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Answer :
To find out how many moles of [tex]\( H_2O \)[/tex] are produced when 11.2 liters of [tex]\( C_8H_{16} \)[/tex] gas reacts completely, we can use the concept of molar volume at STP (Standard Temperature and Pressure). At STP, 1 mole of any gas occupies 22.4 liters.
Here's a step-by-step explanation:
1. Determine the Moles of [tex]\( C_8H_{16} \)[/tex] Gas:
- Given the volume of [tex]\( C_8H_{16} \)[/tex] is 11.2 liters and knowing that 1 mole of any gas occupies 22.4 liters at STP:
[tex]\[
\text{Moles of } C_8H_{16} = \frac{11.2 \text{ liters}}{22.4 \text{ liters/mole}} = 0.5 \text{ moles}
\][/tex]
2. Use the Stoichiometry of the Reaction:
- The balanced chemical equation is:
[tex]\[
C_8H_{16} + 12O_2 \rightarrow 8CO_2 + 8H_2O
\][/tex]
- According to the balanced equation, 1 mole of [tex]\( C_8H_{16} \)[/tex] produces 8 moles of [tex]\( H_2O \)[/tex].
3. Calculate the Moles of [tex]\( H_2O \)[/tex] Produced:
- From the stoichiometry, 0.5 moles of [tex]\( C_8H_{16} \)[/tex] will produce:
[tex]\[
0.5 \times 8 = 4.0 \text{ moles of } H_2O
\][/tex]
Therefore, the number of moles of [tex]\( H_2O \)[/tex] produced is 4.0.
So, the correct answer is A) 4.00.
Here's a step-by-step explanation:
1. Determine the Moles of [tex]\( C_8H_{16} \)[/tex] Gas:
- Given the volume of [tex]\( C_8H_{16} \)[/tex] is 11.2 liters and knowing that 1 mole of any gas occupies 22.4 liters at STP:
[tex]\[
\text{Moles of } C_8H_{16} = \frac{11.2 \text{ liters}}{22.4 \text{ liters/mole}} = 0.5 \text{ moles}
\][/tex]
2. Use the Stoichiometry of the Reaction:
- The balanced chemical equation is:
[tex]\[
C_8H_{16} + 12O_2 \rightarrow 8CO_2 + 8H_2O
\][/tex]
- According to the balanced equation, 1 mole of [tex]\( C_8H_{16} \)[/tex] produces 8 moles of [tex]\( H_2O \)[/tex].
3. Calculate the Moles of [tex]\( H_2O \)[/tex] Produced:
- From the stoichiometry, 0.5 moles of [tex]\( C_8H_{16} \)[/tex] will produce:
[tex]\[
0.5 \times 8 = 4.0 \text{ moles of } H_2O
\][/tex]
Therefore, the number of moles of [tex]\( H_2O \)[/tex] produced is 4.0.
So, the correct answer is A) 4.00.
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