Combustion Chambers

### **Detailed Step-by-Step Solution (GATE AE 2019 Q.30 / AE Q.20)** **1. Intuitive Physical Setup & Given Parameters**: - Fuel: 1 mole of ethanol, $\text{C}_2\text{H}_5\text{OH}$ (or $\text{C}_2\text{H}_6\text{O}$). - Complete combustion yields carbon dioxide ($\text{CO}_2$) and water ($\text{H}_2\text{O}$). **2. Step-by-Step Chemical Stoichiometry Derivation**: 1. **Unbalanced Reaction Equation**: $\text{C}_2\text{H}_5\text{OH} + n\text{O}_2 \longrightarrow a\text{CO}_2 + b\text{H}_2\text{O}$ 2. **Carbon (C) Balance**: - Left side: 2 carbon atoms. - Right side: $a$ carbon atoms $\implies a = 2$. 3. **Hydrogen (H) Balance**: - Left side: $5 + 1 = 6$ hydrogen atoms. - Right side: $2b$ hydrogen atoms $\implies 2b = 6 \implies b = 3$. 4. **Oxygen (O) Balance**: - Left side: $1 + 2n$ oxygen atoms. - Right side: $2a + b = 2(2) + 3 = 4 + 3 = 7$ oxygen atoms. - Setting both sides equal: $1 + 2n = 7 \implies 2n = 6 \implies n = 3$ 5. **Balanced Combustion Reaction**: $\text{C}_2\text{H}_5\text{OH} + 3\text{O}_2 \longrightarrow 2\text{CO}_2 + 3\text{H}_2\text{O}$ Therefore, exactly 3 moles of $\text{O}_2$ are required. **3. Comprehensive Options & Distractor Analysis**: - **Question Type**: Numerical Answer Type (NAT). - **Exact Stoichiometric Integer**: **3.0** (Acceptable Range: [3, 3]). **4. Official Master Key & Exam Takeaway**: - **Official Answer**: **3.0** - **Exam Rule**: For general hydrocarbon $\text{C}_x\text{H}_y\text{O}_z + n\text{O}_2$: $n = x + \frac{y}{4} - \frac{z}{2} = 2 + \frac{6}{4} - \frac{1}{2} = 2 + 1.5 - 0.5 = 3$.