It has been observed that substrate inhibition occurs in the following enzymatic reaction:
E + S → P + E
a. Show that the rate law for substrate inhibition is consistent with the plot in Figure P9-10B of –r_s (mmol/L·min) versus the substrate concentration S (mmol/L).

Figure P9-10B

A graph depicts the Michaelis- Menton plot for substrate inhibition. The horizontal axis represents the substrate concentration S (millimoles per liter) ranging from 0 to
52 in increments of 4. The vertical axis represents the reaction rate, negative r subscript s ( millimoles per liter-minute) ranging from 0 to 0.2 in increments of 0.05. The
reaction rate increases from 0 to 0.175 before the substrate concentration reaches 4. After that point, the reaction rate slowly decreases and reaches 0.03 when the
concentration rate reaches 52. The mentioned values are approximate.

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?
c. What would be the effluent substrate concentration if the total enzyme concentration is reduced by 33%?

Transcribed Image Text:

-rs (mmol/liter min) 0.2 0.15 0.1 10.05 0 8 12 16 20 24 28 32 36 S (mmol/liter) 40 44 48 52