Sodium benzoate, $Na{C}_7{H}_5{O}_2,$ is used as a preservative in foods. Consider a $50\mathrm{.}0mL$ sample of $0\mathrm{.}250M$

$Na{C}_7{H}_5{O}_2$ being titrated by $0\mathrm{.}200MHBr.$ Calculate the $pH$ of the solution: $($The $K_b$ value for the benzoate

ion is $1\mathrm{.}6{10}^{-8})$

a$.$ When no $HBr$ has been added

b$.$ After the addition of $50\mathrm{.}0mL$ of the $HBr$ solution

c$.$ At the equivalence point

d$.$ After the addition of $75\mathrm{.}0mL$ of the $HBr$ solution.