Ternary solid–liquid phase equilibrium and phase diagram for DL-malic acid+fumaric acid+water system and molecular simulation

Solubility of DL-malic acid and fumaric acid in water for binary and ternary systems was determined through high-performance liquid chromatography (HPLC) at atmospheric pressure in this study. Six isothermal ternary phase diagrams were established at temperatures of 283.15, 293.15, 303.15, 313.15, 323.15, and 333.15 K. Every isothermal ternary phase diagram contains three crystalline regions (pure DL-malic acid, pure fumaric acid, and mixture of DL-malic acid and fumaric acid), two co-saturated boundary curves, and one invariant co-saturated point. All diagrams show that the crystalline region of fumaric acid (III) is significantly larger than that of DL-malic acid (II) at six temperatures. Wilson, NRTL, and Margules models were used to correlate and predict binary and ternary system data and the corresponding calculation precision was assessed using relative average deviation (RAD) and root-mean-square deviation (RMSD). The calculated results of Wilson and NRTL models were consistent with experimental data, and maximum values of RAD and RMSD were 2.93 × 10−2 and 3.67 × 10−3, respectively. Margules model can be used to fit solubility data of DL-malic acid unlike those of fumaric acid. Interaction energy and hydrogen bond length of DL-malic acid and fumaric acid with water were calculated via molecular simulation, and the results can be used to explain solubility behavior of DL-malic acid and fumaric acid in water.