To make the discussion more concrete, consider a colloidal particle with Z active surface groups placed at the center of a cubic simulation cell, see Fig. . The cell also contains some number of H 3 O + , Cl -, and Na + ions and is overall charge neutral. We now run the reactive MC simulation to calculate how many of Z surface groups will become protonated. After the system has relaxed to equilibrium, we find that on average N of the surface sites are protonated. The canonical partition function of a colloidal particle with N protonated sites can be written as: