A student investigates the adsorption of an organic dye from an aqueous solution onto activated char — Surface Chemistry Chemistry Question
Question
A student investigates the adsorption of an organic dye from an aqueous solution onto activated charcoal. To test the Freundlich isotherm, they plot $\log(x/m)$ versus $\log C$ (where $C$ is the equilibrium concentration). The plot yields a straight line intersecting the y-axis at $0.4771$. What is the numerical value of the empirical Freundlich constant $k$? (Take $\log 3 = 0.4771$)
💡 Solution & Explanation
The logarithmic form of the Freundlich equation for solutions is $\log(x/m) = \log k + \frac{1}{n}\log C$. When plotted as a linear graph ($y = mx + c$), the y-intercept $c$ is strictly equal to $\log k$. Given that the intercept is $0.4771$, we have $\log k = 0.4771$. Since we are given $\log 3 = 0.4771$, it directly follows that the constant $k$ is $3.0$.