Select the correct answer.
How many moles of $O _2$ are required to generate 18 moles of $H _2 O$ in the given reaction?
$2 C_8 H_{18}+25 O_2 \rightarrow 16 CO_2+18 H_2 O$
A. 2 moles
B. 12 moles
C. 16 moles
D. 18 moles
E. 25 moles
Answer (1)
The balanced chemical equation shows that 25 moles of O 2 produce 18 moles of H 2 O .
Set up a proportion relating moles of O 2 to moles of H 2 O .
Solve the proportion: moles of O 2 = 18 25 × 18 = 25 .
Therefore, 25 moles of O 2 are required. 25
Explanation
Analyze the Balanced Equation We are given the balanced chemical equation:
2 C 8 H 18 + 25 O 2 → 16 C O 2 + 18 H 2 O
We want to find out how many moles of O 2 are needed to produce 18 moles of H 2 O .
Set up the Proportion From the balanced equation, we can see that 25 moles of O 2 produce 18 moles of H 2 O . We can set up a proportion to solve for the moles of O 2 needed.
Solve for Moles of Oxygen The ratio of moles of O 2 to moles of H 2 O is 18 25 . Since we want to produce 18 moles of H 2 O , we can set up the following equation:
moles of O 2 = 18 moles H 2 O 25 moles O 2 × 18 moles H 2 O
moles of O 2 = 25 moles
So, 25 moles of O 2 are required to generate 18 moles of H 2 O .
Final Answer Therefore, the correct answer is E. 25 moles.
Examples
In the combustion of fuels, like in car engines or power plants, it's crucial to understand the molar ratios between reactants and products. This problem demonstrates how to calculate the amount of oxygen needed to produce a specific amount of water, which is vital for optimizing fuel efficiency and reducing emissions. By knowing the exact molar quantities, engineers can design more efficient combustion processes, leading to better fuel economy and a smaller environmental footprint.
