# Freundlich Adsorption Isotherm: Applications and Limitations

## Freundlich Adsorption Isotherm

Herbert Freundlich, in 1909, gave an empirical relationship between the quantity of gas adsorbed by unit mass of solid adsorbent and pressure at a particular temperature. The relationship can be expressed by the following equation-w/m = k . P

^{1/n}

This equation is called Freundlich adsorption isotherm.

Where 'w' is the weight of the gas adsorbed at a particular pressure 'P' by 'm' weight of the adsorbent and 'k' and 'n' are the constants depending on the nature of the gas and solid and also on temperature. The factor 1/n can have values between 0 and 1 (probable range 0.1 to 0.5). Thus, the above equation holds good over a limited range of pressure.

When 1/n = 0,

x/m = constant, the adsorption is independent of pressure.

When 1/n = 1,

x/m = k P

i.e. x/m ∝ P, the adsorption varies directly with pressure.

Both the conditions are supported by experimental results. Taking log in the above equation, we get-

log w/m = log k + 1/n log P

The validity of Freundlich adsorption isotherm can be verified by plotting log w/m vs log p. If it comes to be a straight line, the Freundlich isotherm is valid, otherwise not.

When plotting a graph between w/m vs. equilibrium pressure 'P', a curve line is obtained.

Similarly, when plotting a graph between log w/m vs. log P, a slight curvature is obtained, after a straight line.

The above graph should be a straight line, but it shows slight curvature in actual practice because Freundlich's adsorption isotherm is only applicable at low pressures. It shows curvature at high pressure, especially, with low temperature.

## Applications of Freundlich Adsorption Isotherm

Freundlich adsorption isotherm is also used for the adsorption of solutes from solutions in which case, the equilibrium pressure 'P' is replaced by the equilibrium concentration 'C' of the solute.w/m = k C

^{1/n}

or, log w/m = log k + 1/n log C

**Factors that affect the adsorption of solutes from solution are given below-**

1. Some adsorbents act more effectively than others in the adsorption of solutes.

2. The extent of adsorption decreases with an increase in temperature.

3. The extent of adsorption increases with an increase in the surface area.

4. An equilibrium can be established between the adsorbed amount of solute and the concentration of the solute in the solution, which can limit the adsorption process.

5. The exact mechanism of adsorption from the solution is not clear. Adsorption takes place when a unimolecular layer is formed.

When log w/m is plotted against log C, the resulting curve should be a straight line. Its validity has been tested by the adsorption of acetic acid on charcoal at 25°C and plotting the experimental values of log w/m against log C.

## Limitations of Freundlich Adsorption Isotherm

Freundlich adsorption isotherm is a very useful isotherm for adsorption purposes. However, it still has some limitations which are given below-1. Freundlich adsorption isotherm is purely emperical formula without theoratical foundation.

2. Freundlich adsorption isotherm is only applicable at low pressures.

3. At high pressure and low temperature, a slightly curved line is shown which negates the direct relationship.

4. The constants k and n vary with temperature.