In the adsorption of a gas on soild, Freundlich isotherm is obeyed . The slope of the plot is zero. Thus, the extent of adsorption is

Options

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

Explanation

To solve the problem regarding the adsorption of a gas on a solid where the Freundlich isotherm is obeyed and the slope of the plot is zero, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Freundlich Isotherm Equation**:
The Freundlich isotherm is given by the equation:
\[ \frac{X}{M} = K P^{\frac{1}{n}} \]
where:
- \(X\) = mass of gas adsorbed
- \(M\) = mass of the adsorbent
- \(P\) = pressure of the gas
- \(K\) and \(n\) = constants specific to the system.

2. **Take the Logarithm of Both Sides**:
To analyze the relationship, we take the logarithm of both sides:
\[ \log\left(\frac{X}{M}\right) = \log(K) + \frac{1}{n} \log(P) \]

3. **Identify the Linear Form**:
The above equation can be compared to the linear equation \(y = mx + c\):
- \(y = \log\left(\frac{X}{M}\right)\)
- \(x = \log(P)\)
- \(c = \log(K)\)
- \(m = \frac{1}{n}\) (slope)

4. **Analyze the Given Information**:
The problem states that the slope of the plot is zero. This means:
\[ \frac{1}{n} = 0 \implies n = \infty \]

5. **Interpret the Implication of the Slope Being Zero**:
If \(n\) approaches infinity, the term \(\frac{1}{n} \log(P)\) approaches zero for any finite value of \(P\). This indicates that:
\[ \frac{X}{M} \text{ is constant regardless of } P \]
Therefore, the extent of adsorption (\(X/M\)) does not depend on the pressure of the gas.

6. **Conclusion**:
Since the extent of adsorption is independent of the pressure of the gas, we conclude that the correct answer is:
- The extent of adsorption is independent of the pressure of gas.

### Final Answer:
The extent of adsorption is independent of the pressure of gas.