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Assuming the reaction below occurs at STP, what is the ratio of [tex]\( C_2H_2 \)[/tex] to [tex]\( CO_2 \)[/tex] from the balanced equation?

[tex]\[ 2C_2H_2(g) + 5O_2(g) \rightarrow 4CO_2(g) + 2H_2O(g) \][/tex]

[tex]\[ \text{Ratio of } C_2H_2 \text{ to } CO_2: \][/tex]

[tex]\[ \frac{2}{4} \][/tex] or [tex]\( 1:2 \)[/tex]

Sagot :

GinnyAnswer
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.
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