The reaction below in a certain solvent is first order with respect to $(C{H}_3{)}_{3}CBr$ and zero order with respect to $OH.$ In several experiments, the rate constant $k$ was determined at different temperatures.

$(C{H}_3{)}_{3}CBr+O{H}^{-}(C{H}_3{)}_3$COH$+B{r}^{-}$

A plot of $ln(k)$ versus $\frac{1}{T}$ was constructed resulting in a straight line with a slope value of $-1\mathrm{.}10{10}^{4}K$ and $y-$intercept of $33\mathrm{.}5.$

Assume $k$ has units of $s^{-1}.$

$($a$)$ Determine the activation energy for this reaction.

$k\frac{J}{m}ol$

$($b$)$ Determine the value of the frequency factor $A.$

$s^{-1}$

$($c$)$ Calculate the value of $k$ at $23C.$

$s^{-1}$