Number of moles of oxygen required for the complete combustion of butane are

Options

A. 6
B. 7.5
C. 6.5
D. 7

Answer

To determine the number of moles of oxygen required for the complete combustion of butane (C₄H₁₀), we can follow these steps:

### Step 1: Write the balanced chemical equation for the combustion of butane.
The complete combustion of butane can be represented by the following equation:

\[ \text{C}_4\text{H}_{10} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} \]

### Step 2: Balance the equation.
To balance the equation, we need to ensure that the number of atoms of each element is the same on both sides of the equation.

1. Start with carbon (C): Butane has 4 carbon atoms, so we need 4 CO₂.
\[ \text{C}_4\text{H}_{10} + \text{O}_2 \rightarrow 4 \text{CO}_2 + \text{H}_2\text{O} \]

2. Next, balance hydrogen (H): Butane has 10 hydrogen atoms, so we need 5 H₂O.
\[ \text{C}_4\text{H}_{10} + \text{O}_2 \rightarrow 4 \text{CO}_2 + 5 \text{H}_2\text{O} \]

3. Now, count the total number of oxygen atoms on the right side:
- From 4 CO₂: \( 4 \times 2 = 8 \) oxygen atoms
- From 5 H₂O: \( 5 \times 1 = 5 \) oxygen atoms
- Total = \( 8 + 5 = 13 \) oxygen atoms

4. Since O₂ has 2 oxygen atoms per molecule, we need \( \frac{13}{2} \) moles of O₂.
\[ \text{C}_4\text{H}_{10} + \frac{13}{2} \text{O}_2 \rightarrow 4 \text{CO}_2 + 5 \text{H}_2\text{O} \]

### Step 3: Convert to a whole number if necessary.
To avoid fractions, we can multiply the entire equation by 2:
\[ 2 \text{C}_4\text{H}_{10} + 13 \text{O}_2 \rightarrow 8 \text{CO}_2 + 10 \text{H}_2\text{O} \]

### Conclusion:
Thus, for the complete combustion of 1 mole of butane, \( \frac{13}{2} \) moles of oxygen are required, which is equivalent to 6.5 moles of O₂.

### Final Answer:
**6.5 moles of oxygen are required for the complete combustion of butane.**

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