A universal thermodynamic model of calculating mass action concentrations for structural units or ion couples in ternary and binary strong electrolyte aqueous solution was developed based on the ion and molecule coexistence theory and verified in four kinds of binary aqueous solutions and two kinds of ternary aqueous solutions. The calculated mass action concentrations of structural units or ion couples in four binary aqueous solutions and two ternary solutions at 298.15 K have good agreement with the reported activity data from literatures after shifting the standard state and concentration unit. Therefore, the calculated mass action concentrations of structural units or ion couples from the developed universal thermodynamic model for ternary and binary aqueous solutions can be applied to predict reaction ability of components in ternary and binary strong electrolyte aqueous solutions. It is also proved that the assumptions applied in the developed thermodynamic model are correct and reasonable, i.e., strong electrolyte aqueous solution is composed of cations and anions as simple ions, H2O as simple molecule and other hydrous salt compounds as complex molecules. The calculated mass action concentrations of structural units or ion couples in ternary and binary strong electrolyte aqueous solutions strictly follow the mass action law.