![Q.32 Within the Michaelis-Menten framework, the ratio of 𝑣0/𝑉max when [S] = 20 × Km is ______. (Round off to two decimal places)](https://www.letstalkacademy.com/wp-content/uploads/2026/01/slide_53-6.png)
Q.32 Within the Michaelis-Menten framework, the ratio of 𝑣0/𝑉max
when [S] = 20 × Km is ______.
(Round off to two decimal places)
[S] = 20 × Km equals 0.95
under the Michaelis–Menten framework.
Michaelis-Menten Equation Basics
The Michaelis–Menten equation describing enzyme kinetics is:
v0 =
(Vmax[S]) / (Km + [S])
Dividing both sides by Vmax gives:
v0/Vmax =
[S] / (Km + [S])
This ratio shows how reaction velocity approaches the maximum as substrate
concentration increases and the enzyme becomes saturated.
Exact Calculation for [S] = 20 Km
Substitute [S] = 20Km:
v0/Vmax =
20Km / (Km + 20Km) =
20Km / 21Km =
20 / 21
20/21 ≈ 0.95238
Rounded to two decimal places:
v0/Vmax = 0.95
At such a high substrate concentration (20Km), the enzyme operates
at approximately 95% of Vmax, indicating near saturation.
Common Ratio Values Overview
| [S] Multiple | v0/Vmax | Rounded Value |
|---|---|---|
| 1 Km | 1/2 | 0.50 |
| 3 Km | 3/4 | 0.75 |
| 9 Km | 9/10 | 0.90 |
| 10 Km | 10/11 | 0.91 |
| 20 Km | 20/21 | 0.95 |
These values illustrate the hyperbolic saturation behavior of enzyme kinetics.
Increasing substrate concentration beyond Km yields diminishing
increases in reaction velocity.
Exam Tips and Common Misconceptions
- Options like 0.90 or 0.91 are tempting if
20Km is confused with 9–10Km. - Avoid guessing—use the exact ratio
[S]/(Km + [S]). - For MCQs, remember:
10Km ≈ 91%,
20Km ≈ 95%.
