Herbert Freundlich in 1909 gave an expression known as Freundlich adsorption isotherm, also called Freundlich equation. This equation is an empirical relationship between the quantity of gas adsorbed on the surface of the adsorbent and pressure. It describes the surface heterogeneity of adsorbents and gives an exponential distribution of active sites and their energies.

An adsorption isotherm is a graphical curve that explains the variation in the amount of gas adsorbed by an adsorbent at varying pressure and constant temperature.

## Freundlich Adsorption Equation

The relationship between the quantity of gas adsorbed on the surface of the adsorbent at varying pressure is expressed in the form of equation that is;

w/m = k P^{1/n }(n > 1)

or,

w/m = k C^{1/n }^{ }(n > 1)

where,

- w = mass of gas adsorbed
- m = mass of adsorbent
- k = constant
- n = number of moles
- P = equilibrium pressure in the case of gas phase (gas/solid interaction)
- C = equilibrium concentration in the case of aqueous solution with the solid phase (dissolved/adsorbed species interaction)

In this case, ‘k’ and ‘n’ are constants. They depend on the nature of solids, gases, and their temperatures.

By taking the logarithm on both sides of the above equations we get a linear equation;

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

or,

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

## Graphical representation of Freundlich Adsorption Isotherm

When plotting a graph between (w/m) on y-axis and equilibrium pressure (P) on x-axis, a curve line is obtained.

Similarly, when plotting a graph between log w/m on y-axis and log P on x-axis, 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. This is because Freundlich’s adsorption isotherm is only applicable at low pressures. It shows curvature at high pressure, especially, with low temperature.

### Limitations of Freundlich Adsorption Isotherm

Freundlich adsorption isotherm is a very useful isotherm for adsorption purposes. However, it still has some limitations:

- There is no theoretical background to the Freundlich equation.
- Freundlich adsorption isotherm is only applicable at low pressures.
- At high pressure and low temperature, a slightly curved line is shown which negates the direct relationship.
- The constants used in the Freundlich equation (k and n) vary with temperature.

### Applications of Freundlich Adsorption Isotherm

Adsorption isotherms are immensely important to scientists working on environmental protection and other industrial and laboratory experiments. Following are some of the applications of Freundlich’s adsorption isothermal equation.

- It is used for the adsorption of gases by solids at low pressure.
- It 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

### Adsorption of Solutes from Solutions

Adsorbents that are porous in nature can adsorb dissolved solutes from solutions. They are particularly used to remove color impurities from the solutions such as activated charcoal. For example, when an acetic acid solution is mixed with the activated charcoal, it removes the part of acid by adsorption which decreases the concentration of the solution. Secondly, precipitates act as adsorbents when solutes are separated from the solution.

Factors that affect the adsorption of solutes from solution are:

- Some adsorbents act more effectively than others in the adsorption of solutes.
- The extent of adsorption decreases with an increase in temperature.
- The extent of adsorption increases with an increase in the surface area.
- 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.

The exact mechanism of adsorption from the solution is still not clear. Even so, there is a limit to the adsorption by a given mass of adsorbent. Moreover, adsorption takes place when a unimolecular layer is formed.

Freundlich adsorption isotherm is obeyed by adsorption from solution when there is the use of concentration (C) instead of equilibrium pressure (P).

w/m = k x C^{1/n}

where (w) is the mass of solute adsorbed on a mass (m) of adsorbent. (C) is the equilibrium concentration of the solution when (k) and (n) are constants.

Taking log on both sides of the above equation, a linear Freundlich adsorption equation is obtained:

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

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.

This graph verifies the Freundlich equation when applied to the adsorption of acetic acid on charcoal at 25 °C.

**Additional articles:**

## Concepts Berg

**What is the difference between Freundlich’s and Langmuir’s adsorption isotherms?**

When the amount of adsorbate adsorbed is plotted against changing pressure, Freundlich adsorption isotherms give a straight line with a slight curvature at higher pressure. In comparison, Langmuir adsorption isotherm gives a straight line and is more valid for adsorption on solids.

**What is ‘n’ in Freundlich isotherm?**

Freundlich gives a simple equation:

w/m = k P^{1/n}

- w = mass of gas adsorbed
- m = mass of adsorbent
- k = constant
- n = number of moles
- P = equilibrium pressure in the case of gas phase (gas/solid interaction)

**What are Freundlich’s adsorption isotherm assumptions?**

There are no assumptions of Freundlich adsorption isotherms because it is purely empirical and has no theoretical background.

**What is Langmuir adsorption isotherm?**

It is a straight-line equation. It explains physical adsorption and also gives the concept of chemisorption. It also describes that adsorbed molecules can not interact with each other.

x = k’ b P / (1 + bP)

**Reference Books**

- Surface and Colloid Chemistry: (Principles and Applications) by
**K.S Birdi**(Berkeley, University of California & Unilever, Copenhagen, Denmark) **Essential of Physical Chemistry:**2nd edition By**B.S Bahl**(Gurdaspur, India) and**Arun Bahl**(RSC, UK) and**G.D. Tuli**(Delhi University, India)**Principle of Physical Chemistry**by**Haq Nawaz Bhatti**(University of Agriculture, Faisalabad, Pakistan)

**Reference links**

- Freundlich Equation (Wikipedia)
- Modeling and Interpretation of Adsorption Isotherms (hindawi.com)
- Adsorption isotherms (byjus.com)