UPSC Exam > UPSC Questions > The irreversible zero order reaction \( \math...
Start Learning for Free
The irreversible zero order reaction \( \mathbf{A} \rightarrow \mathbf{B} \) takes place in a porous cylindrical catalyst that is sealed at both ends as shown in figure. Assume dilute concentration and neglect any variations in the axis direction. (4)The steady state concentration profile is \( \frac{C_{A}}{C_{A_{S}}}=1+\frac{\Phi_{O}^{2}}{8}\left[\left(\frac{r}{R}\right)^{2}-1\right] \)Where \( \Phi_{0} \) is the Thiele modulus. For \( \Phi_{0}=4 \). Calculate the followingA. The range of \( r \) where \( \mathrm{C}_{\mathrm{A}}=0 \).B. Percentage of total radius of catalyst remain unused.?
Most Upvoted Answer
The irreversible zero order reaction \( \mathbf{A} \rightarrow \mathbf...
The Steady State Concentration Profile
To analyze the irreversible zero-order reaction \( \mathbf{A} \rightarrow \mathbf{B} \) in a porous cylindrical catalyst, we can use the given concentration profile:
\[
\frac{C_{A}}{C_{A_{S}}} = 1 + \frac{\Phi_{O}^{2}}{8}\left[\left(\frac{r}{R}\right)^{2} - 1\right]
\]
Where \( \Phi_{O} \) is the Thiele modulus.
A. Range of \( r \) where \( C_{A} = 0 \)
To find the range of \( r \) where \( C_{A} = 0 \), set the concentration equation to zero:
\[
0 = 1 + \frac{\Phi_{O}^{2}}{8}\left[\left(\frac{r}{R}\right)^{2} - 1\right]
\]
Solving for \( r \):
\[
\frac{\Phi_{O}^{2}}{8}\left[\left(\frac{r}{R}\right)^{2} - 1\right] = -1
\]
This leads to:
\[
\left(\frac{r}{R}\right)^{2} = 1 - \frac{8}{\Phi_{O}^{2}}
\]
Substituting \( \Phi_{O} = 4 \):
\[
\left(\frac{r}{R}\right)^{2} = 1 - \frac{8}{16} = 0.5
\]
Thus:
\[
\frac{r}{R} = \sqrt{0.5} \Rightarrow r = R \cdot \frac{1}{\sqrt{2}} \approx 0.707R
\]
B. Percentage of Total Radius of Catalyst Remaining Unused
The unused catalyst radius corresponds to the area where \( C_{A} = C_{A_{S}} \).
1. The effective reaction zone is from \( r = 0 \) to \( r = 0.707R \).
2. The total radius of the catalyst is \( R \).
Calculating the percentage of the unused area:
- Radius where \( C_{A} = C_{A_{S}} \): \( R - 0.707R = 0.293R \)
- Percentage of unused catalyst:
\[
\text{Percentage} = \left( \frac{0.293R}{R} \right) \times 100 \approx 29.3\%
\]
Thus, approximately 29.3% of the total radius of the catalyst remains unused, indicating that a significant portion of the catalyst is not participating in the reaction.
To analyze the irreversible zero-order reaction \( \mathbf{A} \rightarrow \mathbf{B} \) in a porous cylindrical catalyst, we can use the given concentration profile:
\[
\frac{C_{A}}{C_{A_{S}}} = 1 + \frac{\Phi_{O}^{2}}{8}\left[\left(\frac{r}{R}\right)^{2} - 1\right]
\]
Where \( \Phi_{O} \) is the Thiele modulus.
A. Range of \( r \) where \( C_{A} = 0 \)
To find the range of \( r \) where \( C_{A} = 0 \), set the concentration equation to zero:
\[
0 = 1 + \frac{\Phi_{O}^{2}}{8}\left[\left(\frac{r}{R}\right)^{2} - 1\right]
\]
Solving for \( r \):
\[
\frac{\Phi_{O}^{2}}{8}\left[\left(\frac{r}{R}\right)^{2} - 1\right] = -1
\]
This leads to:
\[
\left(\frac{r}{R}\right)^{2} = 1 - \frac{8}{\Phi_{O}^{2}}
\]
Substituting \( \Phi_{O} = 4 \):
\[
\left(\frac{r}{R}\right)^{2} = 1 - \frac{8}{16} = 0.5
\]
Thus:
\[
\frac{r}{R} = \sqrt{0.5} \Rightarrow r = R \cdot \frac{1}{\sqrt{2}} \approx 0.707R
\]
B. Percentage of Total Radius of Catalyst Remaining Unused
The unused catalyst radius corresponds to the area where \( C_{A} = C_{A_{S}} \).
