Problem $1$

The enqumatic removal of urea from blood by catalyst $($enzyme$)$ Lurease follows this overall reaction:

ubrace$(N{H}_{2}CON{H}_2$ubrace${)}_{(S)}+$ubrace$(H_2$Oubrace${)}_{(W)}\frac{\text{c}\text{a}\text{t}\text{a}\text{l}\text{y}\text{s}\text{t}}{\text{c}\text{o}\text{n}\text{e}\text{a}\text{s}\text{e}}+$ubrace$(2N{H}_3$ubrace${)}_P+C{O}_2$

The mechanism for this neaction is as follows:

$ES+W\frac{{?}_{-1}}{lar{r}_{k_2}}P+E$

$\{\begin{array}{ccc}& \text{T}\text{h}\text{e}\text{t}\text{o}\text{t}\text{a}\text{l}\text{a}\text{m}\text{o}\text{u}\text{n}\text{t}& \end{array}$

$of$ catalyst $-=A$

$k_{-2}{k}_2$

The total amount

$of$ catalyst $-=A$

$k_{-2}{k}_2$

a$)$ Derive the rate expression for the ovecall react

b$)$ Simplify the rate for the case where the first reversible reaction is in equilibrium and the reaction $ES+WP+E$ is rato limiting $($slow$).$