Supplement 4: Conversion of Equilibrium Constants

Equilibrium constants in electrolyte literature are often presented on the molal scale. For clarity in this section, we will use K_a,m to denote the molality equilibrium constant and K_a to denote the rational (Henry’s law scale) using mole fractions. Recall that the solvent (usually water) is on the Lewis-Randall scale. Using the molality scale for the electrolytes,

On the rational (Henry’s law) mole fraction scale, we have

To convert, consider the ln of each equation and take the difference. Inserting Eqn. 18.170,

For a 1-1 electrolyte such as NaCl, , thus . If a K_a is desired on the Lewis-Randall scale, similar conversions can be done using infinite dilution activity coefficients.