Question

If x is amount of adsorbate and m is amount of adsorbent, which of the following relations is not related to adsorption process?
A. $\dfrac{x}{m}=\text{f(T)}$ at constant P.
B. $P=\text{f(T)}$ at constant $\left( \dfrac{x}{m} \right)$.
C. $\dfrac{x}{m}=P\times T$
D. $\dfrac{x}{m}=\text{f(P)}$ at constant T.

Answer 1

Hint: For this question, you should have an idea about the term adsorption and adsorption isotherm. There are two types of adsorption isotherm i.e. Langmuir’s adsorption isotherm and Freundlich adsorption isotherm. Try to relate the formulas given in the option with these isotherms.

Complete Solution :
Let us first know about what is adsorption and adsorption isotherm.
So, adsorption is a surface phenomenon where atoms or ions or molecules of either liquids, gases or solids (which are dissolved) get retained at the surface of another substance (which is in different phase) through adhesive forces. The substance that retains or gets concentrated at the surface is known as adsorbate whereas the surface is called as the adsorbent.
- The variation in the amount of gas adsorbed by the adsorbent with pressure at constant temperature can be expressed by means of a curve termed as adsorption isotherm.

- Langmuir adsorption isotherm is used to deal with chemical adsorption in particular which fails at high pressure. According to this, the amount of gas adsorbed at very high pressure reaches a constant limiting value. It is expressed as:
$\dfrac{x}{m}=\dfrac{aP}{1+bP}$, where
x is the mass of the gas,
m is the mass of the adsorbent,
P is the pressure,
a and b is the Langmuir parameter.

- Freundlich adsorption isotherm is an empirical relationship between the quantity of gas that is adsorbed by unit mass of solid adsorbent and pressure at a particular temperature and it is expressed as:
$\dfrac{x}{m}=k.{{p}^{\dfrac{1}{n}}}$, where
x is the mass of the gas adsorbed on the solid adsorbent,
m is the mass of the solid adsorbent,
p is the pressure,
k and n are the constants that depend on the nature of the adsorbent and nature of the gas at a temperature.

- It is important to note that adsorption isotherms and adsorption isobars are generally plotted only when either temperature or pressure is kept constant. It cannot be plotted when none of the pressure or temperature is constant.
We can see that; third option is not related to the adsorption process.
So, the correct answer is “Option C”.

Note: It is important to note that, the two adsorption isotherms mentioned above are defined for adsorption process and for ideal gases only which are adsorbate particles and not for any other state of matter.