$[30$ Marks$]$

Question $3$

Adsorption study is carried out in a mini pilot plant by contacting activated carbon with effluent water from a biological process until equilibrium is reached. Activated carbon is added to each of the six pots containing $0\mathrm{.}5$ litres of effluent water with an initial concentration of $2\mathrm{.}54m\frac{g}{L}.$ The obtained equilibrium data, expressed in total organic carbon $($TOC$),$ is presented in Table $3\mathrm{.}1.$ Plot the Langmuir isotherm and determine the values of the constants.

Table $3\mathrm{.}1$: Mini pilot plant equilibrium adsorption data

$\backslash$table$[[$Pot No$.,$Carbon Dosage $($mg$),$TOC $($mg$/$L$)],[1,8\mathrm{.}8,1\mathrm{.}94],[2,19\mathrm{.}4,1\mathrm{.}34],[3,28,1\mathrm{.}04],[4,56,0\mathrm{.}64],[5,112,0\mathrm{.}34],[6,280,0\mathrm{.}14]]$

$[20$ Marks$]$