The equation for Freundlich adsorption isotherm is

Options

A. `x/m=kp^(1//n)`
B. `x=mkp^(1//n)`
C. `x//m=kp^(-n)`
D. All of these

Answer

To solve the question regarding the equation for the Freundlich adsorption isotherm, we can break it down into a step-by-step explanation.

### Step-by-Step Solution:

1. **Understanding the Freundlich Adsorption Isotherm**:
The Freundlich adsorption isotherm describes how the amount of gas adsorbed onto a solid surface varies with pressure. It is particularly useful for heterogeneous surfaces.

2. **The Freundlich Equation**:
The Freundlich adsorption isotherm can be expressed mathematically as:
\[ \frac{x}{m} = k p^{\frac{1}{n}} \]
where:
- \( x \) = mass of the gas adsorbed
- \( m \) = mass of the adsorbent
- \( p \) = pressure of the gas
- \( k \) and \( n \) = constants specific to the system.

3. **Rearranging the Equation**:
The equation can also be rearranged to express \( x \) in terms of \( m \), \( k \), and \( p \):
\[ x = m k p^{\frac{1}{n}} \]

4. **Alternative Form of the Equation**:
We can also express the equation in another form:
\[ \frac{x}{m} = k p^{-n} \]
This is achieved by rewriting \( p^{\frac{1}{n}} \) in a different way, but it still represents the same relationship.

5. **Verifying Options**:
If the question provides multiple options regarding the Freundlich adsorption isotherm equation, we can check each option against the derived equations.
- If an option matches \( \frac{x}{m} = k p^{\frac{1}{n}} \) or \( \frac{x}{m} = k p^{-n} \), it can be considered correct.

6. **Conclusion**:
Based on the derived equations, we conclude that the Freundlich adsorption isotherm can be represented in multiple forms, and all correct representations should be identified as valid.