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**Chemical Engineering 140 August 31, 2015
**

**Problem Set #2
**(Due Wednesday, September 9)

**7. **2.34 also answer part (c)
(c) What is the reaction-rate expression in a batch stirred tank reactor?

**8**. **Given on a previous midterm**
An incompressible, nonvolatile liquid is pumped into the bottom of a closed
tank of volume *Vo* and diameter *D*. At the start of filling, the tank contains only
an inert, ideal gas, such as air, that is insoluble in the liquid. The initial pressure
in the tank is *po*, and the supply liquid volumetric flow rate is proportional to the
difference in the inlet line pressure, *pin* and the pressure in the tank, *p *(which is
constant throughout the tank). The process is isothermal.

a. Draw a sketch of the filling process and describe in words what happens.

b. What is the final pressure in the tank?

c. Perform a mass balance on the gas phase to establish the transient pressure in the tank as a function of the liquid volume.

d. What is the liquid height in the tank at the final pressure?

e. Perform a mass balance on the liquid to derive an implicit expression for the
liquid height in the tank as a function of time in terms of the parameters *po, pin,
Vo, *and *D*.

**9. **A spherical metal drum is slowly filled with benzene as shown in Figure 10.

a. Derive a mathematical formula for *ρ*, the density in kg/m3 of benzene-containing
drum as a function of the following:
*h*, the depth of benzene
*R*, the radius of the spherical tank
*ρb*, the density of benzene
*md*, the mass of the empty metal drum

b. If the diameter of the drum is 2.00 m, the density of the benzene is 0.879 g/cm3,
the mass of the empty metal drum is 200 kg, and *h* = 1.75*R*, will the drum float or
sink if sealed and placed in water? Show your work.

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**Chemical Engineering 140 Problem Set 2 continued August 31, 2015
**

c. Once the benzene in the tank reaches the height *h* = 1.75*R*, benzene flow into the
tank is stopped and the benzene is allowed to drain by gravity out of the tank.
The volumetric flow rate of benzene out of the tank is directly proportional to the
square root of the height of benzene in the tank with a constant of proportionality
equal to 0.0192 m5/2/s. How long does it take the tank to drain of benzene?

Figure 10. Benzene drainage after filling a spherical tank to a set fill height.

**10. **In one paragraph, explain how the MEA CO2 stack-gas separation process
works. Be sure to point out why two columns are needed. Why is the first column
called the absorber column and the second column (from left to right) is called
the stripper column? What is the purpose of heat exchanger at the entrance to
the stripper column?

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