1. The effective reaction zone is from \( r = 0 \) to \( r = 0.707R \).
2. The total radius of the catalyst is \( R \).
Calculating the percentage of the unused area:
- Radius where \( C_{A} = C_{A_{S}} \): \( R - 0.707R = 0.293R \)
- Percentage of unused catalyst:
\[
\text{Percentage} = \left( \frac{0.293R}{R} \right) \times 100 \approx 29.3\%
\]
Thus, approximately 29.3% of the total radius of the catalyst remains unused, indicating that a significant portion of the catalyst is not participating in the reaction.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
The irreversible zero order reaction \( \mathbf{A} \rightarrow \mathbf{B} \) takes place in a porous cylindrical catalyst that is sealed at both ends as shown in figure. Assume dilute concentration and neglect any variations in the axis direction. (4)The steady state concentration profile is \( \frac{C_{A}}{C_{A_{S}}}=1+\frac{\Phi_{O}^{2}}{8}\left[\left(\frac{r}{R}\right)^{2}-1\right] \)Where \( \Phi_{0} \) is the Thiele modulus. For \( \Phi_{0}=4 \). Calculate the followingA. The range of \( r \) where \( \mathrm{C}_{\mathrm{A}}=0 \).B. Percentage of total radius of catalyst remain unused.?
Question Description
The irreversible zero order reaction \( \mathbf{A} \rightarrow \mathbf{B} \) takes place in a porous cylindrical catalyst that is sealed at both ends as shown in figure. Assume dilute concentration and neglect any variations in the axis direction. (4)The steady state concentration profile is \( \frac{C_{A}}{C_{A_{S}}}=1+\frac{\Phi_{O}^{2}}{8}\left[\left(\frac{r}{R}\right)^{2}-1\right] \)Where \( \Phi_{0} \) is the Thiele modulus. For \( \Phi_{0}=4 \). Calculate the followingA. The range of \( r \) where \( \mathrm{C}_{\mathrm{A}}=0 \).B. Percentage of total radius of catalyst remain unused.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The irreversible zero order reaction \( \mathbf{A} \rightarrow \mathbf{B} \) takes place in a porous cylindrical catalyst that is sealed at both ends as shown in figure. Assume dilute concentration and neglect any variations in the axis direction. (4)The steady state concentration profile is \( \frac{C_{A}}{C_{A_{S}}}=1+\frac{\Phi_{O}^{2}}{8}\left[\left(\frac{r}{R}\right)^{2}-1\right] \)Where \( \Phi_{0} \) is the Thiele modulus. For \( \Phi_{0}=4 \). Calculate the followingA. The range of \( r \) where \( \mathrm{C}_{\mathrm{A}}=0 \).B. Percentage of total radius of catalyst remain unused.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The irreversible zero order reaction \( \mathbf{A} \rightarrow \mathbf{B} \) takes place in a porous cylindrical catalyst that is sealed at both ends as shown in figure. Assume dilute concentration and neglect any variations in the axis direction. (4)The steady state concentration profile is \( \frac{C_{A}}{C_{A_{S}}}=1+\frac{\Phi_{O}^{2}}{8}\left[\left(\frac{r}{R}\right)^{2}-1\right] \)Where \( \Phi_{0} \) is the Thiele modulus. For \( \Phi_{0}=4 \). Calculate the followingA. The range of \( r \) where \( \mathrm{C}_{\mathrm{A}}=0 \).B. Percentage of total radius of catalyst remain unused.?.
The irreversible zero order reaction \( \mathbf{A} \rightarrow \mathbf{B} \) takes place in a porous cylindrical catalyst that is sealed at both ends as shown in figure. Assume dilute concentration and neglect any variations in the axis direction. (4)The steady state concentration profile is \( \frac{C_{A}}{C_{A_{S}}}=1+\frac{\Phi_{O}^{2}}{8}\left[\left(\frac{r}{R}\right)^{2}-1\right] \)Where \( \Phi_{0} \) is the Thiele modulus. For \( \Phi_{0}=4 \). Calculate the followingA. The range of \( r \) where \( \mathrm{C}_{\mathrm{A}}=0 \).B. Percentage of total radius of catalyst remain unused.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The irreversible zero order reaction \( \mathbf{A} \rightarrow \mathbf{B} \) takes place in a porous cylindrical catalyst that is sealed at both ends as shown in figure. Assume dilute concentration and neglect any variations in the axis direction. (4)The steady state concentration profile is \( \frac{C_{A}}{C_{A_{S}}}=1+\frac{\Phi_{O}^{2}}{8}\left[\left(\frac{r}{R}\right)^{2}-1\right] \)Where \( \Phi_{0} \) is the Thiele modulus. For \( \Phi_{0}=4 \). Calculate the followingA. The range of \( r \) where \( \mathrm{C}_{\mathrm{A}}=0 \).B. Percentage of total radius of catalyst remain unused.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The irreversible zero order reaction \( \mathbf{A} \rightarrow \mathbf{B} \) takes place in a porous cylindrical catalyst that is sealed at both ends as shown in figure. Assume dilute concentration and neglect any variations in the axis direction. (4)The steady state concentration profile is \( \frac{C_{A}}{C_{A_{S}}}=1+\frac{\Phi_{O}^{2}}{8}\left[\left(\frac{r}{R}\right)^{2}-1\right] \)Where \( \Phi_{0} \) is the Thiele modulus. For \( \Phi_{0}=4 \). Calculate the followingA. The range of \( r \) where \( \mathrm{C}_{\mathrm{A}}=0 \).B. Percentage of total radius of catalyst remain unused.?.
