What is an adsorption isotherm? Describe Freundlich adsorption isotherm.
The plot between the extent of adsorption x/m against the pressure of gas (P) at constant temperature (T) is called the adsorption isotherm.
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.
From the given plot it is clear that at pressure PS, x/m reaches the maximum valve. PS is called the saturation pressure. Three cases arise from the graph now.
Case I- At low pressure:
The plot is straight and sloping, indicating that the pressure in directly proportional to \(\frac{x}{m}\) i.e., \(\frac{x}{m}\) ∝ 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.
\(\frac{x}{m}\) ∝ 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.
\(\frac{x}{m} ∝ P^{\frac{1}{n}}\)
\(\frac{x}{m} = kP^{\frac{1}{n}}\) 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 and the intercept equal to log k.