Freundlich adsorption isotherm is given by the expression `x/m=kP^(1/n)` which of the following conclusions can be draw from this expression?

Options

A. When `1/n=0`, the adsorption is directly proportional to pressure
B. When `n=1,x/m` vs `p` graph is a line parallel to `x`-axis
C. When `1/n=0` the adsorption is independent of pressure
D. When `n=2`, plot off `x/m` vs `p` is a rectangular hyperbola

Explanation

To analyze the Freundlich adsorption isotherm given by the expression \( \frac{x}{m} = kP^{\frac{1}{n}} \), where \( x \) is the mass of the adsorbate, \( m \) is the mass of the adsorbent, \( P \) is the pressure, and \( k \) and \( n \) are constants, we can derive conclusions based on different values of \( n \).

### Step-by-Step Solution:

1. **Understanding the Expression**:
- The Freundlich adsorption isotherm expresses the relationship between the amount of adsorbate adsorbed per unit mass of adsorbent and the pressure of the adsorbate in the gas phase.

2. **Analyzing the Case When \( \frac{1}{n} = 0 \)**:
- If \( \frac{1}{n} = 0 \), then \( n \) approaches infinity, and the expression simplifies to \( \frac{x}{m} = k \).
- This indicates that the adsorption is independent of pressure, meaning the amount adsorbed remains constant regardless of changes in pressure.

**Conclusion**: This statement is true.

3. **Analyzing the Case When \( n = 1 \)**:
- If \( n = 1 \), then \( \frac{x}{m} = kP \).
- This is a linear relationship, and if we plot \( \frac{x}{m} \) versus \( P \), we get a straight line passing through the origin.

**Conclusion**: This statement is false, as the graph is not parallel to the x-axis.

4. **Analyzing the Case When \( n = 2 \)**:
- If \( n = 2 \), then \( \frac{x}{m} = kP^{\frac{1}{2}} \).
- This represents a square root relationship, which does not correspond to a rectangular hyperbola. Instead, it describes a parabolic curve.

**Conclusion**: This statement is false.

5. **Final Conclusion**:
- The only correct conclusion drawn from the expression is that when \( \frac{1}{n} = 0 \), the adsorption is independent of pressure.

### Summary of Conclusions:
- **A**: False (Adsorption is constant, not dependent on pressure)
- **B**: False (Graph is a line through the origin, not parallel to x-axis)
- **C**: True (Adsorption is independent of pressure when \( \frac{1}{n} = 0 \))
- **D**: False (The plot is not a rectangular hyperbola)