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Answer :
To solve this problem, we need to understand the stoichiometric relationship in the given chemical reaction:
[tex]\[ C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O \][/tex]
The question asks us to find out how many liters of [tex]\( O_2 \)[/tex] are required to produce 43.62 liters of [tex]\( CO_2 \)[/tex] at standard temperature and pressure (STP). At STP, gases react in volume proportions equal to their coefficients in the balanced chemical equation, because 1 mole of gas occupies 22.4 liters.
### Step-by-step Solution:
1. Identify the Volume Ratio:
- From the balanced equation, 5 liters of [tex]\( O_2 \)[/tex] produce 3 liters of [tex]\( CO_2 \)[/tex].
- Therefore, the volume ratio between [tex]\( O_2 \)[/tex] and [tex]\( CO_2 \)[/tex] is 5:3.
2. Calculate the Volume of [tex]\( O_2 \)[/tex]:
- Given that 43.62 liters of [tex]\( CO_2 \)[/tex] is produced, we can use the volume ratio to determine the volume of [tex]\( O_2 \)[/tex] needed:
[tex]\[
\text{Volume of } O_2 = \left(\frac{5}{3}\right) \times 43.62
\][/tex]
3. Perform the Calculation:
- [tex]\[
\text{Volume of } O_2 = \frac{5}{3} \times 43.62 = 72.7 \text{ liters}
\][/tex]
Based on this calculation, 72.7 liters of [tex]\( O_2 \)[/tex] are required to produce 43.62 liters of [tex]\( CO_2 \)[/tex] at STP.
Therefore, the correct answer is A. 72.7 liters.
[tex]\[ C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O \][/tex]
The question asks us to find out how many liters of [tex]\( O_2 \)[/tex] are required to produce 43.62 liters of [tex]\( CO_2 \)[/tex] at standard temperature and pressure (STP). At STP, gases react in volume proportions equal to their coefficients in the balanced chemical equation, because 1 mole of gas occupies 22.4 liters.
### Step-by-step Solution:
1. Identify the Volume Ratio:
- From the balanced equation, 5 liters of [tex]\( O_2 \)[/tex] produce 3 liters of [tex]\( CO_2 \)[/tex].
- Therefore, the volume ratio between [tex]\( O_2 \)[/tex] and [tex]\( CO_2 \)[/tex] is 5:3.
2. Calculate the Volume of [tex]\( O_2 \)[/tex]:
- Given that 43.62 liters of [tex]\( CO_2 \)[/tex] is produced, we can use the volume ratio to determine the volume of [tex]\( O_2 \)[/tex] needed:
[tex]\[
\text{Volume of } O_2 = \left(\frac{5}{3}\right) \times 43.62
\][/tex]
3. Perform the Calculation:
- [tex]\[
\text{Volume of } O_2 = \frac{5}{3} \times 43.62 = 72.7 \text{ liters}
\][/tex]
Based on this calculation, 72.7 liters of [tex]\( O_2 \)[/tex] are required to produce 43.62 liters of [tex]\( CO_2 \)[/tex] at STP.
Therefore, the correct answer is A. 72.7 liters.
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