Question

Consider Langmuir adsorption of a gas on a uniform solid surface having N number of surface sites. The free and adsorbed gas molecules are in dynamic equilibrium. If the fractional surface coverage is \( \theta \), the rate of adsorption of the gas is proportional to

• A. \( N\theta \)
• B. \( N(1 - \theta) \)
• C. \( N \left( \frac{\theta}{1 - \theta} \right) \)
• D. \( N \left( \frac{1}{1 - \theta} \right) \)

Hint:

In Langmuir adsorption, the rate of adsorption is proportional to the number of unoccupied sites, which is \( N(1 - \theta) \), where \( \theta \) is the fractional coverage of the surface.

Answer 1

The Correct Option is B

Step 1: Understanding Langmuir adsorption.
Langmuir adsorption is based on the assumption that adsorption occurs at specific sites on the surface and that each site can hold only one molecule. The rate of adsorption depends on the available surface sites, which is proportional to \( (1 - \theta) \), where \( \theta \) is the fractional coverage of the surface.
Step 2: Rate of adsorption expression.
The rate of adsorption is given by the expression: \[ \text{Rate of adsorption} \propto N(1 - \theta) \] This indicates that the rate of adsorption is directly proportional to the number of available sites.
Step 3: Conclusion.
The correct expression for the rate of adsorption is \( N(1 - \theta) \), which is option (B).
Final Answer: \[ \boxed{N(1 - \theta)} \]