A common way to measure $K_d$ values is to measure isotherms in batch

experiments. To this end, the equilibrium concentrations of a given compound in

the solid phase $(C_s)$ and in the aqueous phase $(C_w)$ are determined at various

compound concentrations and$/$or solid$/$water ratios.

Consider the adsorption of $1,4-$dinitrobenzene $(1,4-$DNB$)$ to the homoionic clay

mineral, $K^{+}-$illite. $1,4-$DNB forms electron donor$-$acceptor complexes with clay

minerals. In a series of batch experiments, Hadarlein et al$.,(1996)$ measured the

data at $pH7\mathrm{.}0$ and $20C$ given below and plotted in the figure. Using this data,

estimate $K_d$ values for $1,4-$DNB for equilibrium concentrations of $1,4-$DNB in the

aqueous phase of $0\mathrm{.}20M$ and of $15M$ respectively. Derive appropriate isotherms

for estimating these $K_d$ values.

Hint: you may try fitting with Freundlich isotherm and Langmuir isotherm and compare the

results.