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Answer :
To solve this problem, we need to use the balanced chemical equation:
[tex]\[ C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O \][/tex]
According to this equation:
- 5 liters of [tex]\( O_2 \)[/tex] produce 3 liters of [tex]\( CO_2 \)[/tex].
We are asked to find out how many liters of [tex]\( O_2 \)[/tex] are needed to produce 43.62 liters of [tex]\( CO_2 \)[/tex].
Here is how you can solve it step by step:
1. Determine the ratio:
From the balanced equation, you can see that for every 3 liters of [tex]\( CO_2 \)[/tex] produced, 5 liters of [tex]\( O_2 \)[/tex] are needed. So, the ratio of [tex]\( O_2 \)[/tex] to [tex]\( CO_2 \)[/tex] is 5:3.
2. Calculate the liters of [tex]\( O_2 \)[/tex] needed:
You have 43.62 liters of [tex]\( CO_2 \)[/tex]. To find out how many liters of [tex]\( O_2 \)[/tex] are required, you can set up a proportion based on the ratio:
[tex]\[
\frac{5 \, \text{liters of } O_2}{3 \, \text{liters of } CO_2} = x \, \text{liters of } O_2 / 43.62 \, \text{liters of } CO_2
\][/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[
x = 43.62 \times \frac{5}{3}
\][/tex]
[tex]\[
x = 72.7 \, \text{liters of } O_2
\][/tex]
Therefore, 72.7 liters of [tex]\( O_2 \)[/tex] are needed to produce 43.62 liters of [tex]\( CO_2 \)[/tex] at STP. The correct answer is A. 72.7 liters.
[tex]\[ C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O \][/tex]
According to this equation:
- 5 liters of [tex]\( O_2 \)[/tex] produce 3 liters of [tex]\( CO_2 \)[/tex].
We are asked to find out how many liters of [tex]\( O_2 \)[/tex] are needed to produce 43.62 liters of [tex]\( CO_2 \)[/tex].
Here is how you can solve it step by step:
1. Determine the ratio:
From the balanced equation, you can see that for every 3 liters of [tex]\( CO_2 \)[/tex] produced, 5 liters of [tex]\( O_2 \)[/tex] are needed. So, the ratio of [tex]\( O_2 \)[/tex] to [tex]\( CO_2 \)[/tex] is 5:3.
2. Calculate the liters of [tex]\( O_2 \)[/tex] needed:
You have 43.62 liters of [tex]\( CO_2 \)[/tex]. To find out how many liters of [tex]\( O_2 \)[/tex] are required, you can set up a proportion based on the ratio:
[tex]\[
\frac{5 \, \text{liters of } O_2}{3 \, \text{liters of } CO_2} = x \, \text{liters of } O_2 / 43.62 \, \text{liters of } CO_2
\][/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[
x = 43.62 \times \frac{5}{3}
\][/tex]
[tex]\[
x = 72.7 \, \text{liters of } O_2
\][/tex]
Therefore, 72.7 liters of [tex]\( O_2 \)[/tex] are needed to produce 43.62 liters of [tex]\( CO_2 \)[/tex] at STP. The correct answer is A. 72.7 liters.
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