6.65. Vapor-liquid equilibrium calculations can sometimes be simplified through the use of a quantity called the relative volatility, which may be defined in terms of the following depiction of vapor and liquid phases in equilibrium: Vapor: Y Y Y y; mole fraction of species i in vapor Liquid: XXX x= mole fraction of species i in liquid The relative volatility of species i to species j is αij yılı yıly y;/xx/x If a;; is much greater than 1, species i is much more volatile than species j (i.e., it has a much greate tendency to vaporize at the system temperature and pressure); conversely, if a 1, species i is muc less volatile than species j. The closer a is to 1, the more difficult it is to separate species i fro species j by a process such as distillation or partial condensation of a vapor mixture. (a) Show that the relative volatility of species A to species B, AB, equals the ratio of vapor pressures the system temperature, P/PB, if both species obey Raoult's law and follow ideal-gas behavio (b) Determine the relative volatility of styrene to ethylbenzene at 85°C and the relative volatility benzene to ethylbenzene at the same temperature. Which pair would you classify as more difficu to separate by distillation? (c) Show that for a binary mixture of i and j Yi αijxi 1+ (ajj - 1)xi