The V_max for an enzyme is 9 mg/min. Calculate the K_m if the [S] = 5 mM when the V₀ = 3 mg/min.

• A. 100 M.
• B. 10 M.
• C. 10 mg.
• D. 10 mM.

Answer: (D)

Verified step by step guidance

1. Understand the Michaelis-Menten equation: \( V_0 = \frac{V_{max} [S]}{K_m + [S]} \), where \( V_0 \) is the initial velocity, \( V_{max} \) is the maximum velocity, \( [S] \) is the substrate concentration, and \( K_m \) is the Michaelis constant.
2. Rearrange the Michaelis-Menten equation to solve for \( K_m \): \( K_m = \frac{V_{max} [S]}{V_0} - [S] \).
3. Substitute the given values into the rearranged equation: \( V_{max} = 9 \text{ mg/min} \), \( V_0 = 3 \text{ mg/min} \), and \( [S] = 5 \text{ mM} \).
4. Calculate the term \( \frac{V_{max} [S]}{V_0} \) using the substituted values.
5. Subtract \( [S] \) from the result obtained in the previous step to find \( K_m \).