The most popular adsorption isotherms are the linear, Freundlich and Langmuir equations. Typically these equations are very good at describing experimental data despite their lack of theoretical basis. Their popularity stems in part from their simplicity and from the ease of estimation of their adjustable parameters.

The linear adsorption isotherm equation is,
$x = K_dC$.

The Freundlich adsorption isotherm equation is,

$\frac{X}{m}$
= $KP^{\frac{1}{n}}$
.

Here K and n are parameters depending upon nature of gas and solid.

The Langmuir adsorption isotherm equation is,

$\frac{X}{m}$
= $\frac{aP}{1+bP}$
.

Where a and b are Langmuir parameters.

## Adsorption Isotherm Problems

Some of the solved problems based on Adsorption Isotherm Equation is given below:

Question 1: The volume of hydrogen gas at 1 atm and 273K required to cover 1g of the silica gel is 0.127dm3. Identify the area occupied by the silica gel in each hydrogen molecule in which the molecule occupies an area of 17.3 $\times$ 10-20m2.

Solution:

Number of moles of H2 in 0.127dm= 0.127/22.4 = 5.66 $\times$ 10-3

Therefore, total number of H2 = 5.66 $\times$ 10-3 $\times$ 6.02 $\times$ 1023

Total number of $H_2$ = 34.13 $\times$ 1020

The total area of 1g of the silica gel = 34.13 $\times$ 1020 $\times$ 17.3 $\times$ 10-20

The total area of 1g of the silica gel = 590.449 m2

Question 2: Charcoal absorbs a solute from its aqueous solution and obeys the freundlich isotherm. The following were the data obtained.
 Equilibrium concentration $\times$ 102M 2 4 6 8 x/m 0.185 0.29 0.364 0.428

Determine the values of K. (n = 0.616).

Solution:

$\frac{X}{m}$ = $KP^{\frac{1}{n}}$

0.3155 = K (10)(0.616)

0.3155 = K (6.16)

K = $\frac{0.3155}{6.16}$

K = 0.05121 $\times$ 102M

K = 5.12 M.