For an ideal binary solution of liquids A and B, the plot of 1 x_A versus 1 y_A (where x_A and y_A are the mole fractions of A in the liquid and vapour phases, respectively) is a straight line with a slope of 3 . At a certain temperature, when the vapour phase mole fraction of A is 0.5 , the total vapour pressure of the solution is 200 torr. The vapour pressure of pure component A (in torr) is:

Step-by-step solution

From Raoult's law and Dalton's law, we have P_A = x_A P_A^0 = y_A P_ total and P_B = x_B P_B^0 = y_B P_ total . Equating P_ total from both components gives the relation 1 x_A = ( P_A^0 P_B^0 ) 1 y_A + P_B^0 - P_A^0 P_B^0 . The slope of the 1 x_A vs 1 y_A plot is P_A^0 P_B^0 = 3 , which means P_A^0 = 3 P_B^0 . Given y_A = 0.5 and P_ total = 200 torr, the partial pressures are: P_A = y_A P_ total = 0.5 200 = 100 torr P_B = y_B P_ total = 0.5 200 = 100 torr Using Raoult's law: x_A = P_A P_A^0 = 100 P_A^0 x_B = P_B P_