where K a,acid ≡ 10 -pK a,acid is the acidity constant of the weak acid group and a i ≡ c i c ref exp (βµ ex i ) is the relative activity of particle type i. c i and µ ex i are the concentration and the excess chemical potential of the particle type i, respectively, and β = 1/(k B T ). Here and in the following, we choose the reference concentration c ref = 1 M. Introducing the pH-value of the solution,