The equations for the relation between \(\log _{10}(\frac{\rm{[SH}^{+}\rm{]}}{[S]})+\rm{H}_{0}\) and \(\log _{10}\rm{[H}^{+}\rm{]}+\rm{H}_{0}\) for base S in aqueous mineral acid solution, where \(\rm{H}_{0}\) is Hammett's acidity function and \(\log _{10}\rm{[H}^{+}\rm{]}+\rm{H}_{0}\) represents the activity function \(\frac{\log _{10}(\gamma _{S}\ \gamma _{H^{+}})}{\gamma _{\rm{SH}^{+}}}\) for the nitroaniline reference bases to build \(\rm{H}_{0}\). \[\log _{10}(\frac{[\rm{SH}^{+}]}{[\rm{S}]})- \log _{10}[\rm{H}^{+}]=(\varPhi - 1)\ (\log _{10}\rm{[H}^{+}\rm{]}+\rm{H}_{0})+pK_{\rm{SH}^{+}}\] \[\log _{10}(\frac{[\rm{SH}^{+}]}{[\rm{S}]})+H_{0}=\varPhi \ (\log _{10}[\rm{H}^{+}]+\rm{H}_{0})+pK_{\rm{SH}^{+}}\]