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