An ideal solution contains unknown moles of two volatile liquids A and B. The vapour pressures of pure A and pure B are 400 mm Hg and 600 mm Hg respectively. The total vapour pressure of this initial solution is 520 mm Hg . When 1 mole of liquid A is further added to the solution, the total vapour pressure decreases to 500 mm Hg . The initial number of moles of liquid B in the solution is _______.

Step-by-step solution

Let the initial number of moles of A be x and that of B be y . For the initial solution, the total pressure is: P_T = P_A^ X_A + P_B^ X_B 520 = 400 ( x x+y ) + 600 ( y x+y ) 520(x+y) = 400x + 600y 120x = 80y y = 1.5x (1) When 1 mole of A is added, the new moles of A are (x+1) and the total moles are (x+y+1) . The new total pressure is 500 mm Hg . 500 = 400 ( x+1 x+y+1 ) + 600 ( y x+y+1 ) 500(x+y+1) = 400(x+1) + 600y 500x + 500y + 500 = 400x + 400 + 600y 100x - 100y + 100 = 0 y - x = 1 (2) Substituting equation (1)