Liquids A and B form an ideal solution. At 30^ C , the total vapour pressure of a solution containing 1 ~mol of A and 2 ~mol of B is 250 ~mm Hg . The total vapour pressure becomes 300 ~mm Hg when 1 more mol of A is added to the first solution. The vapour pressures of pure A and B at the same temperature are

Step-by-step solution

Let vapour pressure of A=P_A^0 Vapour pressure of B=P_B^0 In first solution, Mole fraction of A (x_A )= 1 1+2 = 1 3 Mole fraction of B (x_B )= 2 1+2 = 2 3 According to Raoult's law, Total vapour pressure aligned & =250=P_A^0 x_A+P_B^0 x_B & 250= 1 3 P_A^0+ 2 3 P_B^0 aligned In second solution Mole fraction of A (x_A )= 2 2+2 = 2 4 = 1 2 Mole fraction of B (x_B )= 2 4 = 1 2 Total vapour pressure aligned & =300=P_A^0 x_A+P_B^0 x_B & 300= 1 2 P_A^0+ 1 2 P_B^0 aligned Multiplying equation (i) by 1 2 and equation (ii) b