Documentation:CHBE Exam Wiki/Module 2 - Reactors

CHBE 241; Exam resources wiki
Chemical and Biological Engineering
	Welcome to the CHBE Exam Resources Wiki! ; This wiki is intended to host past exams; with fully worked-out hints and solutions
Past Exams
	Final Exam 2016W
	Midterm Exam 1 2016W
	Midterm Exam 2 2016W
Problem Sets
	Module 1 - Process Basics
	Module 2 - Reactors
	Module 3 - Separations 1
	Module 4 - Separations 2
	Module 5 - Non-reactive Energy Balances
	Module 6 - Reactive Energy Balances

Question 1

A stack gas contains mol percentages of 60% N₂, 20% CO₂, 10% O₂ and the rest is water. What is the composition of CO₂ on a dry basis?

Solution

Using a basis of 100 moles, the total number of moles of all the species present excluding water is $90 moles.$
Hence, the total composition of CO₂ on a dry basis is,

$\begin{aligned} \frac{20}{90} & = 0.222 \end{aligned}$

Question 2

Reindeers are a source of great contention in Jasper. Therefore it has been decided that their population should decrease by 100 reindeers/yr. If 500 reindeers are born each year, and wolves/bears eat 300 reindeers/yr, how many reindeers have to be relocated from Jasper to meet the goal?

Solution

Mass balance: $\begin{aligned} accumulation & = in - out + generation - consumption \\ - 100 & = 0 - out + 500 - 300 \\ out & = 300 reindeers/yr \end{aligned}$

Question 3

The waste stream for a natural gas processing facility is treated to remove the sulfur dioxide where the initial concentration of SO₂ is 5 mol% and the remainder is air. In a scrubber, the waste gas is mixed with pure water flowing at 100 L/min. The only mass transfer that occurs in this process is the transfer of some SO₂ into the water. It was found that the concentration of SO₂ in the waste gas vented and exiting water stream are 0.5 wt% and 40 wt% respectively.

Question 3a

Draw a block flow diagram for the described process.

Solution

Question 3b

Calculate the molar flow rates of all the streams

Solution

Step 1 - Determine the molar flow rate for Stream 3
$\begin{aligned} {\dot{n}}_{3} & = 100 L / m i n \cdot \frac{1 g H_{2} O}{1 m l H_{2} O} \cdot \frac{1000 m L}{1 L} \cdot \frac{1 m o l H_{2} O}{18 g H_{2} O} \\ = 5556 m o l / m i n \end{aligned}$

Step 2 - Determine the average molecular weight for Stream 4
$\begin{aligned} \frac{0.4}{64.01 g / m o l} + \frac{0.6}{18 g / m o l} & = \frac{1}{\overline{M W}} \\ \overline{M W} & = 25.2 g / m o l \end{aligned}$

Step 3 - Determine the molar flow rate for Stream 4

Using the water balance,
$\begin{aligned} mass of water out (Stream 4) & = mass of water in (Stream 3) \\ \frac{0.6 w t H_{2} O}{w t s t r e a m} \cdot {\dot{n}}_{4} \cdot \frac{25.2 g}{m o l} & = 5556 m o l / m i n \cdot 18 g / m o l \\ {\dot{n}}_{4} & = 6.6 \cdot 1 0^{3} m o l / m i n \end{aligned}$

Step 4 - Determine the flow rates of Stream 1 and Stream 2

Overall balance,
$\begin{aligned} {\dot{n}}_{1} + 5556 m o l / m i n & = {\dot{n}}_{2} + 6.6 \cdot 1 0^{3} m o l / m i n \end{aligned}$
Air balance,
$\begin{aligned} 0.95 \cdot {\dot{n}}_{1} & = 0.995 \cdot {\dot{n}}_{2} \end{aligned}$

The flow rate of the streams are,
$\begin{aligned} {\dot{n}}_{1} & = 2.34 \cdot 1 0^{4} m o l / m i n \\ {\dot{n}}_{2} & = 2.23 \cdot 1 0^{4} m o l / m i n \end{aligned}$

Question 4

The following equation shows the combustion process of ammonia to produce nitric oxide:
4NH₃ + 5O₂ → 4NO + 6H₂O

Question 4a

Calculate the ratio of O₂ reacted to NO formed on a lb-mol basis

Solution

$\begin{aligned} \frac{5 lb mole O2}{4 lb mole NO} & = 1.25 lb-mole O2 react/lb-mole NO formed \end{aligned}$

Question 4b

If ammonia is fed to a continuous reactor at a rate of 100.0 kmol/h, what oxygen feed rate would correspond to 50.0% excess O₂ ?

