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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 xF = 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 (xF = 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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