The density of a gas A is thrice that of a gas B at the same temperature. The molecular weight of gas B is twice that of A . What will be the ratio of pressure acting on B and A ?

Step-by-step solution

The ideal gas equation is given by PV = nRT , where n = m M . Substituting this, we get PV = m M RT . Rearranging for pressure P , we have P = m V RT M = dRT M , where d is the density and M is the molecular weight. Given the conditions for gas A and gas B at the same temperature T : d_A = 3d_B M_B = 2M_A The ratio of pressure of B to A is given by: P_B P_A = d_B RT / M_B d_A RT / M_A = d_B d_A M_A M_B Substituting the given ratios: P_B P_A = ( d_B 3d_B ) ( M_A 2M_A ) = 1 3 1 2 = 1 6 Answer: 1 6