Question

In Freundlich adsorption isotherm at moderate pressure, the extent of adsorption $(x/m)$ is directly proportional to $P^x$. The value of x is :

• A. 1
• B. zero
• C. $\infty$
• D. $1/n$

Hint:

At very low pressure, $1/n = 1$ (linear). At very high pressure, $1/n = 0$ (independent of pressure). At moderate pressure, it is $1/n$.

Answer 1

The Correct Option is D

The question is about the Freundlich adsorption isotherm, which is an empirical relationship describing the adsorption of solutes from a liquid to a solid surface. The Freundlich adsorption isotherm is expressed as:

x/m = kP^{1/n}

where:

• x/m is the extent of adsorption, which is the amount of adsorbate adsorbed per unit mass of the adsorbent.
• P is the pressure of the gas or concentration of the solute.
• k and 1/n are constants that depend on the nature of the adsorbent and adsorbate, as well as the temperature.

In the Freundlich adsorption isotherm at moderate pressure, it is given that the extent of adsorption is directly proportional to P^x. This means we are looking for the value of x that equates to 1/n in the equation above, as this is the form of the isotherm when expressed with pressure dependencies in terms of exponents.

The given options are:

• 1
• zero
• \infty
• 1/n

Given that the Freundlich isotherm is expressed in the form x/m = kP^{1/n}, it directly shows that x=1/n. Therefore, the correct value for x is 1/n.

Thus, the correct answer is option 4: 1/n.