(Solved): 4) The hydrolysis of urea by urease occurs in a batch bioreactor. The reaction follows a MichaelisM ...

4) The hydrolysis of urea by urease occurs in a batch bioreactor. The reaction follows a MichaelisMenten mechanism. The following kinetic data are available for urea: \( K_{m}^{\prime}=7.7 \times 10^{-2} \mathrm{M}, \mathrm{v}_{\mathrm{m}}=0.5 \) \( \mathrm{mol} /(\mathrm{L} \cdot \mathrm{min}) \). The initial concentration of urea in the reactor is \( 50 \mathrm{M} \). \[ \begin{aligned} E+S & \leftrightarrow E S \stackrel{k_{2}}{\rightarrow} E+P \\ v &=\frac{V_{m}[S]}{K_{m}+[S]} \end{aligned} \] Calculate the concentration of urea in the reactor 10 minutes after the reaction starts.