The equations for the relation between \(\log _{10}(\frac{\text{[SH}^{+}\text{]}}{[S]})+\text{H}_{0}\) and \(\log _{10}\text{[H}^{+}\text{]}+\text{H}_{0}\) for base S in aqueous mineral acid solution, where \(\text{H}_{0}\) is Hammett's @A00081@ and \(\log _{10}\text{[H}^{+}\text{]}+\text{H}_{0}\) represents the activity function \(\frac{\log _{10}(\gamma _{S}\ \gamma _{H^{+}})}{\gamma _{\text{SH}^{+}}}\) for the nitroaniline reference bases to build \(\text{H}_{0}\). \[\log _{10}(\frac{[\text{SH}^{+}]}{[\text{S}]})- \log _{10}[\text{H}^{+}]=(\varPhi - 1)\ (\log _{10}\text{[H}^{+}\text{]}+\text{H}_{0})+pK_{\text{SH}^{+}}\] \[\log _{10}(\frac{[\text{SH}^{+}]}{[\text{S}]})+H_{0}=\varPhi \ (\log _{10}[\text{H}^{+}]+\text{H}_{0})+pK_{\text{SH}^{+}}\]