Chapter 9, Problem 9.10P

It has been observed that substrate inhibition occurs in the following enzymatic reaction:

E + S → P + E

1. (a) Show that the rate law for substrate inhibition is consistent with the plot in Figure P9-10_B of −r_s (mmol/L · min) versus the substrate concentration S (mmol/L).
2. (b) If this reaction is carried out in a CSTR that has a volume of 1000 dm³, to which the volumetric flow rate is 3.2 dm³/min, determine the three possible steady states, noting, if possible, which are stable. The entrance concentration of the substrate is 50 mmol/dm³. What is the highest conversion?
3. (c) What would be the effluent substrate concentration if the total enzyme concentration is reduced by 33%?
4. (d) List ways you can work this problem incorrectly.
5. (e) How could you make this problem more difficult?

Figure P9-10_B Michaelis–Menten plot for substrate inhibition.