Answer :
Sure, I'll help you determine the ratio of [tex]\( \text{C}_2 \text{H}_2 \)[/tex] to [tex]\( \text{CO}_2 \)[/tex] from the given balanced chemical equation step-by-step.
The balanced chemical equation is:
[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]
### Steps to Determine the Ratio
1. Identify the Stoichiometric Coefficients:
- The coefficient in front of [tex]\( \text{C}_2 \text{H}_2 \)[/tex] is 2.
- The coefficient in front of [tex]\( \text{CO}_2 \)[/tex] is 4.
2. Understand the Coefficients' Role:
- These coefficients tell us the mole ratio between the reactants and products.
- Specifically, 2 moles of [tex]\( \text{C}_2 \text{H}_2 \)[/tex] react to produce 4 moles of [tex]\( \text{CO}_2 \)[/tex].
3. Simplify the Ratio:
- To find the ratio of [tex]\( \text{C}_2 \text{H}_2 \)[/tex] to [tex]\( \text{CO}_2 \)[/tex], divide the coefficients.
- Ratio = Coefficient of [tex]\( \text{C}_2 \text{H}_2 \)[/tex] / Coefficient of [tex]\( \text{CO}_2 \)[/tex] = 2 / 4.
4. Simplify the Fraction:
- Simplify the fraction 2/4 to its lowest terms.
- 2/4 is equivalent to 1/2.
Therefore, the simplified ratio of [tex]\( \text{C}_2 \text{H}_2 \)[/tex] to [tex]\( \text{CO}_2 \)[/tex] from the balanced equation is:
[tex]\[ 1:2 \][/tex]
### Conclusion
The volume ratio of [tex]\( \text{C}_2 \text{H}_2 \)[/tex] (green) to [tex]\( \text{CO}_2 \)[/tex] (yellow) is [tex]\( 1:2 \)[/tex] at STP, as per the stoichiometric coefficients of the balanced chemical equation.
So, if you asked for the specific ratio of :
[tex]\[ ? \, \text{L} \, \text{C}_2 \text{H}_2 : ? \, \text{L} \, \text{CO}_2 \][/tex]
The answer is:
[tex]\[ 1 \, \text{L} \, \text{C}_2 \text{H}_2 : 2 \, \text{L} \, \text{CO}_2 \][/tex]
In other terms, the numerical ratio is 0.5.
The balanced chemical equation is:
[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]
### Steps to Determine the Ratio
1. Identify the Stoichiometric Coefficients:
- The coefficient in front of [tex]\( \text{C}_2 \text{H}_2 \)[/tex] is 2.
- The coefficient in front of [tex]\( \text{CO}_2 \)[/tex] is 4.
2. Understand the Coefficients' Role:
- These coefficients tell us the mole ratio between the reactants and products.
- Specifically, 2 moles of [tex]\( \text{C}_2 \text{H}_2 \)[/tex] react to produce 4 moles of [tex]\( \text{CO}_2 \)[/tex].
3. Simplify the Ratio:
- To find the ratio of [tex]\( \text{C}_2 \text{H}_2 \)[/tex] to [tex]\( \text{CO}_2 \)[/tex], divide the coefficients.
- Ratio = Coefficient of [tex]\( \text{C}_2 \text{H}_2 \)[/tex] / Coefficient of [tex]\( \text{CO}_2 \)[/tex] = 2 / 4.
4. Simplify the Fraction:
- Simplify the fraction 2/4 to its lowest terms.
- 2/4 is equivalent to 1/2.
Therefore, the simplified ratio of [tex]\( \text{C}_2 \text{H}_2 \)[/tex] to [tex]\( \text{CO}_2 \)[/tex] from the balanced equation is:
[tex]\[ 1:2 \][/tex]
### Conclusion
The volume ratio of [tex]\( \text{C}_2 \text{H}_2 \)[/tex] (green) to [tex]\( \text{CO}_2 \)[/tex] (yellow) is [tex]\( 1:2 \)[/tex] at STP, as per the stoichiometric coefficients of the balanced chemical equation.
So, if you asked for the specific ratio of :
[tex]\[ ? \, \text{L} \, \text{C}_2 \text{H}_2 : ? \, \text{L} \, \text{CO}_2 \][/tex]
The answer is:
[tex]\[ 1 \, \text{L} \, \text{C}_2 \text{H}_2 : 2 \, \text{L} \, \text{CO}_2 \][/tex]
In other terms, the numerical ratio is 0.5.
