Bunnett–Olsen equations

The equations for the relation between $log 10 ( [SH + ] [S] ) + H 0$ and $log 10 [H + ] + H 0$ for base S in aqueous mineral acid solution, where $H 0$ is Hammett's acidity function and $log 10 [H + ] + H 0$ represents the activity function $log 10 ( γ S γ H + ) γ SH +$ for the nitroaniline reference bases to build $H 0$ .

$log 10 ( [SH + ] [S] ) − log 10 [H + ] = ( Φ − 1 ) ( log 10 [H + ] + H 0 ) + p K SH +$

$log 10 ( [SH + ] [S] ) + H 0 = Φ ( log 10 [H + ] + H 0 ) + p K SH +$