We have a feed that is a binary mixture of methanol and water (55.0 mol% methanol) sent to a system of two flash drums connected together. The vapor from the first drum is cooled, which partially condenses the vapor, and then is fed to the second flash drum. Both drums operate at a pressure of 1.0 atm and are adiabatic. The feed rate to the first drum is 1000 kmol/h. We desire a liquid product from the first drum that is 30.0 mol% methanol ([tex]x_1 = 0.30[/tex]). The second drum operates at a fraction vaporized of [tex](VF)_2 = 0.25[/tex]. The equilibrium data are in Table 2-7.

Task: Sketch the process labeling the different streams.

Equilibrium Data:
| Temperature (°C) | Methanol Liquid (mol%) | Methanol Vapor (mol%) |
|------------------|------------------------|-----------------------|
| 0 | 2.0 | 13.4 |
| 4 | 23.0 | 93.5 |
| 6 | 30.4 | 91.2 |
| 8 | 36.5 | 89.3 |
| 10 | 41.8 | 87.7 |
| 15 | 51.7 | 84.4 |
| 20 | 57.9 | 81.7 |
| 30 | 66.5 | 78.0 |
| 40 | 72.9 | 75.3 |
| 50 | 77.9 | 73.1 |
| 60 | 82.5 | 71.2 |
| 70 | 87.0 | 69.3 |
| 80 | 91.5 | 67.6 |
| 90 | 95.8 | 66.0 |
| 95 | 97.9 | 65.0 |
| 100 | 100.0 | 64.5 |

The question described the process of flash distillation through two sequential drums, with an initial feed of a binary mixture of methanol and water. The first drum produces a liquid product with a specific concentration of methanol, while the second drum takes the partially condensed vapor from the first drum and performs a second distillation.

Explanation:

The process described here is known as flash distillation, which is a separation process widely used in chemical engineering. In this process, a mixture (in this case, a binary mixture of methanol and water) is rapidly vaporized and then chilled to cause part of it to condensate and thereby achieve the separation. In your example, the mixture has a composition of 55.0 mol% methanol and is fed into a system of two sequential flash drums operated at 1 atm.

The first drum is aimed at producing a liquid product with 30.0 mol% methanol. This is achieved through a combination of vaporization and cooling to achieve the desired partial condensation. The partially condensed vapor from the first drum is then sent to a second drum, which operates at a fraction vaporized of 0.25. By managing the conditions in each drum (pressures, feed rates, degree of cooling), it would be possible to control the compositions of the product streams from each drum.

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