Problem $2(20\%)$: In an isothermal batch reactor, and a

catalytic$/$enzymatic reaction with a rate expression of the form:

$-r_A=\frac{k_1{c}_A}{1+k_2{c}_A}$

where $c_{A0}=10mo\frac{l}{L},k_1=3\mathrm{.}5s^{-1},$ and $k_2=0\mathrm{.}45\frac{L}{m}ol$

a$)$ By what percentage must the reaction time be increased to raise

the conversion of A from $0\mathrm{.}9$ to $0\mathrm{.}95?$

b$)$ If the initial conversion is $0\mathrm{.}8,$ what will the final conversion be if

the reaction time is increased by $50\%?$