Bunnett–Olsen equations

https://doi.org/10.1351/goldbook.B00758
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 $$H_{0}$$. $\log _{10}(\frac{\text{[SH}^{+}\text{]}}{\text{[S]}})- \log _{10}\text{[H}^{+}\text{]}=(\varPhi - 1)\ (\log _{10}\text{[H}^{+}\text{]}+H_{0})+pK_{\text{SH}^{+}}$ $\log _{10}(\frac{\text{[SH}^{+}\text{]}}{[S]})+H_{0}=\varPhi \ (\log _{10}\text{[H}^{+}\text{]}+H_{0})+pK_{\mathrm{SH}^{+}}$