Question

What form of Freundlich adsorption equation will take at high pressure?

Answer 1

Hint: The relationship between the amount of gas adsorbed on the solid surface and the pressure applied is given the Freundlich equation. We will use this relationship to find the effect of adsorption when pressure is increased. This equation is also known as Freundlich isotherm.

Complete Answer:
The amount of gas which gets adsorbed on the metal surface when a pressure is applied is given by the equation which is known as Freundlich adsorption equation which can be represented as:
\[\dfrac{x}{m}{\text{ }} = {\text{ }}K{\text{ }}{p^{\dfrac{1}{n}}}\] __________\[(i)\]
Where,
\[x\] is the mass of adsorbate, \[m\] is the mass of adsorbent, \[p\] is the equilibrium pressure , \[K\] is some constant and the value of \[n\] is greater than one.
On taking log both sides it can be written as:
\[ \Rightarrow \log \dfrac{x}{m}{\text{ }} = {\text{ log}}\left( {K{\text{ }}{p^{\dfrac{1}{n}}}} \right)\]
We know that, \[\log \left( {a.b} \right) = \log a + \log b\] , therefore it can be represented as:
\[ \Rightarrow \log \dfrac{x}{m}{\text{ }} = {\text{ log K + log}}{\left( p \right)^{\dfrac{1}{n}}}\]
\[ \Rightarrow \log \dfrac{x}{m}{\text{ }} = {\text{ log K + }}\dfrac{1}{n}{\text{log p}}\]
When pressure is high the value of \[\dfrac{1}{n}\] will be equal to zero and thus the equation \[(i)\] will be reduced as:
\[ \Rightarrow \dfrac{x}{m}{\text{ }} = {\text{ }}K{\text{ }}{p^{\dfrac{1}{n}}}\]
\[ \Rightarrow \dfrac{x}{m}{\text{ }} = {\text{ }}K{\text{ }}{p^0}\]
We know that if power of something is zero then its value will be equal to one, so \[{p^0} = 1\],
\[ \Rightarrow \dfrac{x}{m}{\text{ }} = {\text{ }}K{\text{ }} \times {\text{ 1}}\]
\[ \Rightarrow \dfrac{x}{m}{\text{ }} = {\text{ }}K\]
Thus the amount of gas adsorbed will be constant and it is equal to \[K\]. Hence at high pressure the amount of gas adsorbed becomes independent of the pressure.

Note:
It must be noted that, \[\log \left( {{a^n}} \right) = n\log a\]. Also at high pressure the value of \[n\] becomes infinity therefore \[\dfrac{1}{n}\] will be equal to zero. This is the region ahead of saturation. \[K\] is a constant quantity and hence the amount of gas adsorbed becomes equal to \[K\] which means it becomes constant and independent of pressure applied.