$(35$ points$)$ A wastewater solution having a volume of $2\mathrm{.}5m^3$ contains $0\mathrm{.}25kg$ phenol $\frac{?}{m^3}$ of solution.

This solution is mixed thoroughly in a batch process with $3\mathrm{.}0kg$ of granular activated carbon until

equilibrium is reached.

a$.$ Use the isotherm from Example $3-2$ and calculate the final equilibrium values and the percent

phenol extracted.

b$.$ If we want to remove $90\%$ phenol, how much activated carbon should be added to the solution?

Plot both the isotherm and mass balance curves on the q versus $c$ chart.

c$.$ You find another isotherm in literature that can be used to describe phenol$-$activated carbon data

as $q=\frac{0\mathrm{.}421c}{0\mathrm{.}0315+c}.$ Rework your answers for parts $($a$)$ and $($b$).$