Solutions for The irreversible zero order reaction \( \mathbf{A} \rightarrow \mathbf{B} \) takes place in a porous cylindrical catalyst that is sealed at both ends as shown in figure. Assume dilute concentration and neglect any variations in the axis direction. (4)The steady state concentration profile is \( \frac{C_{A}}{C_{A_{S}}}=1+\frac{\Phi_{O}^{2}}{8}\left[\left(\frac{r}{R}\right)^{2}-1\right] \)Where \( \Phi_{0} \) is the Thiele modulus. For \( \Phi_{0}=4 \). Calculate the followingA. The range of \( r \) where \( \mathrm{C}_{\mathrm{A}}=0 \).B. Percentage of total radius of catalyst remain unused.? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of The irreversible zero order reaction \( \mathbf{A} \rightarrow \mathbf{B} \) takes place in a porous cylindrical catalyst that is sealed at both ends as shown in figure. Assume dilute concentration and neglect any variations in the axis direction. (4)The steady state concentration profile is \( \frac{C_{A}}{C_{A_{S}}}=1+\frac{\Phi_{O}^{2}}{8}\left[\left(\frac{r}{R}\right)^{2}-1\right] \)Where \( \Phi_{0} \) is the Thiele modulus. For \( \Phi_{0}=4 \). Calculate the followingA. The range of \( r \) where \( \mathrm{C}_{\mathrm{A}}=0 \).B. Percentage of total radius of catalyst remain unused.? defined & explained in the simplest way possible. Besides giving the explanation of
The irreversible zero order reaction \( \mathbf{A} \rightarrow \mathbf{B} \) takes place in a porous cylindrical catalyst that is sealed at both ends as shown in figure. Assume dilute concentration and neglect any variations in the axis direction. (4)The steady state concentration profile is \( \frac{C_{A}}{C_{A_{S}}}=1+\frac{\Phi_{O}^{2}}{8}\left[\left(\frac{r}{R}\right)^{2}-1\right] \)Where \( \Phi_{0} \) is the Thiele modulus. For \( \Phi_{0}=4 \). Calculate the followingA. The range of \( r \) where \( \mathrm{C}_{\mathrm{A}}=0 \).B. Percentage of total radius of catalyst remain unused.?, a detailed solution for The irreversible zero order reaction \( \mathbf{A} \rightarrow \mathbf{B} \) takes place in a porous cylindrical catalyst that is sealed at both ends as shown in figure. Assume dilute concentration and neglect any variations in the axis direction. (4)The steady state concentration profile is \( \frac{C_{A}}{C_{A_{S}}}=1+\frac{\Phi_{O}^{2}}{8}\left[\left(\frac{r}{R}\right)^{2}-1\right] \)Where \( \Phi_{0} \) is the Thiele modulus. For \( \Phi_{0}=4 \). Calculate the followingA. The range of \( r \) where \( \mathrm{C}_{\mathrm{A}}=0 \).B. Percentage of total radius of catalyst remain unused.? has been provided alongside types of The irreversible zero order reaction \( \mathbf{A} \rightarrow \mathbf{B} \) takes place in a porous cylindrical catalyst that is sealed at both ends as shown in figure. Assume dilute concentration and neglect any variations in the axis direction. (4)The steady state concentration profile is \( \frac{C_{A}}{C_{A_{S}}}=1+\frac{\Phi_{O}^{2}}{8}\left[\left(\frac{r}{R}\right)^{2}-1\right] \)Where \( \Phi_{0} \) is the Thiele modulus. For \( \Phi_{0}=4 \). Calculate the followingA. The range of \( r \) where \( \mathrm{C}_{\mathrm{A}}=0 \).B. Percentage of total radius of catalyst remain unused.? theory, EduRev gives you an
ample number of questions to practice The irreversible zero order reaction \( \mathbf{A} \rightarrow \mathbf{B} \) takes place in a porous cylindrical catalyst that is sealed at both ends as shown in figure. Assume dilute concentration and neglect any variations in the axis direction. (4)The steady state concentration profile is \( \frac{C_{A}}{C_{A_{S}}}=1+\frac{\Phi_{O}^{2}}{8}\left[\left(\frac{r}{R}\right)^{2}-1\right] \)Where \( \Phi_{0} \) is the Thiele modulus. For \( \Phi_{0}=4 \). Calculate the followingA. The range of \( r \) where \( \mathrm{C}_{\mathrm{A}}=0 \).B. Percentage of total radius of catalyst remain unused.? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup