According to Freundlich adsorption isotherm, the value of x/m at high pressures is 

Options

A. directly proportional to pressure
B. inversely proportional to pressure
C. directly proportional to square of pressure
D. independent of pressure

Answer

To solve the question regarding the Freundlich adsorption isotherm and the behavior of \( \frac{x}{m} \) at high pressures, we can follow these steps:

### Step 1: Understand the Freundlich Adsorption Isotherm
The Freundlich adsorption isotherm is represented by the equation:
\[ \frac{x}{m} = k \cdot p^{\frac{1}{n}} \]
where:
- \( \frac{x}{m} \) is the amount of gas adsorbed per unit mass of the adsorbent,
- \( p \) is the pressure,
- \( k \) and \( n \) are constants that depend on the nature of the gas and the adsorbent.

### Step 2: Analyze the Equation at High Pressures
At high pressures, the behavior of the adsorption can be analyzed by considering the term \( p^{\frac{1}{n}} \):
- As pressure \( p \) increases, the term \( p^{\frac{1}{n}} \) also increases. However, the extent of adsorption approaches a limit.

### Step 3: Determine the Limit of Adsorption
At very high pressures, the adsorption reaches a saturation point where the amount of gas adsorbed does not significantly increase with further increases in pressure. This means that:
\[ \frac{x}{m} \text{ approaches a constant value.} \]
In mathematical terms, this can be interpreted as:
\[ \frac{x}{m} \propto p^0 \quad \text{(which is proportional to 1)} \]
This indicates that \( \frac{x}{m} \) becomes independent of pressure.

### Step 4: Conclusion
From the analysis, we conclude that at high pressures, the value of \( \frac{x}{m} \) becomes independent of pressure. Therefore, the correct answer to the question is:
\[ \text{Option 4: Independent of pressure.} \]