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,

$$\dfrac{x}{m}=kC^{1/n}$$

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 $$1.0\times 10^{-5}$$ 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.