Question

In the van der Waals equation of state, the volume correction factor (b) arises from the repulsive interactions between the gas moleculesConsidering the molecules to behave as hard spheres of radius r, b = Y $\times$ V$_{\text{molecule}}$ $\times$ N$_A$The value of Y is _ _ _.

• A. 8
• B. 2
• C. 16
• D. 4

Hint:

In van der Waals equation, excluded volume per mole is four times the actual molecular volume

Answer 1

The Correct Option is D

Step 1: Meaning of b.
The constant b is the excluded volume that comes from the finite size of the molecules.

Step 2: Excluded volume of a pair.
Two hard spheres of radius r cannot approach closer than 2r, so the excluded sphere has radius 2r and volume eight times the molecular volume.

Step 3: Share it per molecule.
Dividing by two for the pair gives four times the molecular volume per molecule, so b $= 4 V_{\text{molecule}} N_A$.

Step 4: Answer.
\[ \boxed{Y = 4} \]