Now that you know what adsorption is, how do we measure or study it? The process of adsorption is usually plotted and studied using a graph. This is called adsorption isotherm. Different scientists have developed different kinds of adsorption isotherms. Let’s go ahead and learn about this concept in detail.

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## Definition

Adsorption Isotherm is a curve that expresses the variation in the amount of gas adsorbed by the adsorbent with pressure at constant temperature.

## Freundlich Adsorption Isotherm

In 1909, German scientist Freundlich provided an empirical relationship between the amount of gas adsorbed by a unit mass of solid adsorbent and pressure at a particular temperature. It is expressed using the following equation –

x/m = *k.P*^{1/n} (n > 1)

where ‘x’ is the mass of the gas adsorbed on mass ‘m’ of the adsorbent at pressure ‘P’. ‘k’ and ‘n’ are constants that depend on the nature of the adsorbent and the gas at a particular temperature.

The mass of the gas adsorbed per gram of the adsorbent is plotted against pressure in the form of a curve to show the relationship. Here, at a fixed pressure, physical adsorption decreases with increase in temperature. The curves reach saturation at high pressure. Now, if you take the log of the above equation –

log x/m = log *k* + 1/n log *P*

To test the validity of Freundlich isotherm, we can plot log x/m on the y-axis and log P on the x-axis. If the plot shows a straight line, then the Freundlich isotherm is valid, otherwise, it is not. The slope of the straight line gives the value of 1/n, while the intercept on the y-axis gives the value of log *k*.

### Limitations of Freundlich Isotherm

Freundlich isotherm only approximately explains the behaviour of adsorption. The value of 1/n can be between 0 and 1, therefore the equation holds good only over a limited range of pressure.

- When 1/n = 0, x/m is constant, the adsorption is independent of pressure.
- When 1/n =1, x/m =
*k**P,*i.e. x/m ∝*P*, adsorption is directly proportional to pressure.

Experimental results support both of the above mentioned conditions. At high pressure, the experimental isotherms always seem to approach saturation. Freundlich isotherm does not explain this observation and therefore, fails at high pressure.

The Freundlich isotherm was followed by two other isotherms – Langmuir adsorption isotherm and BET adsorption isotherm. Langmuir isotherm assumed that adsorption is monolayer in nature whereas BET isotherm assumed that it is multi-layer.

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## Solved Examples for You

Questions: State whether the following statements are True or False.

- Adsorption isotherm is a curve that expresses the variation in the amount of gas adsorbed by the adsorbent with the temperature at constant pressure.
- Freundlich isotherm fails at high pressure.
- If the plot of log x/m on the y-axis and log
*P*on the x-axis is a straight line, then Freundlich isotherm is valid. - Freundlich isotherm explains the behaviour of adsorption accurately.
- In the equation – x/m =
*k.P*^{1/n}(n > 1), ‘k’ and ‘n’ are constants that depend on the nature of the adsorbent and the gas at a particular temperature.

Solutions:

- False
- True
- True
- False
- True

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