Question

Derive a mathematical expression showing the relationship between the extent of adsorption of a gas on a surface with pressure (within lower and higher ranges). Calculate the extent of adsorption at one atmosphere.

Answer 1

The empirical relationship between the extent of adsorption `(x/m)` and the pressure (P) of a gas at constant temperature is given by the Freundlich adsorption isotherm:

`x/m = kP^(1//n)` where n > 1

Where:

x = Mass of gas adsorbed

m = Mass of adsorbent

P = Equilibrium pressure of the gas

k and n = Empirical constants that depend on the nature of gas and adsorbent.

Behaviour at pressure extremes:

At low pressure:

When P is small, `1/n` ≈ 1

`x/m` = kP

This implies adsorption is directly proportional to pressure.

At high pressure:

As pressure becomes very high, P^1/n ≈ constant, so:

`x/m` = constant

This means the extent of adsorption becomes independent of pressure due to surface saturation.

Final general expression:

`x/m = kP^(1//n)`

Numerical Example:

Let’s assume, k = 0.5, n = 2, P = 1 atm

Using `x/m = kP^(1//n)`

= 0.5 × (1)^1/2

= 0.5

The extent of adsorption at 1 atm is `x/m` = 0.5.