Show that the maximum enzyme catalysed reaction rate will occur for
`[H^(+)]_("opt")=sqrt(k_(1)k_(2)`
The general pH control enzyme catalysed reaction is
`EH_(2)^(2+) hArr EH^(+) hArr E`
Only `EH^(+)` is capable for binding substrate and catalysing the desired reaction,
`k_(1)=([EH^(+)][H^(+)])/([EH_(2)^(2+)]), k_(2) =([E][H(+)])/([EH^(+)]`

Explanation

`k_(1)k_(2)=([E][H^(+)]^(2))/([EH_(2)^(2+)])`
In pH control it may be considered that `[E]~~[EH_(2)^(2+)]`, i.e., enzyme combines almost completely with `H^(+)` ions.
Thus, `k_(1)k_(2)~~[H^(+)],[H^(+)]=sqrt(k_(1)k_(2))`