Question

The Langmuir isotherm for the adsorption of a gas on a solid surface can be expressed as $\theta = \frac{Kp}{1+Kp}$The correct statement(s) about this isotherm is/are

• A. At very low pressures, plot of $\theta$ against $p$ is a straight line passing through the origin with slope equal to $K$
• B. At very high pressures, plot of $\theta$ against $p$ is a straight line parallel to the x-axis with the value of the y-intercept equal to 1
• C. The Langmuir isotherm can also be expressed as $\frac{1}{\theta} = 1 + \frac{1}{Kp}$
• D. The Langmuir isotherm is applicable for multilayer adsorption

Hint:

Langmuir isotherm is for monolayer adsorptionAt low pressure, $\theta \propto p$ and at high pressure, $\theta$ approaches 1

Answer 1

The Correct Option is A, B, C

Step 1: Low pressure limit.
When Kp is small the isotherm becomes $\theta = Kp$, a straight line through the origin. Statement A is correct.

Step 2: High pressure limit.
When Kp is large $\theta$ tends to 1, a line parallel to the pressure axis. Statement B is correct.

Step 3: Reciprocal form.
Taking the reciprocal gives $\frac{1}{\theta} = 1 + \frac{1}{Kp}$, so statement C is correct, while the multilayer claim in D is wrong.

Step 4: Answer.
\[ \boxed{\text{A, B and C}} \]