$($a$)$ Derive an expression for the $pH$ of a weak acid in aqueous medium.

$($b$)$ What will be the $pH$ of a solution of benzoic acid of concentration $6\mathrm{.}1\frac{g}{L}$ in aqueous medium? for $[$:$C_6{H}_5\frac{C}{O}OH={10}^{-4\mathrm{.}2}$