Four ideal gases P, Q, R, and S have their molecular diameters and number densities given as follows: Gas P: diameter = d₀ , number density = n₀ Gas Q: diameter = 2d₀ , number density = 0.5n₀ Gas R: diameter = 0.5d₀ , number density = 2n₀ Gas S: diameter = 0.5d₀ , number density = 0.5n₀ Which of the four gases has the maximum mean free path?

Step-by-step solution

The mean free path of a gas molecule is given by: = 1 2 d^2 n Thus, the mean free path is inversely proportional to the square of the molecular diameter and inversely proportional to the number density ( 1 d^2 n ). Let us calculate the relative factor 1 d^2 n for each gas: For Gas P: 1 (1)^2 1 = 1 For Gas Q: 1 (2)^2 0.5 = 1 4 0.5 = 0.5 For Gas R: 1 (0.5)^2 2 = 1 0.25 2 = 2 For Gas S: 1 (0.5)^2 0.5 = 1 0.25 0.5 = 8 Gas S has the largest relative factor, and therefore it has the maximum mean free path. Answer: Gas S