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 ${\text{90 moles.}}$
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: ${\begin{aligned}{\text{accumulation}}&={\text{in}}-{\text{out}}+{\text{generation}}-{\text{consumption}}\\-100&=0-{\text{out}}+500-300\\{\text{out}}&=300{\text{reindeers/yr}}\\\end{aligned}}$

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
${\begin{aligned}{\dot {n}}_{3}&=100L/min\cdot {\frac {1gH_{2}O}{1mlH_{2}O}}\cdot {\frac {1000mL}{1L}}\cdot {\frac {1molH_{2}O}{18gH_{2}O}}\\&=5556mol/min\\\end{aligned}}$

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

Step 3 - Determine the molar flow rate for Stream 4

Using the water balance,
${\begin{aligned}{\text{mass of water out (Stream 4)}}&={\text{ mass of water in (Stream 3)}}\\{\frac {0.6wtH_{2}O}{wtstream}}\cdot {\dot {n}}_{4}\cdot {\frac {25.2g}{mol}}&=5556mol/min\cdot 18g/mol\\{\dot {n}}_{4}&=6.6\cdot 10^{3}mol/min\\\end{aligned}}$

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

Overall balance,
${\begin{aligned}{\dot {n}}_{1}+5556mol/min&={\dot {n}}_{2}+6.6\cdot 10^{3}mol/min\\\end{aligned}}$
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,
${\begin{aligned}{\dot {n}}_{1}&=2.34\cdot 10^{4}mol/min\\{\dot {n}}_{2}&=2.23\cdot 10^{4}mol/min\\\end{aligned}}$

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

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

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
${\begin{aligned}{\dot {n_{O_{2}}}}_{theoretical}&=100kmol/hr\cdot {\frac {\text{5 lb mole O2}}{\text{4 lb mole NO}}}\\&=125kmol/hr\\\end{aligned}}$
The amount of O₂ fed is
${\begin{aligned}{\dot {n_{O_{2}}}}_{theoretical}\times 1.5&=187.5kmol/hr\\\end{aligned}}$

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:
${\begin{aligned}60kgNH_{3}\cdot {\frac {1kmolNH_{3}}{17kgNH_{3}}}&=3.53kmolNH_{3}\\120kgO_{2}\cdot {\frac {1kmolO_{2}}{32kgO2}}&=3.75kmolO_{2}\\{\frac {n_{O_{2}}}{n_{NH_{3}}}}&={\frac {3.75}{3.53}}\\&=1.06<1.25\end{aligned}}$
Hence, oxygen is the limiting reactant

Required NH₃
${\begin{aligned}{\frac {\text{4 lb mole NH3}}{\text{5 lb mole O2}}}\cdot 3.75kmolO_{2}&=3kmolNH_{3}\end{aligned}}$

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

Extent of reaction:
${\begin{aligned}(n_{O_{2}})_{exhaust}&=(n_{O_{2}})_{feed}-\upsilon _{O_{2}}\cdot \xi \\0&=3.75-(-5)(\xi )\\\xi &=0.75kmol\\\end{aligned}}$

Mass of NO:
${\begin{aligned}{\frac {\text{4 lb mole NO}}{\text{5 lb mole O2}}}\cdot {\frac {\text{30 kg NO}}{\text{1 kmol NO}}}\cdot 3.75kmolO_{2}&=90kgNO\end{aligned}}$

Question 5

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

In the feed, chlorine (Cl₂) and ethane (C₂H₆) are fed at 200 mol/hr and 100 mol/hr respectively. The outlet of the reactor is then fed into a separator where the desired product, C₂H₅Cl is separated in the bottoms while the top fraction contains only HCl, Cl₂ and C₂H₄Cl₂ which is removed from the system. Also, a recycle stream containing Cl₂, C₂H₅Cl and C₂H₆ from the top stream feeds back to the initial feed stream where the 2 streams are mixed before being fed back into the reactor.

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	6 (n4, n6,HCl, n6,Cl2, n6,C2H4Cl2,S1, S2 )
Species balances	5
Other relationships	1 (Selectivity)
DOF	0