![Q.44 In Michaelis-Menten’s equation, if [S] = 15 Km , then the ratio 𝑣0/𝑉max is __________. (Round off to three decimal places)](https://www.letstalkacademy.com/wp-content/uploads/2025/12/slide_44-5.png)
Q.44 In Michaelis–Menten’s equation, if [S] = 15 Km , then the ratio 𝑣0/𝑉max is __________.
(Round off to three decimal places)
The ratio v0/Vmax is 0.938 when [S] = 15 Km in the Michaelis-Menten equation.
Michaelis-Menten Equation
The Michaelis-Menten equation describes enzyme kinetics: v0 = Vmax[S]/(Km + [S]). Dividing both sides by Vmax gives the velocity ratio: v0/Vmax = [S]/(Km + [S]). Substituting [S] = 15 Km yields v0/Vmax = 15Km/(Km + 15Km) = 15/16 = 0.9375, which rounds to 0.938.
Detailed Calculation
Start with the ratio formula: [S]/Km / (1 + [S]/Km). Here, [S]/Km = 15, so 15/(1+15) = 15/16. Compute 15 ÷ 16 = 0.9375; rounding to three decimal places gives 0.938 per standard convention.
Step-by-Step Solution
- Normalize: Let [S]/Km = 15
- Ratio = 15/(1+15) = 15/16
- 15 ÷ 16 = 0.9375 → 0.938 (three decimals)
Common Ratios Explained
| [S]/Km | v0/Vmax | Saturation Level |
|---|---|---|
| 1 Km | 0.500 | Half saturation |
| 9 Km | 0.900 | 90% saturation |
| 15 Km | 0.938 | 93.8% saturation |
| 99 Km | ≈0.990 | Near saturation |
No options provided, but these illustrate saturation trends; 15 Km gives high velocity (93.8% of max).
Biological Significance
High [S] (15 Km) means near-zero-order kinetics—velocity plateaus as enzyme saturates. Km reflects enzyme-substrate affinity; low Km = high affinity.
CSIR NET Exam Tips
- Practice derivations without calculator
- Remember: [S] = 10 Km → 0.909; scales predictably
- Use Lineweaver-Burk plots for verification: 1/v vs 1/[S]
- This matches CSIR NET patterns, like [S]=3 Km (0.750) or 9 Km (0.900)
Final Answer
0.938
