The adsorption isotherm of a gas which is adsorbed on a solid.

**Adsorption
Isotherms**

The extent of adsorption is measured in terms of
the quantity x/m where, x is the mass of the gas (adsorbate)
adsorbed at equilibrium on mass m of the adsorbent. x/m is the mass of the adsorbate adsorbed per
unit mass of the adsorbent. The graph showing variation in x/m with pressure(p)
at a constant temperature is called adsorption isotherm. Let us see the
variation in extent of adsorption in case of gases and of solutes from their solutions.

The adsorption isotherm of a gas which is adsorbed
on a solid is shown in Fig. 17.5. It shows that the extent of adsorption of a
gas on a solid increases with the increase in the pressure of the gas, *p* at three different constant
temperatures. The curves also show that the extent of adsorption, decreases at
a fixed pressure as the temperature is increased (see the dotted line).

Freundlich gave an empirical mathematical
relationship between the extent of adsorption (x/m) and the equilibrium
pressure (p) of the gas as :

In this relation *k* is a constant at a given temperature and depends upon the nature
of the adsorbate and adsorbent. The value of *n* changes with pressure. It is 1 at low pressures and increases
with pressure. The relationship is valid at a constant temperature. Therefore,
it is called **Freundlich Adsorption
Isotherm**. On taking logarithm of the above equation, we get

This is an equation of a straight line and a plot
of log x/m against log p should be a straight line with slope 1/n as depicted
in Fig. 17.6. In actual practice, a straight line is obtained provided the data
at very low and very high pressures is neglected.

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