To find the ratio of [tex]\( C_2H_2 \)[/tex] (acetylene) to [tex]\( CO_2 \)[/tex] (carbon dioxide) from the balanced chemical equation, we need to examine the coefficients of each compound in the balanced equation. The balanced equation for the combustion of acetylene is:
[tex]\[ 2 C_2H_2(g) + 5 O_2(g) \rightarrow 4 CO_2(g) + 2 H_2O(g) \][/tex]
Here are the steps to determine the ratio:
1. Identify the Mole Coefficients:
- For [tex]\( C_2H_2 \)[/tex]: The coefficient is 2.
- For [tex]\( CO_2 \)[/tex]: The coefficient is 4.
2. Establish the Mole Ratio:
- According to the balanced equation, for every 2 moles of [tex]\( C_2H_2 \)[/tex], 4 moles of [tex]\( CO_2 \)[/tex] are produced.
3. Simplify the Ratio:
- To simplify the mole ratio to its smallest whole numbers, we divide both coefficients by the greatest common divisor. Here, we divide by 2:
[tex]\[
\frac{2}{2} = 1 \quad \text{(for } C_2H_2)
\][/tex]
[tex]\[
\frac{4}{2} = 2 \quad \text{(for } CO_2)
\][/tex]
Therefore, the simplified ratio of [tex]\( C_2H_2 \)[/tex] to [tex]\( CO_2 \)[/tex] is:
[tex]\[ 1 : 2 \][/tex]
This means that for every 1 mole of [tex]\( C_2H_2 \)[/tex], 2 moles of [tex]\( CO_2 \)[/tex] are produced.
The ratio is [tex]\( 1 \; C_2H_2 : 2 \; CO_2 \)[/tex].
