Answer:
27 min
Explanation:
The kinetics of an enzyme-catalyzed reaction can be determined by the equation of Michaelis-Menten:
Where v is the velocity in the equilibrium, vmax is the maximum velocity of the reaction (which is directed proportionally of the amount of the enzyme), Km is the equilibrium constant and [S] is the concentration of the substrate.
So, initially, the velocity of the formation of the substrate is 12μmol/9min = 1.33 μmol/min
If Km is a thousand times smaller then [S], then
v = vmax[S]/[S]
v = vmax
vmax = 1.33 μmol/min
For the new experiment, with one-third of the enzyme, the maximum velocity must be one third too, so:
vmax = 1.33/3 = 0.443 μmol/min
Km will still be much smaller then [S], so
v = vmax
v = 0.443 μmol/min
For 12 μmol formed:
0.443 = 12/t
t = 12/0.443
t = 27 min