400 mg/s Quº₂ lufi 2121 2 021²₂ 3 Ques 200 mg/s Q₁ = 120 Q₁ = 40 212=80 223-60 22120 The image above shows a set of reactors in an ammonia fertilizer plant. A chemical catalys used to accelerate the formation of ammonia is injected at 400 mg/s in Reactor 1 and at 200 mg/s in Reactor 3. The system is at steady state which means that the system is stable and nothing (concentration, c in each reactor and flow rates in/out of each tank) is changing with time. The mass flow rate of the catalyst in to each reactor (at steady state) is the same as the mass flow rate out of each reactor and is given by the product of the flow rate, Q times the concentration of catalyst in the upstream reactor, c. For example: For Reactor 3, the mass flow rate of the catalyst coming in is: Q131 +232 + 200mg/s where, c, is the concentration in Reactor 1 and c₂ is the concentration in Reactor 3. The mass flow rate of catalyst going out of Reactor 3 is Q3303 where c3 is the concentration in Reactor 3. Because this is steady state: Q1391 +232 + 200 = Q33C3 The flowrates, Q at each of the connectors between reactors/tanks is given in the figure. 1. Write down the set of the equations that govern catalyst concentrations for each of the tanks. 2. Solve the system of equations for the concentrations, C₁, C₂, C3 using any viable approach discussed in class
400 mg/s Quº₂ lufi 2121 2 021²₂ 3 Ques 200 mg/s Q₁ = 120 Q₁ = 40 212=80 223-60 22120 The image above shows a set of reactors in an ammonia fertilizer plant. A chemical catalys used to accelerate the formation of ammonia is injected at 400 mg/s in Reactor 1 and at 200 mg/s in Reactor 3. The system is at steady state which means that the system is stable and nothing (concentration, c in each reactor and flow rates in/out of each tank) is changing with time. The mass flow rate of the catalyst in to each reactor (at steady state) is the same as the mass flow rate out of each reactor and is given by the product of the flow rate, Q times the concentration of catalyst in the upstream reactor, c. For example: For Reactor 3, the mass flow rate of the catalyst coming in is: Q131 +232 + 200mg/s where, c, is the concentration in Reactor 1 and c₂ is the concentration in Reactor 3. The mass flow rate of catalyst going out of Reactor 3 is Q3303 where c3 is the concentration in Reactor 3. Because this is steady state: Q1391 +232 + 200 = Q33C3 The flowrates, Q at each of the connectors between reactors/tanks is given in the figure. 1. Write down the set of the equations that govern catalyst concentrations for each of the tanks. 2. Solve the system of equations for the concentrations, C₁, C₂, C3 using any viable approach discussed in class
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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![The image shows a set of reactors in an ammonia fertilizer plant. A chemical catalyst used to accelerate the formation of ammonia is injected at 400 mg/s in Reactor 1 and at 200 mg/s in Reactor 3. The system is at a steady state, meaning that the system is stable and nothing (such as concentration, \( c \), in each reactor and flow rates in/out of each tank) is changing with time.
The mass flow rate of the catalyst into each reactor (at steady state) is the same as the mass flow rate out of each reactor. This is given by the product of the flow rate, \( Q \), times the concentration of catalyst in the upstream reactor, \( c \). For example, for Reactor 3, the mass flow rate of the catalyst coming in is:
\[
Q_{13}c_1 + Q_{23}c_2 + 200 \, \text{mg/s}
\]
where \( c_1 \) is the concentration in Reactor 1 and \( c_2 \) is the concentration in Reactor 3.
The mass flow rate of the catalyst going out of Reactor 3 is \( Q_{33}c_3 \), where \( c_3 \) is the concentration in Reactor 3. Because this is steady state:
\[
Q_{13}c_1 + Q_{23}c_2 + 200 = Q_{33}c_3
\]
The flow rates, \( Q \), at each of the connectors between reactors/tanks are given in the figure:
- \( Q_{12} = 120 \)
- \( Q_{21} = 40 \)
- \( Q_{13} = 80 \)
- \( Q_{23} = 60 \)
- \( Q_{31} = 20 \)
Tasks:
1. Write down the set of equations that govern catalyst concentrations for each of the tanks.
2. Solve the system of equations for the concentrations, \( c_1 \), \( c_2 \), \( c_3 \) using any viable approach discussed in class.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F20ef5b89-bdf5-4ebf-bc1c-34f412b810c9%2F242b056f-aeb6-41f4-ae17-ab13e238710a%2Fic2ov8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image shows a set of reactors in an ammonia fertilizer plant. A chemical catalyst used to accelerate the formation of ammonia is injected at 400 mg/s in Reactor 1 and at 200 mg/s in Reactor 3. The system is at a steady state, meaning that the system is stable and nothing (such as concentration, \( c \), in each reactor and flow rates in/out of each tank) is changing with time.
The mass flow rate of the catalyst into each reactor (at steady state) is the same as the mass flow rate out of each reactor. This is given by the product of the flow rate, \( Q \), times the concentration of catalyst in the upstream reactor, \( c \). For example, for Reactor 3, the mass flow rate of the catalyst coming in is:
\[
Q_{13}c_1 + Q_{23}c_2 + 200 \, \text{mg/s}
\]
where \( c_1 \) is the concentration in Reactor 1 and \( c_2 \) is the concentration in Reactor 3.
The mass flow rate of the catalyst going out of Reactor 3 is \( Q_{33}c_3 \), where \( c_3 \) is the concentration in Reactor 3. Because this is steady state:
\[
Q_{13}c_1 + Q_{23}c_2 + 200 = Q_{33}c_3
\]
The flow rates, \( Q \), at each of the connectors between reactors/tanks are given in the figure:
- \( Q_{12} = 120 \)
- \( Q_{21} = 40 \)
- \( Q_{13} = 80 \)
- \( Q_{23} = 60 \)
- \( Q_{31} = 20 \)
Tasks:
1. Write down the set of equations that govern catalyst concentrations for each of the tanks.
2. Solve the system of equations for the concentrations, \( c_1 \), \( c_2 \), \( c_3 \) using any viable approach discussed in class.
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