n moles of He gas is placed in a vessel of volume V L at T K. If V1 is free volume of He, then the d — States of Matter and Gaseous State Chemistry Question

💡 Solution & Explanation

free volume v1 = v - b, so the co-volume b = v - v1. since b = 4 × n × na × (4/3 π r^3) and r = d/2: b = n × na × (16/3) π (d^3 / 8) = n × na × (2/3) π d^3. equating this to v - v1: v - v1 = n × na × (2/3) π d^3 → d^3 = 3(v - v1) / (2π na n) → d = [(3(v - v1)) / (2π na n)]^(1/3).