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Asked May 1, 2019

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Step 1

A mixture of 2 moles of Toluene and 3 moles of o-xylene is given.

(a) To calculate the dew point and the liquid composition, consider the following steps:

- Calculate the overall mole fraction for the more volatile component (
*x*), i.e. Toluene, in the gaseous mixture._{T}*x*= 2/2+3 = 0.4_{T}

- On the pressure-versus-mole fraction graph, locate the point where the mole fraction is 0.4 on the
*x*-axis. - From this point on the
*x*-axis, go up till you hit the dew point curve. From here, go left till you hit the bubble point curve. Now, if you move down to the*x*-axis, the point where you hit the*x*-axis will give the liquid composition of Toluene, which is 0.2. After hitting the bubble point curve, if you continue going left to the*y*-axis, we get the dew point pressure as 260 mm Hg.

Do the same for calculating the dewpoint temperature on the T-vs-mole fraction graph. The dew point temperature is 104.6 ^{0}C.

(b) To calculate the bubble point and the vapor composition, consider the following steps:

- Calculate the overall mole fraction for the more volatile component, i.e. Toluene, in the gaseous mixture.
*x*= 2/5 = 0.4_{T}

- On the Pressure-versus-mole fraction graph, locate the point where the mole fraction is 0.4 on the
*x*-axis. - From this point on the
*x*-axis, go up till you hit the bubble point curve. From here, go right till you hit the dew point curve. Now, if you move down to the*x*-axis, the point where you hit the*x*-axis will give the vapor composition of Toluene, which is 0.68. After hitting the dew point curve, if you go left to the*y*-axis, we get the bubble point pressure as 348 mm Hg.

Do the same for calculating the bubble point temperature on the T-versus-mole fraction graph. The bubble point temperature is 95 ^{0}C.

Step 2

(c) To calculate the composition and the molar amounts of the components of the mixture at a pressure of 300 mm Hg and temperature of 100 ^{0}C, consider the following steps.

- Take either of the two curves and solve using the P-versus-mole fraction curve.
- This curve is plotted at a constant temperature of 100
^{0}C. As both the requirements are satisfied, we draw a tie line between the dew point and bubble point curve at a pressure of 300 mm Hg. The end points of the tie line give the composition of the more volatile component, i.e. Toluene, in the liquid and vapor phase as 0.3 and 0.55, respectively.

Since the mixture is binary, the sum of the mole fractions of Toluene and o-Xylene will be one. Therefore, the composition of o-xylene in the liquid phase is given as: *x _{x} *= 1-0.3 = 0.7

Composition of o-xylene in the vapor phase is given as: *y _{x} *= 1-0.55 = 0.45

Step 3

To calculate molar amounts of liquid (*L*) and vapor (*V*), apply overall mole balance, which is given by equation (1), where *F* is the total moles fed. Now, apply component balance for Toluene, which is given by equation (2), where *x*,* y* and *xf* are mole fractions of Toluene in the liquid phase, vapor phase and in the feed, respectively.

On solving equations (1) and (2), we get equati...

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