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2C₂H₂(g) + 5O₂(g) → 4CO₂(g) + 2H₂O(g)

How many liters of C₂H₂ are required to produce 8 L of CO₂, assuming the reaction is at STP?

The ratios are:
[tex]\(\frac{2 \, \text{L} \, \text{C}_2 \text{H}_2}{4 \, \text{L} \, \text{CO}_2}\)[/tex] or [tex]\(\frac{4 \, \text{L} \, \text{CO}_2}{2 \, \text{L} \, \text{C}_2 \text{H}_2}\)[/tex].

? L C₂H₂
L C₂H₂ ☐



Answer :

GinnyAnswer
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]

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