The connection between Young's rule for apparent molar volumes and a Young's rule for density

It is shown that the Young's rule approximation for apparent molar volumes is equivalent to a Young's rule approximation for density, provided that volumetric concentrations are used. If the densities of the constituent binary solutions are evaluated at the molar ionic strength S of the ternary solution, for example, then $$d(S) = y_1 d_1 (S) + y_2 d_2 (S)$$ where the y _i are ionic strength fractions. However, if the binary solution densities d _i are evaluated at the same total equivalent concentration E of the ternary solution, then the coefficients of d_i become equivalent fractions, etc. A small correction term can be included to improve agreement with experiment, and the results are easily extended to multicomponent systems. This form of the density rule does not follow from Young's rule if the various quantities are in molality or other mass units. Relations among various types of apparent volumes are clarified. Three binary evaluation strategies are considered for both volume and mass units, based on evaluating binary solution densities at constant molarity, constant equivalents, and constant ionic strength. Some binary approximation examples are given for aqueous solutions.