A plot of log((x)/(M)) against logP for the adsorption of a...

A plot of $\log \left(\frac{x}{M}\right)$ against $\log P$ for the adsorption of a gas on a solid gives a straight line with slope equal to:
(a) $\frac{1}{n}$
(b) $n$
(c) $\log \mathrm{K}$
(d) $\mathrm{K}$

Key Concepts

Freundlich Adsorption Isotherm

The Freundlich adsorption isotherm is an empirical model that describes the adsorption process on heterogeneous surfaces. It is commonly represented by the equation x/M = K * P^(1/n), where x/M is the amount of gas adsorbed per unit mass of the solid, P is the pressure of the gas, K is an equilibrium constant, and 1/n is a parameter that indicates the adsorption intensity or surface heterogeneity. This model highlights the nonlinear relationship between the adsorbed amount and the pressure.

Logarithmic Transformation

Logarithmic transformation is a mathematical technique used to convert a power law relationship into a linear one. By taking the logarithm of both sides of the Freundlich equation, log(x/M) = log(K) + (1/n) * log(P), the nonlinear relationship becomes linear. This transformation simplifies the analysis, allowing researchers to determine parameters like 1/n and log(K) from the slope and intercept of the resulting straight-line plot.

Interpretation of Slope in Log-Log Plots

In log-log plots, the slope of the line represents the exponent in the original power law equation. For the Freundlich adsorption isotherm, the slope of the plot of log(x/M) versus log(P) directly corresponds to 1/n. This interpretation allows for a straightforward determination of the adsorption intensity factor, which is critical for understanding the adsorption mechanism on the solid surface.

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