Carbonic anhydrase catalyzes the hydration of CO2. The Km of carbonic anhydrase for CO2 is 12 mM. The initial velocity (V0) of the enzyme-catalyzed reaction was 4.5 μmole*mL-1*sec-1 when [CO2] = 36 mM. Calculate the Vmax of carbonic anhydrase.
A
8.1 x 102 M s-1.
B
6 x 10-3 M s-1.
C
2.5 x 10-4 M s-1.
D
7.3 x 10-5 M s-1.
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1
Understand that the problem involves enzyme kinetics, specifically using the Michaelis-Menten equation: V0 = (Vmax * [S]) / (Km + [S]), where V0 is the initial velocity, Vmax is the maximum velocity, [S] is the substrate concentration, and Km is the Michaelis constant.
Identify the given values: Km = 12 mM, V0 = 4.5 μmole*mL^-1*sec^-1, and [CO2] = 36 mM. Note that V0 is given in different units, so it may need conversion to match the units of Vmax.
Rearrange the Michaelis-Menten equation to solve for Vmax: Vmax = V0 * (Km + [S]) / [S].
Substitute the known values into the rearranged equation: Vmax = 4.5 μmole*mL^-1*sec^-1 * (12 mM + 36 mM) / 36 mM.
Convert the units of V0 from μmole*mL^-1*sec^-1 to M s^-1 if necessary, to ensure consistency with the units of Vmax, and then perform the calculation to find Vmax.