A mixture of A and B is adsorbed on a solid for which the...

A mixture of A and B is adsorbed on a solid for which the adsorption isotherm follows the Langmuir equation. If the mole fractions in the gas at equilibrium are $y_{\mathrm{A}}$ and $y_{\mathrm{B}},$ what is the equation for the adsorption isotherm in terms of total pressure? What is the expression for the mole fraction of A in the adsorbed gas in terms of $K_{\mathrm{A}}, K_{\mathrm{B}}, y_{\mathrm{A}},$ and $y_{\mathrm{B}} ?$

Key Concepts

Langmuir Adsorption Isotherm

The Langmuir adsorption isotherm is a model that describes the adsorption of molecules onto a homogeneous solid surface, assuming that adsorption occurs at specific homogeneous sites within the surface. It further assumes that each site can accommodate only one molecule and that there are no interactions between the adsorbed molecules, leading to a saturation point or monolayer coverage.

Equilibrium Adsorption Constants

Equilibrium adsorption constants (often denoted as K values) quantify the affinity of each gas component for the adsorbent surface. They are crucial in determining how the adsorption capacity varies with pressure and are used to relate the pressure of each component to the amount adsorbed on the surface.

Total Pressure and Partial Pressure Dependency

In adsorption processes involving gas mixtures, the total pressure of the system is partitioned into the partial pressures of the individual components based on their mole fractions. These partial pressures directly influence the extent of adsorption for each component, and the overall adsorption behavior can be expressed in terms of total pressure by incorporating the mole fractions.

Adsorbed Phase Composition

The composition of the adsorbed phase often differs from that of the bulk gas mixture because different components may have different adsorption affinities. By combining equilibrium constants with the gas-phase mole fractions, one can derive expressions for the mole fractions in the adsorbed phase, which reveal preferential adsorption and selectivity in multicomponent systems.

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