Vapor composition from bubble-point temp.

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The discussion focuses on calculating the vapor composition from a mixture of 30 mol% pentane and 70 mol% hexane at 1 atm and 60°C. Using Antoine's equation, the saturation pressures were determined as p*pentane = 1392.95 mmHg and p*hexane = 484.96 mmHg at the bubble-point temperature of 55.1°C. The correct application of Raoult's law reveals that the mole fraction of pentane in the vapor phase is y = 0.550, correcting the initial miscalculation of 0.382. This highlights the importance of distinguishing between vapor and liquid mole fractions in phase equilibrium calculations.

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Suppose you have a mixture of 30 mol% pentane and 70 mol% hexane at 1 atm and 60oC.

If the Tbubble-point = 55.1oC, calculate the composition of vapor of the first bubble as the mixture is heated.

I found p*pentane = 1392.95 and p*hexane = 484.96 using Antoine's equation with T = 55.1.

Now I suppose I must use Raoult's law as:

yaP = xap*a(@55.1oC)

Using this I get xpentane = (0.7*760)/1392.96 = 0.382

However, the answer sheet says xpentane = 0.55.

Can anyone figure where I'm mistaken?
 
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You applied the equation incorrectly. y is the mole fraction in the vapor, and x is the mole fraction in the liquid.

y = (0.3)(1392.96)/760=0.550