To write the chemical equations for the combustion reactions of the given hydrocarbons, we need to follow a systematic approach. A combustion reaction typically involves a hydrocarbon reacting with oxygen (O₂) to produce carbon dioxide (CO₂) and water (H₂O).
### Step-by-Step Solution:
**(i) Combustion of Butane (C₄H₁₀)**
1. **Write the unbalanced equation:**
\[
\text{C}_4\text{H}_{10} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}
\]
2. **Balance the carbon atoms:**
- Butane has 4 carbon atoms, so we need 4 CO₂.
\[
\text{C}_4\text{H}_{10} + \text{O}_2 \rightarrow 4\text{CO}_2 + \text{H}_2\text{O}
\]
3. **Balance the hydrogen atoms:**
- Butane has 10 hydrogen atoms, so we need 5 H₂O.
\[
\text{C}_4\text{H}_{10} + \text{O}_2 \rightarrow 4\text{CO}_2 + 5\text{H}_2\text{O}
\]
4. **Balance the oxygen atoms:**
- On the right side, we have \(4 \times 2 = 8\) from CO₂ and \(5 \times 1 = 5\) from H₂O, totaling 13 oxygen atoms.
- Therefore, we need \( \frac{13}{2} \) O₂.
\[
\text{C}_4\text{H}_{10} + \frac{13}{2}\text{O}_2 \rightarrow 4\text{CO}_2 + 5\text{H}_2\text{O}
\]
5. **Final balanced equation (multiply through by 2 to eliminate the fraction):**
\[
2\text{C}_4\text{H}_{10} + 13\text{O}_2 \rightarrow 8\text{CO}_2 + 10\text{H}_2\text{O}
\]
---
**(ii) Combustion of Pentene (C₅H₁₀)**
1. **Write the unbalanced equation:**
\[
\text{C}_5\text{H}_{10} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}
\]
2. **Balance the carbon atoms:**
- Pentene has 5 carbon atoms, so we need 5 CO₂.
\[
\text{C}_5\text{H}_{10} + \text{O}_2 \rightarrow 5\text{CO}_2 + \text{H}_2\text{O}
\]
3. **Balance the hydrogen atoms:**
- Pentene has 10 hydrogen atoms, so we need 5 H₂O.
\[
\text{C}_5\text{H}_{10} + \text{O}_2 \rightarrow 5\text{CO}_2 + 5\text{H}_2\text{O}
\]
4. **Balance the oxygen atoms:**
- On the right side, we have \(5 \times 2 = 10\) from CO₂ and \(5 \times 1 = 5\) from H₂O, totaling 15 oxygen atoms.
- Therefore, we need \( \frac{15}{2} \) O₂.
\[
\text{C}_5\text{H}_{10} + \frac{15}{2}\text{O}_2 \rightarrow 5\text{CO}_2 + 5\text{H}_2\text{O}
\]
5. **Final balanced equation (multiply through by 2):**
\[
2\text{C}_5\text{H}_{10} + 15\text{O}_2 \rightarrow 10\text{CO}_2 + 10\text{H}_2\text{O}
\]
---
**(iii) Combustion of Hexyne (C₆H₁₀)**
1. **Write the unbalanced equation:**
\[
\text{C}_6\text{H}_{10} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}
\]
2. **Balance the carbon atoms:**
- Hexyne has 6 carbon atoms, so we need 6 CO₂.
\[
\text{C}_6\text{H}_{10} + \text{O}_2 \rightarrow 6\text{CO}_2 + \text{H}_2\text{O}
\]
3. **Balance the hydrogen atoms:**
- Hexyne has 10 hydrogen atoms, so we need 5 H₂O.
\[
\text{C}_6\text{H}_{10} + \text{O}_2 \rightarrow 6\text{CO}_2 + 5\text{H}_2\text{O}
\]
4. **Balance the oxygen atoms:**
- On the right side, we have \(6 \times 2 = 12\) from CO₂ and \(5 \times 1 = 5\) from H₂O, totaling 17 oxygen atoms.
- Therefore, we need \( \frac{17}{2} \) O₂.
\[
\text{C}_6\text{H}_{10} + \frac{17}{2}\text{O}_2 \rightarrow 6\text{CO}_2 + 5\text{H}_2\text{O}
\]
5. **Final balanced equation (multiply through by 2):**
\[
2\text{C}_6\text{H}_{10} + 17\text{O}_2 \rightarrow 12\text{CO}_2 + 10\text{H}_2\text{O}
\]
---
**(iv) Combustion of Toluene (C₇H₈)**
1. **Write the unbalanced equation:**
\[
\text{C}_7\text{H}_8 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}
\]
2. **Balance the carbon atoms:**
- Toluene has 7 carbon atoms, so we need 7 CO₂.
\[
\text{C}_7\text{H}_8 + \text{O}_2 \rightarrow 7\text{CO}_2 + \text{H}_2\text{O}
\]
3. **Balance the hydrogen atoms:**
- Toluene has 8 hydrogen atoms, so we need 4 H₂O.
\[
\text{C}_7\text{H}_8 + \text{O}_2 \rightarrow 7\text{CO}_2 + 4\text{H}_2\text{O}
\]
4. **Balance the oxygen atoms:**
- On the right side, we have \(7 \times 2 = 14\) from CO₂ and \(4 \times 1 = 4\) from H₂O, totaling 18 oxygen atoms.
- Therefore, we need \( \frac{18}{2} \) O₂.
\[
\text{C}_7\text{H}_8 + \frac{18}{2}\text{O}_2 \rightarrow 7\text{CO}_2 + 4\text{H}_2\text{O}
\]
5. **Final balanced equation (multiply through by 2):**
\[
2\text{C}_7\text{H}_8 + 18\text{O}_2 \rightarrow 14\text{CO}_2 + 8\text{H}_2\text{O}
\]
### Final Summary of Combustion Reactions:
1. **Butane:**
\[
2\text{C}_4\text{H}_{10} + 13\text{O}_2 \rightarrow 8\text{CO}_2 + 10\text{H}_2\text{O}
\]
2. **Pentene:**
\[
2\text{C}_5\text{H}_{10} + 15\text{O}_2 \rightarrow 10\text{CO}_2 + 10\text{H}_2\text{O}
\]
3. **Hexyne:**
\[
2\text{C}_6\text{H}_{10} + 17\text{O}_2 \rightarrow 12\text{CO}_2 + 10\text{H}_2\text{O}
\]
4. **Toluene:**
\[
2\text{C}_7\text{H}_8 + 18\text{O}_2 \rightarrow 14\text{CO}_2 + 8\text{H}_2\text{O}
\]
