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1. The enzyme catalyzed reaction Tm(S-P/K) (Ks + S + aP) is carried out in a well-mixed continuous flow reactor. The conservation equations for S and P are d.S dt dP dt S→ P, r = = D(So – S) – r, D = , S(0) = Si P(0) = P₁ The enzyme loading, PE, is included in r and rm. Following information is available: So = 2 mol/L, Po = 0, Ks = 0.05 mol/L, K = 8, a = 0.25, rm/D = 2 mol/L. = = D(Po − P) +r, (a). Working with the conservation equations for S and P to eliminate r and appropriate integration with respect to t, establish that the reactor trajectories vary with t as [So+ Po-S(t)- P(t)] = [So + Po - Si - Pi] exp(-Dt), and [S(t) + P(t)] = [So + Po] at very large t, including for steady state operation.

1. The enzyme catalyzed reaction Tm(S-P/K) (Ks + S + aP) is carried out in a well-mixed continuous flow reactor. The conservation equations for S and P are d.S dt dP dt S→ P, r = = D(So – S) – r, D = , S(0) = Si P(0) = P₁ The enzyme loading, PE, is included in r and rm. Following information is available: So = 2 mol/L, Po = 0, Ks = 0.05 mol/L, K = 8, a = 0.25, rm/D = 2 mol/L. = = D(Po − P) +r, (a). Working with the conservation equations for S and P to eliminate r and appropriate integration with respect to t, establish that the reactor trajectories vary with t as [So+ Po-S(t)- P(t)] = [So + Po - Si - Pi] exp(-Dt), and [S(t) + P(t)] = [So + Po] at very large t, including for steady state operation.

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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1. The enzyme catalyzed reaction rm(S – P/K) (Ks + S + aP) is carried out in a well-mixed continuous flow reactor. The conservation equations for S and P are ds dt dP dt ds d(Dt) S→ P, r = = D(So - S) - r, D(Po − P) +r, The enzyme loading, PE, is included in r and rm. Following information is available: So Po = 0, Ks = 0.05 mol/L, K = 8, a = 0.25, rm/D = 2 mol/L. (a). Working with the conservation equations for S and P to eliminate r and appropriate integration with respect to t, establish that the reactor trajectories vary with t as [So + PoS(t)- P(t)] = [So + Po – S; – P¿] exp(-Dt), and [S(t) + P(t)] = [So + Po] at very large t, including for steady state operation. (b). Using the stoichiometric relation in (a), compute S and P in a steady state operation of the well-mixed reactor. (c). Consider the start-up operation of the reactor with Si So and Pi = 0. Deduce that [S(t) + P(t)] = So and the mass balance for S reduces to = = ƒ(S), ƒ(S) V V P(0) = P₁ = D = So S 9 S(0) = Si rm(S – P/K) D(Ks+S+ aP)] = 2 mol/L, with f(S) = 0 at steady state. Integrate the mass balance for S using the method of separation of variables and the roots of f(S) = 0 identified in (b) to compute Dt required to reduce S from So to 1 mol/L. Use partial fractions expansion for integration.
Transcribed Image Text:1. The enzyme catalyzed reaction rm(S – P/K) (Ks + S + aP) is carried out in a well-mixed continuous flow reactor. The conservation equations for S and P are ds dt dP dt ds d(Dt) S→ P, r = = D(So - S) - r, D(Po − P) +r, The enzyme loading, PE, is included in r and rm. Following information is available: So Po = 0, Ks = 0.05 mol/L, K = 8, a = 0.25, rm/D = 2 mol/L. (a). Working with the conservation equations for S and P to eliminate r and appropriate integration with respect to t, establish that the reactor trajectories vary with t as [So + PoS(t)- P(t)] = [So + Po – S; – P¿] exp(-Dt), and [S(t) + P(t)] = [So + Po] at very large t, including for steady state operation. (b). Using the stoichiometric relation in (a), compute S and P in a steady state operation of the well-mixed reactor. (c). Consider the start-up operation of the reactor with Si So and Pi = 0. Deduce that [S(t) + P(t)] = So and the mass balance for S reduces to = = ƒ(S), ƒ(S) V V P(0) = P₁ = D = So S 9 S(0) = Si rm(S – P/K) D(Ks+S+ aP)] = 2 mol/L, with f(S) = 0 at steady state. Integrate the mass balance for S using the method of separation of variables and the roots of f(S) = 0 identified in (b) to compute Dt required to reduce S from So to 1 mol/L. Use partial fractions expansion for integration.
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