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

Options

A. 1
B. Zero
C. `infty`
D. `(1)/(n)`

Answer

To solve the problem regarding the Freundlich adsorption isotherm, we need to analyze the relationship given in the question and derive the value of \( x \).

### Step-by-Step Solution:

1. **Understanding the Freundlich Adsorption Isotherm**:
The Freundlich adsorption isotherm is expressed as:
\[ \frac{x}{m} = k \cdot P^{1/n} \]
where:
- \( x \) = mass of the adsorbate
- \( m \) = mass of the adsorbent
- \( P \) = pressure
- \( k \) = constant
- \( n \) = a constant that is greater than 1.

2. **Identifying the Proportionality**:
According to the question, at moderate pressure, the extent of adsorption \( \frac{x}{m} \) is directly proportional to \( P^x \). This can be written as:
\[ \frac{x}{m} \propto P^x \]

3. **Comparing the Two Expressions**:
From the Freundlich equation, we have:
\[ \frac{x}{m} = k \cdot P^{1/n} \]
and from the question, we have:
\[ \frac{x}{m} \propto P^x \]
This implies that:
\[ k \cdot P^{1/n} \propto P^x \]

4. **Equating the Powers of \( P \)**:
Since both expressions are proportional to \( P \), we can equate the exponents of \( P \):
\[ \frac{1}{n} = x \]

5. **Final Result**:
Therefore, the value of \( x \) is:
\[ x = \frac{1}{n} \]

6. **Conclusion**:
The correct answer is option D, which states that \( x = \frac{1}{n} \).