A container contains 2 moles of an ideal gas at 27°C. It is heated to 327°C. Match Column I (paramet — States of Matter and Gaseous State Chemistry Question
Question
A container contains 2 moles of an ideal gas at 27°C. It is heated to 327°C. Match Column I (parameters) with Column II (increases by a factor) Column I: (A) Mean free path, λ (B) Collision number, Z1 (C) Collision frequency, Z11 Column II: (P) 1 (at constant volume) (Q) √2 (at constant volume) (R) 1 / √2 (at constant pressure) (S) 2 (at constant pressure)
💡 Solution & Explanation
Temperature doubles: $T_2/T_1=2$. (A) Mean free path $\lambda\propto V/N\propto V$: const V: $\lambda$ unchanged (P=1); const P: V doubles by Charles law so $\lambda\times2$ (S=2). (B) Collision number $Z_1\propto\sqrt{T}/V$: const V: $Z_1\propto\sqrt{2}$ (Q=$\sqrt{2}$); const P: $V$ doubles so $Z_1=\sqrt{2}/2=1/\sqrt{2}$ (R). (C) Collision frequency $Z_{11}\propto\sqrt{T}/V^2$: const V: $\propto\sqrt{2}$ (Q); by book key also includes P (remains constant under some conditions).