Question

What is an adsorption isotherm? Describe Freundlich adsorption isotherm.

Answer 1

Answer:-

The adsorption isotherm is the plot between the extent of adsorption ($\frac{x}{m}$)against the pressure of gas (P) at constant temperature (T).

★ Freundlich adsorption isotherm:-

An empirical relationship between the quantity of gas adsorbed by the unit mass of solid adsorbent and pressure at a specific temperature is given by Freundlich adsorption isotherm.

$\frac{x}{m}$ reaches the maximum value at pressure Ps, observed from the given plot.

Ps is called the saturation pressure.

★ Note:- Three cases arise from the graph now.

$\to$ Case I - At low pressure:-

The pressure in the straight and sloping plot is directly proportional to $\frac{x}{m}$

i.e, $\frac{x}{m}$ ∝ P

$\frac{x}{m}$ = kP ( k is constant ).

$\to$ Case II - At high pressure:-

$\frac{x}{m}$ becomes independent of P values when pressure exceeds the saturated pressure,

$\frac{x}{m}$ ∝ ${P}^{o}$

$\frac{x}{m}$ ∝ ${kP}^{o}$

$\to$ Case lll – At intermediate pressure:-

$\frac{x}{m}$depends on P raised to the powers between 0 and 1, at intermediate pressure. This relationship is known as the Freundlich adsorption isotherm.

$\sf \implies \dfrac{x}{m}\;\alpha\;P^{\frac{1}{n}}\;\dfrac{x}{m}\;\alphaP^{\frac{1}{n}} = K\;P^{\frac{1}{n}}\quad n>1$

$\textbf{Now\: taking\:log:-}\\ \sf \implies log\;\dfrac{x}{m}=log\;k+\dfrac{1}{n}\;log\;P$

On plotting the graph between ($\log\frac{x}{m})$ and log P, a straight line is obtained with the slope equal to $\frac{1}{n}$.