Ncert Exercises & Solutions

5.5 What is an adsorption isotherm? Describe Freundlich adsorption isotherm.

Step 1:

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

The graph is as follows:

Step 2:

Freundlich adsorption isotherm:

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

Case I- At low pressure:

The plot is straight and sloping, indicating that the pressure directly proportional to

${\frac{x}{m}}_{i . e .,} \frac{x}{m} α P .$
$\frac{x}{m} = kP (k is a constant)$

Case II - At high pressure:

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

$\frac{x}{m} α P °$
$\frac{x}{m} = k P °$

Case III - At intermediate pressure:

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

$\frac{x}{m} α P^{\frac{1}{n}}$
$\frac{x}{m} = k P^{\frac{1}{n}} n > 1$
$Now, taking \log :$
$\log \frac{x}{m} = \log k + \frac{1}{n} \log P$

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

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