The total vapour pressure (in torr) of an ideal binary solution containing components A and B is given by the equation P = 300 - 100 x_A , where x_A is the mole fraction of component A in the liquid phase. When the mole fraction of A in the liquid phase is 0.5 , its mole fraction in the vapour phase is y 10⁻² . The value of y is ________.

Step-by-step solution

The total pressure of an ideal binary solution is given by: P_T = P_A^o x_A + P_B^o (1 - x_A) P_T = P_B^o + (P_A^o - P_B^o)x_A Comparing this with the given equation P = 300 - 100 x_A , we get: P_B^o = 300 torr P_A^o - P_B^o = -100 P_A^o = 300 - 100 = 200 torr For a solution with x_A = 0.5 : Partial pressure of A, P_A = P_A^o x_A = 200 0.5 = 100 torr Total pressure, P_T = 300 - 100(0.5) = 250 torr The mole fraction of A in the vapour phase ( y_A ) is: y_A = P_A P_T = 100 250 = 0.4 Given y_A = y 10⁻² 0.4 = y 10⁻² y