Question

What happens to the Vmax of an enzyme-catalyzed reaction when the substrate concentration is equal to the Km?

• A. (V = V_{max})
• B. (V = \frac{V_{max}}{2})
• C. (V = 2V_{max})
• D. (V = 0)

Hint:

{Key enzyme kinetics rule:} \ When ( [S] = K_m ), the reaction velocity is (\frac{V_{max}}{2}).

Answer 1

The Correct Option is B

Concept: The relationship between substrate concentration and reaction velocity in enzyme-catalyzed reactions is described by the Michaelis–Menten equation: [ V = \frac{V_{max}[S]}{K_m + [S]} ] where (V) is the reaction velocity, (V_{max}) is the maximum velocity, (K_m) is the Michaelis constant, and ([S]) is the substrate concentration.
Step 1:Substitute the condition ( [S] = K_m ).
If the substrate concentration equals the Michaelis constant: [ V = \frac{V_{max}K_m}{K_m + K_m} ]
Step 2:Simplify the expression.} [ V = \frac{V_{max}K_m}{2K_m} ]
Step 3:Final result.} [ V = \frac{V_{max}}{2} ] Thus, when the substrate concentration equals (K_m), the reaction velocity is half of the maximum velocity.