Which of the following does not represent freundlich
adsorption isotherm?

Options

A. `log frac{x}{m} = 1/n log p+ llog k`
B. `n log frac{x}{m} = log p + n log k `
C. `x/m = kp^(1/n)`
D. `(x/m)^(n) = kp`

Answer

To determine which of the given options does not represent the Freundlich adsorption isotherm, we need to analyze each option in relation to the Freundlich equation. The Freundlich adsorption isotherm is typically expressed as:

\[ \frac{x}{m} = k p^{\frac{1}{n}} \]

Where:
- \( x \) = mass of the adsorbate
- \( m \) = mass of the adsorbent
- \( p \) = pressure
- \( k \) and \( n \) = constants specific to the system

Let's evaluate each option:

### Option 1:
\[ \log \left(\frac{x}{m}\right) = \frac{1}{n} \log(p) + \log(k) \]

This can be derived from the Freundlich equation by taking the logarithm of both sides. This option represents the Freundlich isotherm.

### Option 2:
\[ n \log \left(\frac{x}{m}\right) = \log(p) + n \log(k) \]

This can also be derived from the Freundlich equation by multiplying the logarithmic form by \( n \). This option also represents the Freundlich isotherm.

### Option 3:
\[ \frac{x}{m} = \frac{kp}{k_t} \cdot p^{\frac{1}{n}} \]

This equation does not match the standard form of the Freundlich isotherm. It introduces an additional term \( k_t \) which is not part of the Freundlich isotherm. Therefore, this option does not represent the Freundlich isotherm.

### Option 4:
\[ \left(\frac{x}{m}\right)^n = kp \]

This equation can be rearranged to resemble the Freundlich isotherm, but it does not maintain the correct mathematical relationship as per the original Freundlich equation. Therefore, this option does not represent the Freundlich isotherm.

### Conclusion:
The options that do not represent the Freundlich adsorption isotherm are **Option 3** and **Option 4**.

### Final Answer:
**Option 3 and Option 4 do not represent the Freundlich adsorption isotherm.**

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