Freundlich equation applies to the adsorption of solute from dilute solutions, over a small concentration range.

The Freundlich equation is an empirical equation that describes the adsorption phenomenon. It is commonly used to analyze the adsorption of solutes from dilute solutions, particularly over a small concentration range. The equation is expressed as:

q = K * C^n

where:
- q is the amount of solute adsorbed per unit mass of adsorbent (mg/g)
- K is the Freundlich constant, which is related to the adsorption capacity of the adsorbent
- C is the equilibrium concentration of the solute in the solution (mg/L)
- n is the Freundlich exponent, which represents the intensity of adsorption

Explanation:

1. Dilute solutions:
The Freundlich equation is most applicable to dilute solutions, where the solute concentration is relatively low. This is because the equation assumes that the adsorption process occurs on a heterogeneous surface with different adsorption sites. In dilute solutions, the adsorbent surface is more likely to be available for adsorption, and the adsorption sites are not saturated.

2. Small concentration range:
The Freundlich equation is particularly useful for analyzing adsorption over a small concentration range. This is because the equation is an empirical equation and does not take into account the detailed mechanisms of adsorption. It is a simplified model that works well within a limited concentration range, where the adsorption process is assumed to be linear or approximately linear.

3. Adsorption from gaseous solutions at high pressure:
The Freundlich equation is not suitable for describing the adsorption of solutes from gaseous solutions at high pressure. In these cases, the adsorption process is often more complex and may involve multilayer adsorption or other phenomena that cannot be accurately represented by the Freundlich equation.

4. Concentrated solutions:
Similarly, the Freundlich equation is not suitable for concentrated solutions, where the solute concentration is high. In concentrated solutions, the adsorption sites on the adsorbent surface may become saturated, leading to a decrease in adsorption capacity and a deviation from the linear behavior assumed by the Freundlich equation.

In conclusion, the Freundlich equation is most applicable to the adsorption of solutes from dilute solutions over a small concentration range. It provides a simplified model for analyzing adsorption phenomena but may not accurately represent adsorption from gaseous solutions at high pressure or concentrated solutions.