a solution has 1:4 mole ratio of pentane to hexane . the vapour pressures of the pure hydrocarbons at 20 celcius and 440 mm Hg for pentane and 120 mm Hg for hexane . the mole fraction of pentane in the vapor phase would be

Let the pentane be 1 mole and hexane be 4 mole.
Total number of moles of pentane and hexane in mixture = 1 + 4 = 5 mol 
Mole fraction of pentane in solution = 1/5
Mole fraction of hexane in solution = 4/5
Total pressure of solution :
P_s = X_P P_P^o + X_H P_H^o 
    = 1/5 (440 mm Hg) + 4/5 (120 mm Hg)
   = 88 mm Hg + 96 mm Hg
  = 184 mm Hg  

Mole fraction of pentane in vapour phase = X_P P_P^o/ P_s ​
                                                                 = 88 / 184
                                                                 = 0.478