Question:easy
Km value is defined as?
Km value is defined as?
Show Hint
Set v = Vmax/2 in the Michaelis-Menten equation and Km equals that substrate concentration.
Updated On: Jun 24, 2026
- Substrate concentration at Vmax/2
- Substrate concentration of twice Vmax
- Substrate concentration of thrice Vmax
- Substrate concentration of one third Vmax
Show Solution
The Correct Option is A
Solution and Explanation
Step 1: Start from the Michaelis-Menten velocity expression $v = \dfrac{V_{max}[S]}{K_m + [S]}$, which links reaction rate to substrate level.
Step 2: To find the meaning of Km, set the velocity equal to one half of the maximum, $v = V_{max}/2$. Putting this into the equation and simplifying yields $K_m + [S] = 2[S]$, so $K_m = [S]$ exactly at half-maximal rate.
Step 3: Thus Km equals the substrate concentration that produces a velocity equal to Vmax divided by two. It measures affinity: smaller Km, tighter binding. Definitions invoking twice, thrice or a third of Vmax do not arise from the kinetics and are wrong.
Step 4: The correct definition is the substrate concentration at half of Vmax.
\[\boxed{[S]\ \text{at}\ V_{max}/2}\]
Step 2: To find the meaning of Km, set the velocity equal to one half of the maximum, $v = V_{max}/2$. Putting this into the equation and simplifying yields $K_m + [S] = 2[S]$, so $K_m = [S]$ exactly at half-maximal rate.
Step 3: Thus Km equals the substrate concentration that produces a velocity equal to Vmax divided by two. It measures affinity: smaller Km, tighter binding. Definitions invoking twice, thrice or a third of Vmax do not arise from the kinetics and are wrong.
Step 4: The correct definition is the substrate concentration at half of Vmax.
\[\boxed{[S]\ \text{at}\ V_{max}/2}\]
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