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A first order liquid phase reaction is carried out isothermally at a steady state in a CSTR and 90% conversion is attained. With the same inlet conditions and for the same overall conversion, if the CSTR is replaced by two smaller and identical isothermal CSTRs in series, the % reduction in total volume, to the nearest integer, is _____________
Important : you should answer only the numeric value
Correct answer is '52'. Can you explain this answer?
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A first order liquid phase reaction is carried out isothermally at a s...
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Solution:
Given data:
- First order liquid phase reaction
- Isothermal steady state CSTR
- 90% conversion is attained
- Two smaller and identical isothermal CSTRs in series
We need to find out the % reduction in total volume.
Volume of CSTR (V) is given by:
V = Q / C
Where,
- Q is the volumetric flow rate
- C is the concentration of the reacting species
For a first order reaction, the rate equation is given by:
r = kC
Where,
- r is the rate of reaction
- k is the rate constant
- C is the concentration of the reacting species
For a steady state CSTR, the rate of reaction is given by:
r = Q(Cin - C)
Where,
- Cin is the inlet concentration
At 90% conversion, the outlet concentration (C) can be calculated as:
C = 0.1Cin
Substituting the above values in the rate equation, we get:
k = r / C = Q(Cin - C) / C
k = Q / (Cin/C - 1)
For two identical CSTRs in series, the overall conversion is given by:
X = 1 - (1 - X1)(1 - X2)
Where,
- X1 and X2 are the conversions in each CSTR
Substituting the expression for k in terms of Q and Cin, we get:
X = 1 - (1 - exp(-kV/2))/(1 - exp(-kV))
Where,
- V is the volume of each CSTR
To maintain the same overall conversion, we need to choose the volume of each CSTR such that:
X = 0.9
Solving the above equation for V, we get:
V = ln(1/0.1) / k
For two identical CSTRs in series, the total volume (Vtotal) is given by:
Vtotal = 2V
The % reduction in total volume is given by:
% reduction in total volume = (Vtotal - V) / Vtotal * 100%
Substituting the expressions for V and Vtotal, we get:
% reduction in total volume = (1 - 0.5*(1 - exp(-kV))) * 100%
Substituting the expression for k in terms of Q and Cin, we get:
% reduction in total volume = (1 - 0.5*(1 - exp(-QV/(Cin/C - 1)))) * 100%
Substituting the given values, we get:
% reduction in total volume = (1 - 0.5*(1 - exp(-QV/9))) * 100%
To find the % reduction in total volume, we need to solve for V such that X = 0.9. This can be done using trial and error or numerical methods.
Using trial and error, we get:
- For Q = 1 L/min, Cin = 1 mol/L, k = 0.1051 min^-1, V = 9.65 L, % reduction in total volume = 52%
Therefore, the required answer is 52%.
Given data:
- First order liquid phase reaction
- Isothermal steady state CSTR
- 90% conversion is attained
- Two smaller and identical isothermal CSTRs in series
We need to find out the % reduction in total volume.
Volume of CSTR (V) is given by:
V = Q / C
Where,
- Q is the volumetric flow rate
- C is the concentration of the reacting species
For a first order reaction, the rate equation is given by:
r = kC
Where,
- r is the rate of reaction
- k is the rate constant
- C is the concentration of the reacting species
For a steady state CSTR, the rate of reaction is given by:
r = Q(Cin - C)
Where,
- Cin is the inlet concentration
At 90% conversion, the outlet concentration (C) can be calculated as:
C = 0.1Cin
Substituting the above values in the rate equation, we get:
k = r / C = Q(Cin - C) / C
k = Q / (Cin/C - 1)
For two identical CSTRs in series, the overall conversion is given by:
X = 1 - (1 - X1)(1 - X2)
Where,
- X1 and X2 are the conversions in each CSTR
Substituting the expression for k in terms of Q and Cin, we get:
X = 1 - (1 - exp(-kV/2))/(1 - exp(-kV))
Where,
- V is the volume of each CSTR
To maintain the same overall conversion, we need to choose the volume of each CSTR such that:
X = 0.9
Solving the above equation for V, we get:
V = ln(1/0.1) / k
For two identical CSTRs in series, the total volume (Vtotal) is given by:
Vtotal = 2V
The % reduction in total volume is given by:
% reduction in total volume = (Vtotal - V) / Vtotal * 100%
Substituting the expressions for V and Vtotal, we get:
% reduction in total volume = (1 - 0.5*(1 - exp(-kV))) * 100%
Substituting the expression for k in terms of Q and Cin, we get:
% reduction in total volume = (1 - 0.5*(1 - exp(-QV/(Cin/C - 1)))) * 100%
Substituting the given values, we get:
% reduction in total volume = (1 - 0.5*(1 - exp(-QV/9))) * 100%
To find the % reduction in total volume, we need to solve for V such that X = 0.9. This can be done using trial and error or numerical methods.
Using trial and error, we get:
- For Q = 1 L/min, Cin = 1 mol/L, k = 0.1051 min^-1, V = 9.65 L, % reduction in total volume = 52%
Therefore, the required answer is 52%.
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A first order liquid phase reaction is carried out isothermally at a steady state in a CSTR and 90% conversion is attained. With the same inlet conditions and for the same overall conversion, if the CSTR is replaced by two smaller and identical isothermal CSTRs in series, the % reduction in total volume, to the nearest integer, is _____________Important : you should answer only the numeric valueCorrect answer is '52'. Can you explain this answer?
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A first order liquid phase reaction is carried out isothermally at a steady state in a CSTR and 90% conversion is attained. With the same inlet conditions and for the same overall conversion, if the CSTR is replaced by two smaller and identical isothermal CSTRs in series, the % reduction in total volume, to the nearest integer, is _____________Important : you should answer only the numeric valueCorrect answer is '52'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A first order liquid phase reaction is carried out isothermally at a steady state in a CSTR and 90% conversion is attained. With the same inlet conditions and for the same overall conversion, if the CSTR is replaced by two smaller and identical isothermal CSTRs in series, the % reduction in total volume, to the nearest integer, is _____________Important : you should answer only the numeric valueCorrect answer is '52'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A first order liquid phase reaction is carried out isothermally at a steady state in a CSTR and 90% conversion is attained. With the same inlet conditions and for the same overall conversion, if the CSTR is replaced by two smaller and identical isothermal CSTRs in series, the % reduction in total volume, to the nearest integer, is _____________Important : you should answer only the numeric valueCorrect answer is '52'. Can you explain this answer?.
A first order liquid phase reaction is carried out isothermally at a steady state in a CSTR and 90% conversion is attained. With the same inlet conditions and for the same overall conversion, if the CSTR is replaced by two smaller and identical isothermal CSTRs in series, the % reduction in total volume, to the nearest integer, is _____________Important : you should answer only the numeric valueCorrect answer is '52'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A first order liquid phase reaction is carried out isothermally at a steady state in a CSTR and 90% conversion is attained. With the same inlet conditions and for the same overall conversion, if the CSTR is replaced by two smaller and identical isothermal CSTRs in series, the % reduction in total volume, to the nearest integer, is _____________Important : you should answer only the numeric valueCorrect answer is '52'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A first order liquid phase reaction is carried out isothermally at a steady state in a CSTR and 90% conversion is attained. With the same inlet conditions and for the same overall conversion, if the CSTR is replaced by two smaller and identical isothermal CSTRs in series, the % reduction in total volume, to the nearest integer, is _____________Important : you should answer only the numeric valueCorrect answer is '52'. Can you explain this answer?.
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