Final answer:
The initial reaction velocity (v0) when substrate concentration is 0.5 x Km and Vmax is 2.4 x 10^-6 mol L^-1 min^-1 is calculated using the Michaelis-Menten equation, resulting in 1.2 x 10^-6 mol L^-1 min^-1.
Step-by-step explanation:
The student is asking about the initial reaction velocity (v0) of an enzyme reaction where the substrate concentration is 0.5 × Km and the Vmax is given as 2.4 × 10-6 mol L-1 min-1. To find this, one can utilize the Michaelis-Menten equation: v = (Vmax [S]) / (Km + [S]). Substituting the given values and understanding that [S] is 0.5 × Km simplifies the formula, allowing us to calculate v0.
In the given scenario, we substitute 0.5 × Km for [S] and simplify to find that v = (Vmax × 0.5 × Km) / (Km + 0.5 × Km), which further simplifies to v = 0.5 × Vmax since the Km terms cancel out when simplified. Therefore, the initial reaction velocity (v0) observed is 0.5 × Vmax, which calculates to 0.5 × 2.4 × 10-6 or 1.2 × 10-6 mol L-1 min-1.