To determine the ratio of [tex]\( \text{C}_2\text{H}_2 \)[/tex] to [tex]\( \text{CO}_2 \)[/tex] from the balanced equation, we can follow these steps:
1. First, consider the balanced chemical equation:
[tex]\[
2 \text{C}_2\text{H}_2(g) + 5 \text{O}_2(g) \rightarrow 4 \text{CO}_2(g) + 2 \text{H}_2\text{O}(g)
\][/tex]
2. From the balanced equation, identify the coefficients (the numbers in front of each compound) for [tex]\( \text{C}_2\text{H}_2 \)[/tex] and [tex]\( \text{CO}_2 \)[/tex]:
- The coefficient for [tex]\( \text{C}_2\text{H}_2 \)[/tex] is 2.
- The coefficient for [tex]\( \text{CO}_2 \)[/tex] is 4.
3. The ratio of [tex]\( \text{C}_2\text{H}_2 \)[/tex] to [tex]\( \text{CO}_2 \)[/tex] is given by the coefficients from the balanced equation. Thus, the ratio can be written as:
[tex]\[
\text{Ratio of } \text{C}_2\text{H}_2 \text{ to } \text{CO}_2 = \frac{2}{4} = 0.5
\][/tex]
4. Therefore, the final ratio of [tex]\( \text{C}_2\text{H}_2 \)[/tex] to [tex]\( \text{CO}_2 \)[/tex] is:
[tex]\[
2 \text{C}_2\text{H}_2 : 4 \text{CO}_2
\][/tex]
At STP (Standard Temperature and Pressure), this means for every 2 liters of [tex]\( \text{C}_2\text{H}_2 \)[/tex], 4 liters of [tex]\( \text{CO}_2 \)[/tex] are produced.
