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[tex]\[
2 C_2 H_2(g) + 5 O_2(g) \rightarrow 4 CO_2(g) + 2 H_2O(g)
\][/tex]

How many liters of \(C_2 H_2\) are required to produce \(8 \, \text{L}\) of \(CO_2\), assuming the reaction is at STP?

The ratios are: [tex]\(\frac{2 \, \text{L} \, C_2 H_2}{4 \, \text{L} \, CO_2}\)[/tex] or [tex]\(\frac{4 \, \text{L} \, CO_2}{2 \, \text{L} \, C_2 H_2}\)[/tex].



Answer :

GinnyAnswer
To determine how many liters of \( C_2H_2 \) are required to produce 8 liters of \( CO_2 \) from the given balanced chemical equation:
[tex]\[ 2 C_2H_2 (g) + 5 O_2 (g) \rightarrow 4 CO_2 (g) + 2 H_2O (g) \][/tex]
we need to use stoichiometric relationships derived from the balanced equation.

### Step-by-Step Solution

1. Identify the given information and the required quantity:
- Given: 8 liters of \( CO_2 \)
- Required: Liters of \( C_2H_2 \) needed to produce 8 liters of \( CO_2 \)

2. Analyze the balanced chemical equation:
- The coefficients in the balanced equation indicate the stoichiometric ratios of reactants and products. According to the equation:
[tex]\[ 2 \text{ L of } C_2H_2 \text{ produces } 4 \text{ L of } CO_2 \][/tex]

3. Determine the ratio required for the conversion:
- From the equation, the ratio of liters of \( C_2H_2 \) to liters of \( CO_2 \) is:
[tex]\[ \frac{2 \text{ L } C_2H_2}{4 \text{ L } CO_2} = \frac{1}{2} \][/tex]

4. Use this ratio to calculate the required liters of \( C_2H_2 \):
- Given that 8 liters of \( CO_2 \) are produced, we need to find how many liters of \( C_2H_2 \) are needed:
[tex]\[ \text{Liters of } C_2H_2 = \text{Liters of } CO_2 \times \frac{1}{2} \][/tex]

5. Perform the calculation:
- Substitute the liters of \( CO_2 \) (8 L) into the equation:
[tex]\[ \text{Liters of } C_2H_2 = 8 \text{ L } CO_2 \times \frac{1}{2} \][/tex]
[tex]\[ \text{Liters of } C_2H_2 = 4 \text{ L } \][/tex]

### Conclusion

To produce 8 liters of [tex]\( CO_2 \)[/tex], you need 4 liters of [tex]\( C_2H_2 \)[/tex]. This result is derived from the stoichiometric relationship given in the balanced chemical equation.

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