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: McGraw-Hill Education
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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.](https://content.bartleby.com/qna-images/question/20ef5b89-bdf5-4ebf-bc1c-34f412b810c9/242b056f-aeb6-41f4-ae17-ab13e238710a/ic2ov8_processed.jpeg)
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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