Consider the set of reversible, first-order reactions k k k3 A=B=C=D=E k-1 k-2 k-3 k-4 taking...
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Consider the set of reversible, first-order reactions k₁ k₂ k3 A=B=C=D=E k-1 k-2 k-3 k-4 taking place in a well-mixed, batch reactor. The reactions are all elementary reactions with corresponding first-order rate expressions. Let the concentration of the species be arranged in a column vector c = [CA CB C CC CD CE] (a) Write the mass balance for the well-mixed, batch reactor of constant volume dc dt k4 = Kc What is K for this problem? (b) What is the solution of this mass balance for initial condition c(0) = co? What calculation do you do to find out if this solution is stable? (c) Determine the rank of matrix K. Hint: focus on the rows of K. Justify your answer. From the fundamental theorem of linear algebra, what is the dimension of the null space of K? (d) What is the condition for a steady-state solution of the model? Is the steady state unique? Why or why not? Consider the set of reversible, first-order reactions k₁ k₂ k3 A=B=C=D=E k-1 k-2 k-3 k-4 taking place in a well-mixed, batch reactor. The reactions are all elementary reactions with corresponding first-order rate expressions. Let the concentration of the species be arranged in a column vector c = [CA CB C CC CD CE] (a) Write the mass balance for the well-mixed, batch reactor of constant volume dc dt k4 = Kc What is K for this problem? (b) What is the solution of this mass balance for initial condition c(0) = co? What calculation do you do to find out if this solution is stable? (c) Determine the rank of matrix K. Hint: focus on the rows of K. Justify your answer. From the fundamental theorem of linear algebra, what is the dimension of the null space of K? (d) What is the condition for a steady-state solution of the model? Is the steady state unique? Why or why not?
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Answer The reactions can be represented as follows 1Ak1BForward reaction 2Bk1AReverse reaction 3Bk2CForward reaction 4Ck2BReverse reaction 5Ck3DForwar... View the full answer
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