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An irreversible, first-order reaction takes place in four well mixed reactors (Fig. P12.10),
Thus, the rate at which A is transformed to B can be represented as
The reactors have different volumes, and because they are operated at different temperatures, each has a different reaction rate:
Reactor | V, L |
|
1 | 25 | 0.05 |
2 | 75 | 0.1 |
3 | 100 | 0.5 |
4 | 25 | 0.1 |
Determine the concentration of A and B in each of the reactors at steady state.
FIGURE P12.10
To calculate:
Answer to Problem 10P
Solution:
Explanation of Solution
Given Information:
Write the provided values of the volume and rate of reaction.
Formula used:
Write system of linear equations in matrix form.
And,
The term
Calculation:
Consider the provided diagram for an irreversible first order reaction takes place in four will-mixed reactors.
Balance the mass for A in reactor 1 at steady-state.
Substitute
Further solve.
Balance the mass for A in reactor 2 at steady-state.
Substitute
Further solve.
Balance the mass for A in reactor 3 at steady-state.
Substitute
Further solve.
Balance the mass for A in reactor 4 at steady-state.
Substitute
Further solve.
Balance the mass for B in reactor 1 at steady-state.
Substitute
Further solve.
Balance the mass for B in reactor 2 at steady-state.
Substitute
Further solve.
Balance the mass for B in reactor 3 at steady-state.
Substitute
Further solve.
Balance the mass for B in reactor 4 at steady-state.
Substitute
Further solve.
Now, write all the equations, to find linear system of equations.
Write the above linear equations in matrix form as written in symbolized form.
Here, coefficient matrix A is,
Column matrix
Column matrix B is,
Substitute the values in the matrix equation form.
Solve for
Code:
Type the above code into MATLAB command window and press enter to find the result.
Result is obtained as follows:
Hence,
Hence, the concentration of A and B is,
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