PROBLEM #1 (40 points) Within the space provided provide short answers to all parts. (5 POINTS) Why are both DUHEM'S THEOREM AND GIBBS PHASE RULE VERY IMPORTANT IN PHASE EQUILIBRIUM? (5 POINTS) WHAT IS THE DIFFERENCE BETWEEN A FLUID THAT OBEYS RAOULT'S LAW AND A REAL FLUID? (15 POINTS) BUBBLE POINT PRESSURE CALCULATION: A liquid mixture of ace- tone(1)/methanol(2) system is at equilibrium with a vapor from which it is formed. At 55C the vapor pressures are determined to be Prat = 97.2497 kPa, Paat = 68.3364 kPa. Furthermore, at 55C the activity coefficients of the species are 7 = exp(0.64.c) and 72 = exp(0.64x). Given that the composition of the liquid phase is 35 mole percent acetone and the rest methanol, determine the: (i) bubble point pressure of the system at equilibrium and; (ii) composition of the vapor in equilibrium with the liquid. Solution