According to Freundlich adsorption isotherm the amount of gas adsorbed per unit mass of the solid adsorbent varies directly with pressure when the value of n is

Options

A. 0
B. 3
C. 2
D. 1

Explanation

To solve the problem regarding the Freundlich adsorption isotherm, we need to analyze the relationship between the amount of gas adsorbed per unit mass of the solid adsorbent (denoted as \( \frac{X}{M} \)) and the pressure (denoted as \( P \)).

### Step-by-Step Solution:

1. **Understanding the Freundlich Adsorption Isotherm**:
The Freundlich adsorption isotherm is given by the equation:
\[ \frac{X}{M} = K P^{\frac{1}{n}} \]
where:
- \( \frac{X}{M} \) is the amount of gas adsorbed per unit mass of the solid,
- \( K \) is a constant,
- \( P \) is the pressure,
- \( n \) is a constant that reflects the adsorption intensity.

2. **Analyzing the Direct Variation**:
The question states that \( \frac{X}{M} \) varies directly with pressure \( P \). This means that we want to express \( \frac{X}{M} \) in a form that is directly proportional to \( P \).

3. **Setting Up the Proportionality**:
For \( \frac{X}{M} \) to be directly proportional to \( P \), we can express this relationship as:
\[ \frac{X}{M} \propto P \]
This implies that:
\[ \frac{X}{M} = K P \]
Here, the exponent of \( P \) must be 1.

4. **Determining the Value of \( n \)**:
From the original Freundlich equation, we have:
\[ \frac{X}{M} = K P^{\frac{1}{n}} \]
For this to be equal to \( K P \), we need:
\[ P^{\frac{1}{n}} = P^1 \]
This equality holds true when:
\[ \frac{1}{n} = 1 \implies n = 1 \]

5. **Conclusion**:
Therefore, the value of \( n \) must be 1 for the amount of gas adsorbed per unit mass of the solid adsorbent to vary directly with pressure.

### Final Answer:
The value of \( n \) is 1.

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