Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
If the chemical composition of proteins in an organism is CHi sOoNo.3.So.004, the mass percentage of
carbon in the proteins is
Given data: Atomic weights (Da) of C = 12, H = 1, O = 16, N = 14, and S = 32.
Official Answer Key:
52.00 to 54.00
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2017 Q.46)**
**1. Governing Concept & Definition**:
- **Topic**: Biochemistry & Elemental Composition of Proteins
- For average protein elemental formula $\text{CH}_{1.58}\text{O}_{0.31}\text{N}_{0.28}\text{S}_{0.004}$, the mass percentage of carbon is:
$\%C = \frac{12 \times c}{\text{Molecular Weight}} \times 100\%$
**2. Detailed Step-by-Step Calculation**:
- Molar mass $= 12(1) + 1.58(1) + 16(0.31) + 14(0.28) + 32(0.004) \approx 12 + 1.58 + 4.96 + 3.92 + 0.128 = 22.588\text{ g/C-mol}$.
- Carbon mass percentage:
$\%C = \frac{12}{22.588} \times 100\% \approx 53.12\%$
**3. Final Answer**:
- **Calculated Value**: **53.1%**
- **Official GATE Accepted Range**: **52.0 to 54.0**
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