GATE MT 2021 Q6. Elements A and B have the same crystal structure. For a dilute solution of B in A, which one of the following is true? (Given: D𝑯𝒎𝒊𝒙 – Mixing enthalpy, aB – Activity of B and XB – Mole fraction of B)

Answer:- Option D

Hmix:- Enthalpy change during the formation of a binary solution of A & B

Activity:- It is a measure of the effective or free concentration of a species under non-ideal conditions.

Since it is given in the question that A & B have the same CRYSTAL STRUCTURE, which is the most important criteria for extensive solid solubility according to HUME-ROTHERY RULES this implies that there will be an attraction between A & B so Hmixing will be<0 

Now, from RAOULT’S LAW, we have,

Activity= Activity coefficient *  Mole fraction(X)

Since there is an attraction between A & B,

ACTIVITY COEFFICIENT will be< 1

This implies (Activity) of A will be< (Mole fraction) of A