Solution

The theoretical amount of O₂ reacted is
$\begin{aligned} {\dot{n_{O_{2}}}}_{t h e o r e t i c a l} & = 100 k m o l / h r \cdot \frac{5 lb mole O2}{4 lb mole NO} \\ = 125 k m o l / h r \end{aligned}$
The amount of O₂ fed is
$\begin{aligned} {\dot{n_{O_{2}}}}_{t h e o r e t i c a l} \times 1.5 & = 187.5 k m o l / h r \end{aligned}$

Question 4c

If 120 kg of oxygen and 60 kg of ammonia are fed into a batch reactor, determine

the limiting reactant
the percentage at which the other reactant is in excess
extent of reaction
mass of NO produced

Solution

Limiting reactant:
$\begin{aligned} 60 k g N H_{3} \cdot \frac{1 k m o l N H_{3}}{17 k g N H_{3}} & = 3.53 k m o l N H_{3} \\ 120 k g O_{2} \cdot \frac{1 k m o l O_{2}}{32 k g O 2} & = 3.75 k m o l O_{2} \\ \frac{n_{O_{2}}}{n_{N H_{3}}} & = \frac{3.75}{3.53} \\ = 1.06 < 1.25 \end{aligned}$
Hence, oxygen is the limiting reactant

Required NH₃
$\begin{aligned} \frac{4 lb mole NH3}{5 lb mole O2} \cdot 3.75 k m o l O_{2} & = 3 k m o l N H_{3} \end{aligned}$

Excess NH₃
$\begin{aligned} \frac{3.53 - 3}{3} \times 100 % & = 17.7 % \end{aligned}$

Extent of reaction:
$\begin{aligned} (n_{O_{2}})_{e x h a u s t} & = (n_{O_{2}})_{f e e d} - υ_{O_{2}} \cdot ξ \\ 0 & = 3.75 - (- 5) (ξ) \\ ξ & = 0.75 k m o l \end{aligned}$

Mass of NO:
$\begin{aligned} \frac{4 lb mole NO}{5 lb mole O2} \cdot \frac{30 kg NO}{1 kmol NO} \cdot 3.75 k m o l O_{2} & = 90 k g N O \end{aligned}$

Question 5

The production of monochloroethane (C₂H₅Cl) follows the following process in a reactor.
$C_{2} H_{6} + C l_{2} \to C_{2} H_{5} C l + H C l$
$C_{2} H_{5} C l + C l_{2} \to C_{2} H_{4} C l_{2} + H C l$
where dichloroethane (C₂H₄Cl₂) is the undesired product. The selectivity of the desired to the undesired product is 3:1.

The fresh feed to the process contains chlorine (Cl₂) and ethane (C₂H₆) at 200 mol/hr and 100 mol/hr, respectively. The outlet of the reactor is then fed into a separator where all of the desired product, C₂H₅Cl is separated in the bottoms. The single-pass conversion is not 100%. Therefore, most of the top stream of the separator is recycled back and mixed with the fresh feed before being they are fed to the reactor. A small fraction of the top stream of the separator is purged.

Question 5a

Draw a block flow diagram showing the important unit operations and streams in the process described above.

Solution

Question 5b

Perform a degree of freedom analysis for the overall process and show whether the system is fully specified.

Solution
Parameter	Values
Unknowns	5 (n₄, n_6,HCl, n_6,Cl₂, n_{6,C₂H₄Cl₂},n_6,C₂H₆)
atomic balances	3 (C, H, Cl)
Other relationships	1 (Selectivity)
DOF	1