Adsorption of a gas follows Freundlich adsorption isotherm....

Adsorption of a gas follows Freundlich adsorption isotherm. $x$ is the mass of the gas adsorbed on mass $\mathrm{m}$ of the adsorbent. The plot of $\frac{x}{m}$ versus $\log p$ is shown in the given graph. $\frac{x}{m}$ is proportional to :(a) $p^{2 / 3}$ (b) $p^{3 / 2}$ (c) $p^{3}$ (d) $p^{2}$

Adsorption of a gas follows Freundlich adsorption isotherm. $x$ is the
mass of the gas adsorbed on mass $\mathrm{m}$ of the adsorbent. The plot of $\frac{x}{m}$
versus $\log p$ is shown in the given graph. $\frac{x}{m}$ is proportional to :(a) $p^{2 / 3}$
(b) $p^{3 / 2}$
(c) $p^{3}$
(d) $p^{2}$

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Key Concepts

Adsorption Isotherms

Adsorption isotherms are models that describe the relationship between the amount of substance adsorbed on a surface and the pressure (or concentration) of that substance in the contacting phase at constant temperature. They are essential for understanding surface phenomena, determining adsorption capacities, and designing systems in catalysis, separation, and environmental applications.

Freundlich Adsorption Isotherm

The Freundlich adsorption isotherm is an empirical model used to describe adsorption on heterogeneous surfaces. It is typically expressed in the form x/m = k * p^(1/n), where x/m is the amount of gas adsorbed per unit mass of adsorbent, p is the pressure of the gas, and k and n are constants. This model implies that the adsorption process is non-uniform and the amount adsorbed increases with pressure at a rate that depends on the exponent 1/n.

Logarithmic Transformation of Isotherms

Taking the logarithm of the Freundlich isotherm equation transforms it into a linear relationship: log(x/m) = log k + (1/n) log p. This linear form is beneficial for analyzing experimental data, as the slope of the straight-line plot gives the value of 1/n, which indicates the intensity or favorability of the adsorption process.

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