In the reaction 2 H_2 + O_2 → 2 H_2O, how many moles of O_2 are required to completely react with 27.4 mol of H_2?

• A. 27.4 mol
• B. 54.8 mol
• C. 13.7 mol
• D. 6.85 mol

Answer: (C)

Verified step by step guidance

1. Identify the balanced chemical equation: \$2 \mathrm{H}_2 + \mathrm{O}_2 \rightarrow 2 \mathrm{H}_2\mathrm{O}$.
2. Determine the mole ratio between \(\mathrm{H}_2\) and \(\mathrm{O}_2\) from the balanced equation. For every 2 moles of \(\mathrm{H}_2\), 1 mole of \(\mathrm{O}_2\) is required.
3. Set up a proportion to find the moles of \(\mathrm{O}_2\) needed for 27.4 moles of \(\mathrm{H}_2\): \(\frac{2 \text{ mol } \mathrm{H}_2}{1 \text{ mol } \mathrm{O}_2} = \frac{27.4 \text{ mol } \mathrm{H}_2}{x \text{ mol } \mathrm{O}_2}\).
4. Solve for \(x\) (moles of \(\mathrm{O}_2\)): \(x = \frac{27.4 \times 1}{2}\).
5. Interpret the result as the number of moles of \(\mathrm{O}_2\) required to completely react with 27.4 moles of \(\mathrm{H}_2\).