CBE 250 Midterm Fall 2014 Name:October 24, 2014

Instructions

This exam has four (5) double-sided pages including this page.

Closed notes/closed books. Equations useful/needed to solve the problems are included.

Calculators are permitted for arithmetic only (no graphing). By signing the honor pledge you are signifying that you used a calculator for arithmetic only.

No headphones, cell phones, smartphones, iPods, iPads, laptops, or other electronic devices are permitted. Do not use any device that can access the internet.

Write all answers in exam book. For problems 1 and 4, write your answers on the graphs provided. Use a ruler to draw lines on the graphs.

Show all work for maximum credit.

I will be in the hallway if there are questions.

Sign the honor pledge on your exam book.

1) (50 pts) A distillation column operating at a pressure of 1 kg/cm2 is separating ethanol and water. The flow to the column is 50 kg/hr of a mixture of 40 wt % ethanol and 60 wt % water at 40 °C. The reflux ratio of the column is 2. We desire a distillate composition of 90 wt % ethanol and a bottoms composition of 10 wt % ethanol. The column is equipped with a total condenser and a partial reboiler.

a. (2 pts) Draw and label the process diagram showing all flow rates, compositions, and enthalpies

b. (4 pts) Convert the weight fractions for the feed, distillate and bottoms to mol fractions. The density of water is 1 g/cm3

and ethanol is 0.79 g/cm3. The molecular weight of water is 18 g/mol, and ethanol is 46 g/mol.

c. (7 pts) Write the overall mass and energy balances for the system, and write the mass balance on ethanol, the light key.

d. (6 pts) Solve for the mass flow rates of the bottoms and distillate.e. (12 pts) Use the Ponchon-Savarit chart on the next page to

determine the enthalpies (kcal/hr) required by the reboiler and condenser.

f. (3 pts) What is the approximate temperature of the reboiler?g. (6 pts) What is the value of q for the feed? Plot the q-line on the

attached McCabe-Thiele diagramh. (10 pts) Determine the number of equilibrium stages required for

the separation and determine the optimal feed stage.

1) continued, Ponchon-Savarit diagram

1) continued, draw answers for parts g and h on this graph

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

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x, liquid mol fraction

y, v

ap

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mo

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1) continued, extra graph for scratch work

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

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x, liquid mol fraction

y, v

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2) (20 pts) One way to account for non-idealities in the gas phase is to use the compressibility factor to modify the ideal gas law:

P= ZRTv

In your homework, you considered the van der Waals equation of state

P= RTv−b

− a

v2

And derived the values of a and b using the criticality conditions:

a=9RT C vC8

, b=vC3

Where Tc and vc are the critical temperature and volume, respectively.

a. (10 pts) Determine the value of the compressibility factor at the critical point, Zc. Show all work for full credit.

b. (10 pts) Given your solution to part a, express the constants a and b in terms of the critical pressure and critical temperature. Your final expression should not contain vc.

3) (12 pts) A liquid waste stream from a chemical plant is composed of mostly water with a small amount of acetone. This stream is contacted with air to remove the acetone. The process is being carried out at atmospheric pressure and 317 K. The infinite dilution activity coefficient for acetone in water at this temperature is 8.3. The vapor pressures of water and acetone at this temperature are 68 mmHg and 488 mmHg, respectively.

a. (2 pts) Is this process absorption or stripping? Explain why in one sentence

b. (10 pts) Compute an expression for the equilibrium data for acetone at the process conditions.

4) (18 pts) You have a series of flash drums set up so that the liquid stream of flash separator j enters as the feed of separator j+1 (see drawing).

Each of the flash separators operates at a slight vacuum of 30.4 kPa. Each of the flash units is set up such that 50% of the feed is vaporized. You wish to use this cascade to separate water and ethylene glycol. The feed to the first flash unit is 80 mol% water.

a. (12 pts) How many flash separators do you need in order to get an ethylene glycol product that contains 5 mol% water or less? Equilibrium data are given on the following page.

b. (6 pts) What is the percent recovery of ethylene glycol in the liquid stream at the end of the cascade?

Useful equation: operating line equation for flash separator

4) continued, water/ethylene glycol VLE data

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x water

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4) continued, water/ethylene glycol VLE data (extra copy)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

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x water

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