Problem $2.(100$ points$)$ An appealing partial solution to the greenhouse gas problem is

to convert biomass into liquid fuels. Most of biomass is composed of linked C$6$ sugars

$(C_6{H}_{12}{O}_6)$ and $C5$ sugars $(C_5{H}_{10}{O}_5),$ which can be broken down by an enzyme secreted

by fungi. Ideally, the sugars could then be converted into ethanol or other liquids in

subsequent reactions.

This mechanism is proposed for the enzymatic breakdown:

$C_{11}{H}_{22}{O}_{11}+$ Enzyme $$ Complex $,(reaction1)$

Complex $$ Enzyme $+C_6{H}_{12}{O}_6+C_5{H}_{10}{O}_5,(reaction2)$

Reaction $1$ is expected to be reversible under some conditions, but reaction $2$ is

expected to be irreversible.

Experimental rate data on this enzyme from low$-$conversion batch$-$reactor

experiments can be fit to this expression:

$d\frac{C_5{H}_{10}{O}_5}{d}t=r=a[C_{11}{H}_{22}{O}_{11}{]}_0\frac{[\text{E}\text{n}\text{z}\text{y}\text{m}\text{e}{]}_0}{1+b^{**}[C_{11}{H}_{22}{O}_{11}{]}_0}$

$a=2{10}^4$ liter $\frac{?}{?}$ mole$-$second $,b={10}^8$ liter $\frac{?}{?}$ mole.

where $[C_{11}{H}_{22}{O}_{11}{]}_0$ and $[$Enzyme