This paper presents in a concise way the mathematical models and experimental data of phase transitions of pure substances and solutions with new ansatz and calculation methods. In chap. 2 and chap. 3 we deal with the theoretical basics of solutions and mixtures. In chap. 4, the theory of equations-of-state is formulated, and in chap. 5 the calculation results for four pure substances (benzene, ethanol, argon, carbon dioxide) are presented and commented. In chap. 6, the equation-of-state and mixing rules for mixtures are formulated, and the calculation results for an example solution (benzene-ethanol) are discussed and compared with measured values. The paper introduces two novel methods: 1) Exact algebraic solution for phase diagrams based on Peng-Robinson and Mie-Grueneisen equation-of-state; 2) A new ansatz for mixture phase diagrams based on the weighted sum of partial pressures.
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