Question

The adsorption of gases on solid can be described by Freundlich's equation $\frac{x}{m}=k{P}^{1/n}$
(a)How are the value of K and n determined experimentally?
(b) Explain, why should the value of n be equal to or greater than one .

Answer 1

According to Fraundlich adsorption isotherm, the quantity of unit mass of solid absorbent and pressure at a particular temperature is expressed as, $\frac{x}{m}=K{p}^{\frac{1}{n}}⟶\left(i\right)$

where $x$ is mass of the gas absorbed at pressure $p$,.

$K$ and $n$ are constants which depends on the nature of the absorbent and the gas at a particular temperature.

From $\left(i\right)$, $\log \frac{x}{m}=\log K+\frac{1}{n}\log p$

Thus if we plot a graph of $\log \frac{x}{m}$ and $\log p$ a straight line will be obtained.

The slope of the line $=\frac{1}{n}$

intercept$=K$

Look at the structure,

Thus the values of $K$ and $n$ are determined,

The factor $\frac{1}{n}$ can have the value between $0$ & $1$.

$\left(i\right)$ When $\frac{1}{n}=0,\frac{x}{m}=constant$

The absorption is independent of pressure.

$\left(ii\right)$ When $\frac{1}{n}=1,\frac{x}{m}=Kp,$ i.e. $\frac{x}{m}\alpha p$

The adsorption varies directly with pressure.

Freundlich isotherm fails to explain the adsorption behaviour, i.e.at high pressure and low pressure .

$\therefore$ $n>1$