The RMS speeds of the molecules of two gases A and B are in the ratio 0.866: 1 at 27°C for A and 127 — States of Matter and Gaseous State Chemistry Question

💡 Solution & Explanation

Given: u_A / u_B = 0.866 = (√3)/2. Since u = √(3RT/M): u_A / u_B = √(T_A × M_B / (T_B × M_A)) = 1.5/2 → 3/4 = T_A × M_B / (T_B × M_A). Given T_A = 300 K, T_B = 400 K: 3/4 = (300 × M_B) / (400 × M_A) = 3/4 × M_B / M_A → M_B / M_A = 1 → M_A = M_B. The molecular masses of A and B must be equal. Molar masses: $N_2$ (28) and $CO$ (28); $O_2$ (32) and N2H4 (32); $N_2O$ (44) and $CO_2$ (44).