Question

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason $R$
Assertion A: Amongst $He, Ne, Ar$ and $Kr$; $1 g$ of activated charcoal adsorbs more of $Kr$
Reason R: The critical volume $V_c\left( cm ^3 mol ^{-1}\right)$ and critical pressure $P_e$ (atm) is highest for Krypton but the compressibility factor at critical point $Z_c$ is lowest for Krypton 
In the light of the above statements, choose the correct answer from the options given below

• A. Both $A$ and $R$ are true but $R$ is NOT the correct explanation of $A$
• B. Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
• C. A is false but $R$ is true
• D. $A$ is true but $R$ is false

Hint:

The adsorption of gases on activated charcoal depends on molecular size and van der Waals forces, not directly on critical parameters like Vc,Pc, or Zc.

Answer 1

The Correct Option is D

To resolve the given question, we need to assess both the assertion and the reason independently and then determine if the reason is a valid explanation for the assertion.

1. Understanding Assertion A: The assertion states that 1 gram of activated charcoal adsorbs more of Krypton (Kr) as compared to Helium (He), Neon (Ne), and Argon (Ar). The extent of adsorption on charcoal generally depends on the polarizability and the size of the gas molecules. Larger and more polarizable gas molecules are adsorbed more effectively. Among He, Ne, Ar, and Kr, Kr has the largest atomic size and the highest polarizability, making Kr the most adsorbed by charcoal. Therefore, Assertion A is true.
2. Understanding Reason R: The reason states that the critical volume and critical pressure are highest for Kr, whereas the compressibility factor at the critical point is lowest for Kr. However, these factors do not directly influence the adsorption capacity of activated charcoal. The adsorption is primarily affected by the van der Waals forces and the size of the gas molecules rather than their critical constants. Therefore, Reason R is false.

Since Assertion A is true and Reason R is false, the correct answer is:

"$A$ is true but $R$ is false"

The adsorption process on charcoal is more related to the molecular properties such as size and polarizability rather than the critical properties as mentioned in the reason.