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# According to Langmuir adsoptiom=n isotherm, the amount of gas adsorbed by the unit surface area is:[a, b, n, k are constant and P = Pressure of gas]A. $k.{{P}^{n}}$B. $\dfrac{1\,+\,bP}{aP}$C. $k.{{P}^{1/n}}$D. $\dfrac{aP}{1\,+\,bP}$

Last updated date: 11th Sep 2024
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Hint: The Langmuir adsorption isotherm is used to describe the equilibrium between adsorbate and adsorbent system, where the adsorbate adsorption is limited to one molecular layer at or before a relative pressure of unity is reached.

The Langmuir adsorption model gives an explanation of adsorption by assuming an adsorbate behaves as an ideal gas at isothermal conditions. According to the model, adsorption and desorption are reversible processes. This model even explains the effect of pressure i.e at these conditions the adsorbate's partial pressure,$\rho A$ is related to the volume of it, V, adsorbed onto a solid adsorbent. The adsorbent is assumed to be an ideal solid surface composed of a series of distinct sites capable of binding the adsorbate. The adsorbate binding is treated as a chemical reaction between the adsorbate gaseous molecule ${{A}_{g}}$ and an empty sorption site, S. This reaction yields an adsorbed species ${{A}_{ad}}$ with an associated equilibrium constant${{K}_{eq}}$:
${{A}_{g}}\,+\,S\,\rightleftharpoons \,{{A}_{ad}}$
According to Langmuir adsorption isotherm the quantity of gas adsorbed by unit area is given by:
The Langmuir adsorption equation is the following:

${{\theta }_{A}}\,=\,\dfrac{V}{{{V}_{m}}}\,=\,\dfrac{{{K}_{eq}}^{A}pA}{1\,+\,{{K}_{eq}}^{A}pA}$,
Where $\theta$ is the fractional occupancy of the adsorption sites, i.e., the ratio of $V$, the volume of gas adsorbed onto the solid, to ${{V}_{m}}$, the volume of a gas molecules monolayer covering the entire surface of the solid and completely occupied by the adsorbate. The volume of a gas molecules monolayer covering the entire surface of the solid and completely occupied by the adsorbate.
The above equation can be modified to
X = $\dfrac{aP}{1\,+\,bP}$

So, the correct answer is Option D.