The Donnan osmotic pressure of a solution containing charged colloidal entities is divided into electrostatic and non-electrostatic contributions. The expression adopted for the former contribution is obtained from a general thermodynamic treatment of the diffuse double layer. Expressions are derived which allow for specific binding and which also provide a definition of amounts bound electrostatically. When the approximation is made that the electrostatic binding of indifferent coions Γ_coions is negligible the equations which result have the same form as those that apply to non-interacting uncharged systems and can be handled in the same way. The treatment provides a basis for a successful but somewhat arbitrary approach developed previously. In particular an expression for the activity coefficient of unbound counterions and coions is justified. The prediction (based on the application of the Poisson—Boltzmann equation to cell models) that Γ_coions is negative is contradicted by work concerning the significance of single ionic chemical potentials.