Final answer:
To calculate the rate of carbon dioxide decomposition catalyzed by carbonic anhydrase using the Michaelis-Menten equation, one needs the enzyme concentration, the Km value, the K2 constant, and the concentration of carbon dioxide ([CO2]). However, as the [CO2] is not provided, we cannot compute the rate exactly.
Step-by-step explanation:
Carbon dioxide is converted in the blood to HCO3− (bicarbonate ion) and H3O+ by the enzyme carbonic anhydrase. Given the Michaelis-Menten constants (Km and K2), and the enzyme concentration, the rate of carbon dioxide decomposition can be calculated. The constants provided are Km = 8.0 × 10−5 M and K2 = 6.0 × 105 s−1, and the enzyme concentration is 4.5 × 10−6 M.
The rate of reaction is given by the Michaelis-Menten equation V = (Vmax ⋅ [S]) / (Km + [S]), where Vmax is the maximum reaction rate, and [S] is the substrate concentration. Vmax can be determined by multiplying the enzyme concentration by the rate constant K2. Hence, Vmax = enzyme concentration ⋅ K2 = 4.5 × 10−6 M × 6.0 × 105 s−1. Assuming the substrate concentration [S] is 0.024 M (the concentration of the hydrogen carbonate ion), and using the given Km, the rate (V) can be calculated.
However, without the substrate concentration [S], it is not possible to calculate the exact rate of the reaction using the provided data. Hence, an accurate calculation requires the concentration of carbon dioxide ([CO2]) in the blood, which could potentially be estimated or measured directly.