$3.$b$)$ It is proposed to install a granular activated carbon $($GAC$)$ filter to adsorb trace

metals from a raw water source. In order to establish the adsorbent capacity of the

filter, $5$ g samples of GAC were added to $100$ mL samples of varying

concentrations of raw water. The initial $($before addition of GAC$)$ and final $($after

addition of GAC$)$ concentrations of the water samples are provided in Table $1.$ It

is known that the GAC exhibits Langmuir isotherm characteristics.

Establish the maximum adsorption capacity $(q_{\text{m}\text{a}\text{x}})$ and equilibrium constant

$($binding strength$)($k$)$ by plotting the equilibrium concentrations $(C_e)$ against $(\frac{c_e}{q_e})$

on graph paper provided.

Table $1$ Initial and final trace metal concentrations of $100$ mL raw water

samples

Aide$-$m$$moire: $-$

Langmuir isotherm, $q_e=\frac{q_{\text{m}\text{a}\text{x}}k{C}_e}{1+k{C}_e}$

where:$-$

$q_e=$ amount adsorbed $at$ equilibrium $(mg$ adsorbate $\frac{?}{g}$ adsorbent$)$;

$q_{\text{m}\text{a}\text{x}}=$ maximum adsorption capacity $(mg{g}^{-1})$

$k=$ equilibrium constant $or$ binding strength $(Lm{g}^{-1})$

$C_e=$ equilibrium $(final)$ concentration $in$ solution $(mg{L}^{-1})$