calculate the mole fraction of toulenein the vapour phase which is in equilibrium with a solution of benzene and toulenehaving a mole fraction of toulene 0.5 (the vapour pressure of pure benzene is 119 torr and that of toulene is 37 torr at the same temperature)

Dear Student,

Please find below the solution to the asked query:
Vapour pressure of toluene p_Ao = 37 torr
Vapour pressure of benzene p_B^o = 119 torr
Mole fraction of toluene = 0.5  (present in the solution)[given]

x_A = 0.5   , therefore x_B = 0.5   [since x_A + x_B =1]
According to Raoults Law.
                    P  = p_A+ p_B
                        = ​x_A p_A^o + ​x_B p_B^o
                        = ​​0.5(37)   + 0.5 (119)
                        = 18.5  +59.5
                     P = 78 torr

Again , ​​ ​x_A  = p_A/P
                  = p_A/(p_A+ p_B)
                 =  18.5/78
                = 0.237


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