Reference no: EM132267686

Problem 1 - Enzyme reactions can be inhibited when the substrate-enzyme complex reacts with the substrate itself, yielding an unreactive complex. The overall enzyme reaction S ^EP is said to be substrate-inhibited if it can be described by the following mechanism:

1) S+E^k_1 S_{k_1}E^#

2) S E^{# k_2} P+E

3) S E^# +S^k_3 S E_{k_3} S

Questions -

a) Use the Pseudo Steady State Hypothesis (PSSH) on all substrate-enzyme complexes to derive an expression for the overall formation rate of the product P as a function of measurable quantities.

b) Apply the Langmuir-Hinshelwood approach to derive an expression for the overall formation rate of the product P as a function of measurable quantities. (Hint: In class, we used this algorithm for surface reactions on solid catalysts only.)

c) Compare your answers to questions (a) and (b). Discuss your findings.

Problem 2 - The gas phase reaction 2A B C with an elementary rate law is carried out in a batch reactor filled with fresh catalyst. The catalyst activity decays with an approximately zero-order rate law.

Question - What is the conversion after an hour?

Data -

Volume of reactor: 1 L

Catalyst weight: 1 kg

k_D = 0.02 min-1

N_A0 = 10 mol

k_r = 0.001 L²/(kg-cat·mol·min)

Problem 3 - Consider the following liquid dissociation reaction, which is catalyzed by a solid catalyst:

A+S^ad A^K S

2A S^S B^K S S C

B S ^K_D B S

Assume that you use a fluidized-bed reactor and porous catalyst particles to carry out the reaction, and that the operating conditions (T, X, etc.) in your reactor are such that the intrinsic rate can be approximated by: r_BkC_A. You can also assume that the reaction is not limited by external mass transfer.

Questions -

a) Use the mechanism to derive an expression for the net reaction rate. (Hint: Do not use the approximate rate here.)

b) Is the overall process limited by the catalytic reaction, or by pore diffusion? Why or why not? (Hint: Use the approximate rate here.)

c) Depending on your answer to question (b), what change to this reactor would you suggest to make the process reaction limited/pore-diffusion limited?

d) Extra credit (+10): give a quantitative answer to question (c).

Data -

Diameter of catalyst particle: 2 cm

Specific surface area of catalyst: 250 m²/g bulk

Density of catalyst material: 4 g/cm³ effective

Reaction rate constant k'' = 4·10^-6 cm/s

Effective diffusion constant: D_eff = 0.1 cm²/s.