Questions: Write and balance the equation for the complete combustion of acetylene, C2H2. Phase symbols and energy changes 등 are optional.

Write and balance the equation for the complete combustion of acetylene, C2H2. Phase symbols and energy changes 등 are optional.
Transcript text: Write and balance the equation for the complete combustion of acetylene, $\mathrm{C}_{2} \mathrm{H}_{2}$. Phase symbols and energy changes 등 are optional.
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Solution

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Solution Steps

Step 1: Identify the Reactants and Products

The complete combustion of acetylene (\(\mathrm{C}_2\mathrm{H}_2\)) involves reacting it with oxygen (\(\mathrm{O}_2\)) to produce carbon dioxide (\(\mathrm{CO}_2\)) and water (\(\mathrm{H}_2\mathrm{O}\)).

Step 2: Write the Unbalanced Chemical Equation

The unbalanced chemical equation for the combustion of acetylene is: \[ \mathrm{C}_2\mathrm{H}_2 + \mathrm{O}_2 \rightarrow \mathrm{CO}_2 + \mathrm{H}_2\mathrm{O} \]

Step 3: Balance the Chemical Equation

  1. Balance Carbon Atoms: There are 2 carbon atoms in \(\mathrm{C}_2\mathrm{H}_2\), so we need 2 \(\mathrm{CO}_2\) molecules: \[ \mathrm{C}_2\mathrm{H}_2 + \mathrm{O}_2 \rightarrow 2\mathrm{CO}_2 + \mathrm{H}_2\mathrm{O} \]

  2. Balance Hydrogen Atoms: There are 2 hydrogen atoms in \(\mathrm{C}_2\mathrm{H}_2\), so we need 1 \(\mathrm{H}_2\mathrm{O}\) molecule: \[ \mathrm{C}_2\mathrm{H}_2 + \mathrm{O}_2 \rightarrow 2\mathrm{CO}_2 + \mathrm{H}_2\mathrm{O} \]

  3. Balance Oxygen Atoms: There are 4 oxygen atoms in 2 \(\mathrm{CO}_2\) and 1 oxygen atom in \(\mathrm{H}_2\mathrm{O}\), totaling 5 oxygen atoms. Therefore, we need \(\frac{5}{2}\) \(\mathrm{O}_2\) molecules: \[ \mathrm{C}_2\mathrm{H}_2 + \frac{5}{2}\mathrm{O}_2 \rightarrow 2\mathrm{CO}_2 + \mathrm{H}_2\mathrm{O} \]

  4. Clear Fraction by Multiplying Through by 2: To eliminate the fraction, multiply the entire equation by 2: \[ 2\mathrm{C}_2\mathrm{H}_2 + 5\mathrm{O}_2 \rightarrow 4\mathrm{CO}_2 + 2\mathrm{H}_2\mathrm{O} \]

Final Answer

The balanced chemical equation for the complete combustion of acetylene is: \[ \boxed{2\mathrm{C}_2\mathrm{H}_2 + 5\mathrm{O}_2 \rightarrow 4\mathrm{CO}_2 + 2\mathrm{H}_2\mathrm{O}} \]

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