where a A + is the thermodynamic activity of the cation A + . We assumed an activity of 0.1, which for an ideal solution correspond to a cation concentration of 0.1 M. The derivation of the Gibbs free energy of adsorption for the independent processes of deprotonation and cation adsorption is provided in the Supplementary Information (SI). For both processes of deprotonation and alkali metal cation adsorption at NiOOH(0001)/water, the total free energy is given by,