What is theta ,b and p in langmuir istherm?
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The Langmuir adsorption model explains adsorption by assuming an adsorbatebehaves as an ideal gas at isothermalconditions. At these conditions the adsorbate's partial pressure, {\displaystyle p_{A}}, is related to the volume of it, V, adsorbed onto a solid adsorbent. The adsorbent, as indicated in the figure, is assumed to be an ideal solid surface composed of series of distinct sites capable of binding the adsorbate. The adsorbate binding is treated as a chemical reaction between the adsorbate molecule {\displaystyle A_{\text{g}}} and an empty site, S. This reaction yields an adsorbed complex {\displaystyle A_{\text{ad}}} with an associated equilibrium constant {\displaystyle K_{\text{eq}}}:
{\displaystyle {\ce {{A_{g}}+S<=>A_{ad}}}}
From these assumptions the Langmuir isotherm can be derived (see below), which states that
{\displaystyle \theta _{A}={\frac {V}{V_{\text{m}}}}={\frac {K_{\text{eq}}^{A}\,p_{A}}{1+K_{\text{eq}}^{A}\,p_{A}}},}
where {\displaystyle \theta _{A}} is the fractional occupancy of the adsorption sites, and {\displaystyle V_{\text{m}}} is the volume of the monolayer. A continuous monolayer of adsorbate molecules surrounding a homogeneous solid surface is the conceptual basis for this adsorption model.[1]
The Langmuir isotherm is formally equivalent to the Hill equation in biochemistry.
The Langmuir adsorption model explains adsorption by assuming an adsorbatebehaves as an ideal gas at isothermalconditions. At these conditions the adsorbate's partial pressure, {\displaystyle p_{A}}, is related to the volume of it, V, adsorbed onto a solid adsorbent. The adsorbent, as indicated in the figure, is assumed to be an ideal solid surface composed of series of distinct sites capable of binding the adsorbate. The adsorbate binding is treated as a chemical reaction between the adsorbate molecule {\displaystyle A_{\text{g}}} and an empty site, S. This reaction yields an adsorbed complex {\displaystyle A_{\text{ad}}} with an associated equilibrium constant {\displaystyle K_{\text{eq}}}:
{\displaystyle {\ce {{A_{g}}+S<=>A_{ad}}}}
From these assumptions the Langmuir isotherm can be derived (see below), which states that
{\displaystyle \theta _{A}={\frac {V}{V_{\text{m}}}}={\frac {K_{\text{eq}}^{A}\,p_{A}}{1+K_{\text{eq}}^{A}\,p_{A}}},}
where {\displaystyle \theta _{A}} is the fractional occupancy of the adsorption sites, and {\displaystyle V_{\text{m}}} is the volume of the monolayer. A continuous monolayer of adsorbate molecules surrounding a homogeneous solid surface is the conceptual basis for this adsorption model.[1]
The Langmuir isotherm is formally equivalent to the Hill equation in biochemistry.
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