To balance the combustion reaction of methane (CH₄) with oxygen (O₂) to produce carbon dioxide (CO₂) and water (H₂O), we can follow these steps:
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Write the unbalanced equation: \[ \text{CH}_4 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} \]
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Count the number of each type of atom on both sides of the equation:
- Left side: 1 C, 4 H, 2 O (from O₂)
- Right side: 1 C (from CO₂), 2 H (from H₂O), and to balance the number of oxygen atoms, we need to determine how many O₂ molecules and H₂O we will use.
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Balance the carbon atoms:
- There is 1 carbon atom in CH₄ and 1 in CO₂. This is already balanced.
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Balance the hydrogen atoms:
- There are 4 hydrogen atoms in CH₄ and 2 in H₂O. To balance, we need 2 water molecules: \[ \text{CH}_4 + \text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \]
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Now, count the oxygen atoms on the right side:
- From CO₂: 2 O
- From 2 H₂O: 2 × 1 = 2 O
- Total: 2 + 2 = 4 O
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Now balance the oxygen atoms:
- We need 4 oxygen atoms on the left side (from O₂), which means we need 2 O₂ molecules: \[ \text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \]
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Now we rewrite the balanced equation with coefficients: \[ 1\text{CH}_4 + 2\text{O}_2 \rightarrow 1\text{CO}_2 + 2\text{H}_2\text{O} \]
The final balanced equation is: \[ \text{1 CH}_4 + \text{2 O}_2 \rightarrow \text{1 CO}_2 + \text{2 H}_2\text{O} \]
So the coefficients are: 1, 2, 1, 2.