Problem $2$: $(40$ points$)$

Given$)$ Sorption by PAC $($powered activated carbon$)$ is often used to remove VOC $($volatile organic carbon$)$ such as benzene from water. To characterize interphase mass transfer of benzene between water and PAC, laboratory experiment was conducted using completely mixed batch reactors. The specific surface area per mass of PAC $(a_s)$ is $5,000c\frac{m^2}{g}.$ Exactly $0\mathrm{.}1g$ of PAC was added in $1L$ water. Keeping CMBR sterile conditions, no decay of benzene occurred in water phase as well as PAC phase.

CMBR $($Completely Mixed Batch Reactor$)$ Experiment to Characterize Inter$-$phase Mass Transfer between PAC and Water

er$-$phase concentration of benzene ter$-$phase volume

$($Assumption: no reaction in water phase$)$

$$ Solid phase $($sorbent$)$: powdered activated carbon $($PAC$)$

$m$ : the added mass of PAC

as: specific surface area per mass of PAC

Co: water$-$phase benzene concentration on the surface of PAC $($assuming $Co=0)$

In the above CMBR condition, water$-$phase benzene concentrations $(Cw)$ were measured at different time points as seen in the following table.

$$ Table $1>$ CMBR Experiment Results

$\backslash$table$[[$Time $($min$),$Benzene concentration in Water Phase, $Cw(\frac{g}{L})$