Chapter 6, Problem 6.71P

A methanol-water feed stream is introduced to a vaporizer in which a molar fraction f of the feed is vaporized. The feed has a methanol mole fraction of x_F= 0.4, and the vaporizer operates at a pressure of 1 atm absolute and 80°C. Vapor and liquid leaving the device are in equilibrium at the temperature and pressure of the system and have methanol mole fractions of y and x, respectively.

A Txy diagram for methanol-water mixtures at 1 arm absolute is shown below. The feed to the vaporizer and the liquid and vapor product streams are shown as points B, A, and C, respectively.

(a) Prove that f can be determined from the equation

Use this result to determine f for the speci?c conditions cited above

(b) Use the Txy diagram to estimate the minimum and maximum temperatures at which the given feed stream could be separated into vapor and liquid fractions at 1 atm. In each case, what fraction of the feed would be vaporized?

(c) The vapor at C is sent to a condenser operated at constant pressure (1 atm). The liquid and vapor product streams leaving the condenser are in equilibrium and in a ratio of 1 mol vapor/1 mol liquid. Estimate the temperature and compositions of the two streams leaving the condenser.