Question $3(20$ pts$).$ The following data were obtained for the adsorption of benzene onto activated carbon in systems that have reached equilibrium.

a$)$ Determine the parameters for sorption of benzene on activated carbon according to the Langmuir isotherm.

b$)$ A batch treatment process has been designed to reduce the benzen concentration in a wastewater from $20\mathrm{.}0$ to $0\mathrm{.}1m\frac{g}{L}$ by adding an appropriate dose of activated carbon and mixing the suspension long enough for equilibrium to be reached. What is the minimum dose of activated carbon needed to meet

the treatment goal? What fraction of the activated carbon surface sites will be occupied?

c$)$ As a safety measure, the carbon dose added to each batch is $20\%$ larger than the requirement calculated in part $b.$ If a batch of water containing $30m\frac{g}{L}$ benzene is received, will the treatment goal of $0\mathrm{.}1m\frac{g}{L}$ be reached?