- Analyze the balanced chemical equation \(2H_2 + O_2 \rightarrow 2H_2O\) to determine the stoichiometry.
- Identify the mole ratio between oxygen and water as \(1:2\).
- Calculate the total amount of water produced: \(13.35 \text{ mol } O_2 \times 2 = 26.70 \text{ mol } H_2O\).
- Select the corresponding option, which is \(\boxed{b}\).
Explanation
- Problem Analysis and Stoichiometry
The provided chemical reaction is:
\[2H_2 + O_2 \rightarrow 2H_2O\]
This balanced equation shows the relationship between reactants and products. Specifically, the stoichiometric coefficients indicate that 1 mole of oxygen (\(O_2\)) reacts with 2 moles of hydrogen (\(H_2\)) to produce 2 moles of water (\(H_2O\)). We are given that we have \(13.35 \text{ mol}\) of \(O_2\) and we assume an excess of \(H_2\), meaning the entire amount of \(O_2\) will be consumed in the reaction.
- Calculation of Product Amount
Based on the balanced equation, the molar ratio of oxygen to water is:
\[\text{Ratio} = \frac{2 \text{ mol } H_2O}{1 \text{ mol } O_2}\]
To find the amount of water produced, we multiply the given amount of oxygen by this ratio:
\[\text{Moles of } H_2O = 13.35 \text{ mol } O_2 \times \frac{2 \text{ mol } H_2O}{1 \text{ mol } O_2}\]
\[\text{Moles of } H_2O = 13.35 \times 2 = 26.70 \text{ mol}\]
Thus, \(26.70 \text{ moles}\) of water are produced.
- Final Conclusion
Comparing our result of \(26.70 \text{ mol}\) to the provided options:
A\(6.675 \text{ mol}\)
B\(26.70 \text{ mol}\)
C\(53.40 \text{ mol}\)
D\(66.75 \text{ mol}\)
The calculated value matches option b. Therefore, the final answer is \(\boxed{b}\).
Examples
Stoichiometry is a fundamental concept in chemistry that allows us to predict the amounts of substances consumed or produced in a reaction. For instance, if you are working in a laboratory to synthesize water, understanding that you need double the amount of oxygen in terms of moles to produce water helps in preparing the exact quantities of reactants. This avoids wasting materials and ensures the reaction proceeds to completion, which is essential for industrial processes, pharmaceutical manufacturing, and environmental monitoring.