At what speed of the molecules, the value of the Maxwell distribution function f(c) for the temperat — States of Matter and Gaseous State Chemistry Question

💡 Solution & Explanation

Equating f(C) at T and nT: (1/T)^3/2 e^(-MC^2/2RT) = (1/nT)^3/2 e^(-MC^2/2R(nT)) → n^3/2 = e^(MC^2/2RT × (1 - 1/n)). Taking natural log: 1.5 ln n = MC^2/2RT × (n-1)/n → C^2 = 3 R T n ln n / [M (n-1)] → C = √[(3RT n ln n) / (M(n-1))].