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 I 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 are 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?

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Temperature (°C) 110 100 90 80 70 60 0 f Liquid = B CH3OH-water vapor-liquid equilibrium data P= 1 atm 0.2 0.4 0.6 0.8 x, v (CH₂OH liquid and vapor mole fractions) Vapor moles of vapor moles of liquid XFX y - x