In Freundlich adsorption isotherm at moderate pressure, the extent oof adsorption `(x/m)` is directly proportional to `P^x`. The value of x is

Options

A. zero
B. `1/n`
C. 1
D. `oo`

Answer

To solve the question regarding the Freundlich adsorption isotherm at moderate pressure, we need to analyze the relationship between the extent of adsorption (x/m) and pressure (P).

### Step-by-Step Solution:

1. **Understanding the Freundlich Adsorption Isotherm**:
The Freundlich adsorption isotherm describes how the amount of gas adsorbed on a solid surface varies with pressure at a constant temperature. It is given by the equation:
\[ \frac{x}{m} = k P^{1/n} \]
where:
- \( \frac{x}{m} \) is the extent of adsorption,
- \( P \) is the pressure,
- \( k \) is a constant,
- \( n \) is a constant that indicates the degree of non-linearity of the adsorption.

2. **Identifying the Relationship at Moderate Pressure**:
At moderate pressure, the extent of adsorption \( \frac{x}{m} \) is directly proportional to \( P^x \). This means we can express this relationship as:
\[ \frac{x}{m} \propto P^x \]

3. **Comparing the Two Relationships**:
From the Freundlich isotherm equation, we see that:
\[ \frac{x}{m} \propto P^{1/n} \]
Therefore, we can equate the two expressions:
\[ P^x \propto P^{1/n} \]

4. **Equating the Exponents**:
Since the pressures are the same, we can equate the exponents:
\[ x = \frac{1}{n} \]

5. **Conclusion**:
The value of \( x \) in the context of the Freundlich adsorption isotherm at moderate pressure is \( \frac{1}{n} \).

### Final Answer:
The value of \( x \) is \( \frac{1}{n} \).

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