Question

According to Freundlich adsorption isotherm, which of the following is/are correct?
(A) $\dfrac{x}{m}\alpha {{p}^{1/2}}$
(B) $\dfrac{x}{m}\alpha {{p}^{1}}$
(C) $\dfrac{x}{m}\alpha {{p}^{1/m}}$
(D) All the above.

Answer 1

Hint: Freundlich in his findings, considered temperature to be constant and tried to find a relation between the mass of gas adsorbed and the pressure of the surrounding. Understand physical adsorption given under the chapter surface chemistry. Also remember that the adsorption isotherm given by Freundlich depended on the amount of pressure like high or low and the formula would change accordingly. So do expect more than one option to match the formula.

Complete step-by-step answer:
Physisorption, also called physical adsorption, is a process in which the electronic structure of the molecule/atom is attached upon adsorption. The main interacting force in physical adsorption is the Van der Waals force. Although the interacting force is very weak, it plays a crucial role in nature. Due to weak forces being present, it is observed that easily liquefiable gases are readily adsorbed on the surface of adsorbent. When sufficient pressure is applied, it is seen that the layer of adsorbent adsorbs multiple layers of attacking particles called adsorbate. The enthalpy of adsorption is low and negative in polarity. The value varies between -20 to -40 kJ/mol. An adsorption isotherm is a graph that depicts the variation in the amount of adsorbate(x) adsorbed on the surface called adsorbent along with the change in pressure assuming the temperature to be constant. According to Freundlich's adsorption isotherm, it is seen that,
$\dfrac{x}{m}\alpha {{p}^{1/n}}$ where, the value of n$\ge $ 1.
In the above expressions, p is considered to be the pressure at equilibrium and the term $\dfrac{\text{x}}{\text{m}}$ is the mass of gas adsorbed per unit mass of the adsorbent substance. At low pressure, it is seen that $\dfrac{\text{x}}{\text{m}}$ is directly proportional to the equilibrium pressure. It is commonly expressed as,
$\dfrac{\text{x}}{\text{m}}$ = K.p
Where K is an arbitrary constant.
-However, at high pressure, $\dfrac{\text{x}}{\text{m}}$ becomes almost constant i.e. reaches its saturation value.
$\dfrac{\text{x}}{\text{m}}$= K
At the intermediate range of pressure, $\dfrac{\text{x}}{\text{m}}$ will depend mainly upon the power of pressure which lies between the values 0 and 1. This can be expressed as:
$\dfrac{x}{m}=K.{{p}^{1/n}}$
It is seen that all the 3 options mentioned in the question are used in the Freundlich's adsorption isotherm.

Therefore, the correct answer becomes option (D) i.e. All of the above.

Note: It is important to know that the Freundlich adsorption isotherm and its formulae are exclusively for gases that are adsorbate particles and not for any other state of matter. So always check the state of adsorbate before applying the formulae.