Based on Langmuir adsorption isotherm ,at very high pressures the amount of gas adsorbed

Options

A. Increases first and decreases later with pressure
B. Reaches a constant limiting value
C. Goes on decreasing with pressure
D. Goes on increasing with pressure

Answer

To solve the question based on the Langmuir adsorption isotherm at very high pressures, we will follow these steps:

### Step 1: Understand the Langmuir Adsorption Isotherm
The Langmuir adsorption isotherm is given by the equation:
\[ \frac{x}{m} = \frac{AP}{1 + BP} \]
where:
- \( x \) = amount of gas adsorbed
- \( m \) = mass of the adsorbent
- \( P \) = pressure
- \( A \) and \( B \) = Langmuir constants

### Step 2: Analyze the Equation at High Pressures
At very high pressures, the term \( BP \) becomes significantly larger than 1. Thus, we can simplify the equation:
\[ \frac{x}{m} = \frac{AP}{1 + BP} \approx \frac{AP}{BP} \]
This simplification is valid because, at high pressure, \( 1 \) becomes negligible compared to \( BP \).

### Step 3: Simplify the Equation Further
Now, we can simplify the expression:
\[ \frac{x}{m} \approx \frac{A}{B} \]
This shows that at very high pressures, the extent of adsorption \( \frac{x}{m} \) approaches a constant value, which is \( \frac{A}{B} \).

### Step 4: Conclusion
Therefore, at very high pressures, the amount of gas adsorbed reaches a constant limiting value. This means that as pressure increases, the amount of gas that can be adsorbed does not continue to increase indefinitely but instead levels off.

### Final Answer
At very high pressures, the amount of gas adsorbed reaches a constant limiting value.

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