At 50°c, 1.2 bar, the system n-pentane (1), n-hexane (2), and n-heptane (3) exists in vapor-liquid equilibrium. the mole fractions of the two phases are x1=0.6, x2=0.2, and x3=0.2 in the liquid, and y1=0.87, y2=0.1, and y3=0.03 in the vapor. the system contains an equal number of total moles of vapor and total moles of liquid.

a) calculate the fugacity and the fugacity coefficient of each component in the vapor. justify any assumptions that you make.
b) again justifying any assumptions that you make, determine the activity coefficients (lewis reference state) for each species in the liquid.
c) as accurately as you can (given the data available), determine the vapor pressures of the three species at 50°c.
d) to what pressure would it be necessary to compress this mixture to condense all of the vapor?