Three gram-moles of benzene and 7 gram-moles of toluene are placed in a closed cylinder equipped with a piston. The cylinder is immersed in a boiling-water bath that maintains the temperature at 100°C. The force exerted on the piston can be varied to adjust the cylinder pressure to any desired value. The pressure is initially 1000 mm Hg and is gradually lowered to 600 mm Hg. Use the P_xy diagram of Figure 6.4-1 to convince yourself that the cylinder initially contains only liquid benzene and toluene and to answer the following questions.

(a) At what pressure does the first vapor bubble form? What is its composition?

(b) At what pressure does the last droplet of liquid evaporate? What is its composition?

(c) What are the liquid and vapor compositions in equilibrium with each other when the pressure is 750 mm Hg? What is the ratio (moles vapor/mole liquid) at this point?

(d) Estimate the volume of the cylinder contents when the pressure is (1) 1000 mm Hg, (ii) 750 mm Hg, and (iii) 600 mm Hg.