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 atm 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 specific conditions cited above (x_F = 0:4; T = 80°C).

(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.

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110 CH,OH-water vapor-liquid equilibrium data P = 1 atm 100 90 Vapor 80 70 Liquid 0.2 0.6 0.4 0.8 x, y (CH;OH liquid and vapor mole fractions) Temperatue (°C) moles of vapor moles of liquid y-XF