JEE Advanced 2026 · Paper 2, Chemistry question 11

At a given temperature, 0.45 g of acetic acid in 50 mL of water is shaken with 1.0 g of charcoal and the pH of the resulting solution is 3.0. Assume the adsorption of acetic acid from the aqueous solution by charcoal follows Freundlich isotherm,
$$\frac xm=kC^{1/n}$$
If the plot of $\log_{10}(x/m)$ against $\log_{10}C$ gives a straight line with slope 1, the value of $k$ in L mol$^{-1}$ is ____.

Given: The molar mass of acetic acid is 60 g mol$^{-1}$.
The acid dissociation constant of acetic acid is $1.0\times10^{-5}$ at the given temperature.
$x$ is the mass (in grams) of acetic acid adsorbed.
$m$ is the mass (in grams) of charcoal.
$C$ is the equilibrium concentration of acetic acid in the solution after the adsorption is complete.
$k$ and $n$ are constants for acetic acid-charcoal system at the given temperature.