To determine how many liters of [tex]\( C_2H_2 \)[/tex] (acetylene) are required to produce 8 liters of [tex]\( CO_2 \)[/tex] (carbon dioxide) at standard temperature and pressure (STP), we can use the stoichiometric ratios given by the balanced chemical equation.
The balanced equation is:
[tex]\[
2 C_2H_2(g) + 5 O_2(g) \rightarrow 4 CO_2(g) + 2 H_2O(g)
\][/tex]
This equation tells us the molar (and hence volume, since at STP, volume ratios are the same as mole ratios) relationships of the reactants and products. Specifically:
- 2 liters of [tex]\( C_2H_2 \)[/tex] produce 4 liters of [tex]\( CO_2 \)[/tex].
We can use the ratio of [tex]\( C_2H_2 \)[/tex] to [tex]\( CO_2 \)[/tex] to find out how much [tex]\( C_2H_2 \)[/tex] is required to produce 8 liters of [tex]\( CO_2 \)[/tex].
1. Identify the ratio from the balanced equation:
[tex]\[
\frac{2 L \, C_2H_2}{4 L \, CO_2}
\][/tex]
2. Simplify this ratio:
[tex]\[
\frac{2}{4} = \frac{1}{2}
\][/tex]
3. Use this ratio to find the required volume of [tex]\( C_2H_2 \)[/tex]:
If 4 liters of [tex]\( CO_2 \)[/tex] require 2 liters of [tex]\( C_2H_2 \)[/tex],
then 8 liters of [tex]\( CO_2 \)[/tex] will require:
[tex]\[
8 L \, CO_2 \times \frac{1 L \, C_2H_2}{2 L \, CO_2} = 4 L \, C_2H_2
\][/tex]
Therefore, the answer is:
[tex]\[ 4 \, \text{liters of} \, C_2H_2 \][/tex]
