Langmuir Isotherm Equation

The Langmuir isotherm is a model used in surface chemistry to describe the relationship between the pressure of a gas and the amount of gas adsorbed onto a solid surface at a constant temperature.

Key Variables

• Y: Mass of gas adsorbed per gram of adsorbent.
• p: Pressure of the gas.
• Y_m: Maximum adsorption capacity (mass of gas adsorbed per gram of adsorbent when the surface is fully covered, i.e., the monolayer capacity).
• b: Langmuir constant, related to the adsorption energy.

The Langmuir Isotherm Formula

The Langmuir adsorption isotherm is mathematically expressed as:

$Y = \frac{Y_m \cdot b \cdot p}{1 + b \cdot p}$

Analysis of Options

Comparing the standard Langmuir isotherm equation with the provided options:

• Option 1: $Y = Ym.b.p/(1+b.p)$ - This matches the derived Langmuir isotherm equation.
• Option 2: $1/Y = Ym.b.p/(1+b.p)$ - Incorrect rearrangement.
• Option 3: $Y = 1/(Ym.b.p/(1+b.p))$ - Incorrect inversion.
• Option 4: $Y = Ym.b.p/(1-b.p)$ - The denominator term is incorrect.

Conclusion

The correct expression for the Langmuir isotherm, relating the amount adsorbed (Y) to pressure (p), is given by Option 1.