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 question regarding the Freundlich adsorption isotherm, we need to analyze the relationship between the extent of adsorption and pressure at moderate pressure conditions.

### Step-by-Step Solution:

1. **Understanding the Freundlich Adsorption Isotherm**:
- The Freundlich adsorption isotherm describes how the extent of adsorption (x/m) varies with pressure (P) at constant temperature.
- The general equation is given by:
\[ \frac{x}{m} = k P^{\frac{1}{n}} \]
where:
- \( x \) = mass of adsorbate,
- \( m \) = mass of adsorbent,
- \( k \) = a constant,
- \( P \) = pressure,
- \( n \) = a constant (where \( n > 0 \)).

2. **Identifying the Relationship at Moderate Pressure**:
- The problem states that at moderate pressure, the extent of adsorption \( \frac{x}{m} \) is directly proportional to \( P^x \).
- This can be expressed mathematically as:
\[ \frac{x}{m} \propto P^x \]

3. **Comparing the Two Expressions**:
- From the Freundlich isotherm, we have:
\[ \frac{x}{m} = k P^{\frac{1}{n}} \]
- From the given condition, we have:
\[ \frac{x}{m} \propto P^x \]
- To find the value of \( x \), we can equate the exponents of \( P \) from both expressions:
\[ \frac{1}{n} = x \]

4. **Conclusion**:
- Thus, the value of \( x \) is:
\[ x = \frac{1}{n} \]

### Final Answer:
The value of \( x \) in the equation \( \frac{x}{m} \propto P^x \) at moderate pressure in the Freundlich adsorption isotherm is \( \frac{1}{n} \).