Freundlich adsorption isotherm is expressed as equation :

Question

Accepted Answer

The Freundlich adsorption isotherm is an empirical model that describes the adsorption of substances onto a surface. It is particularly useful for understanding adsorption on heterogeneous surfaces. The correct expression for the Freundlich adsorption isotherm is given by:

$$
\frac{x}{m} = kP^{1/n}
$$

where:
- $ \frac{x}{m} $ is the amount of adsorbate per unit mass of adsorbent.
- $ k $ is the Freundlich constant, which is indicative of the adsorption capacity.
- $ P $ is the pressure of the adsorbate (or concentration in the case of solutions).
- $ n $ is a constant that indicates the intensity of the adsorption.

### Explanation for Option 4:

Option 4 correctly represents the Freundlich adsorption isotherm equation. The equation $\frac{x}{m} = kP^{1/n}$ captures the relationship between the amount of adsorbate adsorbed per unit mass of adsorbent and the pressure (or concentration) of the adsorbate. The term $P^{1/n}$ reflects the non-linear nature of adsorption, which is characteristic of the Freundlich isotherm. This equation is widely accepted and used in the study of adsorption processes.

### Explanation for Incorrect Options:

1. **Option 1: $\frac{m}{x} = kP^{1/n}$**
   - This equation incorrectly places the mass of the adsorbent ($m$) in the numerator and the amount of adsorbate ($x$) in the denominator. The Freundlich isotherm is concerned with the ratio of adsorbate to adsorbent, not the inverse.

2. **Option 2: $\frac{x}{m} = kP^{n}$**
   - This equation suggests a linear relationship with respect to $P^n$, which does not align with the empirical nature of the Freundlich isotherm. The exponent should be $1/n$ to reflect the correct non-linear relationship.

3. **Option 3: $\frac{m}{x} = kP^{n}$**
   - Similar to Option 1, this equation incorrectly inverts the ratio of adsorbate to adsorbent. Additionally, it uses $P^n$ instead of $P^{1/n}$, which does not represent the Freundlich isotherm.

In conclusion, Option 4 is the correct representation of the Freundlich adsorption isotherm, as it accurately describes the empirical relationship between the amount of adsorbate adsorbed and the pressure or concentration of the adsorbate.