

中文翻译：

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288.15 K时含锂，钾，镁和硫酸盐的四元体系的实验和热力学建模研究

用等温溶解法研究了四元体系（Li + K + Mg + SO ₄ + H ₂ O）在288.15 K时的固液相平衡。分别绘制了溶解度，密度和折射率的图。四元系统的溶解度图包括三个不变点，这些不变点与三个盐和五个结晶区共饱和。两种复盐K ₂ SO ₄ ·MgSO ₄ ·6H ₂ O和Li ₂ SO ₄ ·K ₂ SO ₄被发现，没有形成固溶体。电解质水溶液的Pitzer理论及其扩展的Har​​vie-Møller-Weare（HMW）模型用于计算四元体系的溶解度。计算结果与实验结果之间的比较表明，扩展的HMW模型获得的预测溶解度与实验数据吻合良好。