Two identical vessels are completely filled with two ideal gases A and B. If the ratio of mass of gas A to that of gas B is 1:2 and the ratio of rms speed of molecules of gas A to that of gas B is 2:1, the ratio of pressure exerted by molecules of gas B, on the walls of vessel to that by molecules of gas A is

Step-by-step solution

The pressure exerted by an ideal gas is given by P = 1 3 v_ rms ^2 = 1 3 m V v_ rms ^2 Since the vessels are identical, the volume V is the same for both gases. Therefore, P m v_ rms ^2 The ratio of pressures is given by: P_B P_A = m_B m_A ( v_ rms, B v_ rms, A )^2 Given m_A m_B = 1 2 m_B m_A = 2 And v_ rms, A v_ rms, B = 2 1 v_ rms, B v_ rms, A = 1 2 Substituting the values: P_B P_A = 2 ( 1 2 )^2 = 2 1 4 = 1 2 The ratio of pressure exerted by gas B to that by gas A is 1 : 2 . Answer: 1 : 2