Given the reaction: C2H6O + 3 O2 → 2 CO2 + 3 H2O, how many molecules of C2H6O are required to react completely with 1.36 mol of O2?

• A. 2.72 × 10^{23} molecules
• B. 2.73 × 10^{23} molecules
• C. 4.08 × 10^{23} molecules
• D. 2.72 × 10^{22} molecules

Answer: (D)

Verified step by step guidance

1. Identify the balanced chemical equation: \(\mathrm{C_2H_6O + 3\ O_2 \rightarrow 2\ CO_2 + 3\ H_2O}\), which shows that 1 mole of \(\mathrm{C_2H_6O}\) reacts with 3 moles of \(\mathrm{O_2}\).
2. Use the mole ratio from the balanced equation to find the moles of \(\mathrm{C_2H_6O}\) needed for 1.36 moles of \(\mathrm{O_2}\). The ratio is \(\frac{1\ \text{mol}\ \mathrm{C_2H_6O}}{3\ \text{mol}\ \mathrm{O_2}}\), so calculate moles of \(\mathrm{C_2H_6O}\) as \$1.36\ \text{mol}\ \mathrm{O_2} \times \frac{1\ \text{mol}\ \mathrm{C_2H_6O}}{3\ \text{mol}\ \mathrm{O_2}}$.
3. Convert the moles of \(\mathrm{C_2H_6O}\) to molecules using Avogadro's number, \$6.022 \times 10^{23}\( molecules/mol, by multiplying the moles of \)\mathrm{C_2H_6O}$ by this constant.
4. Write the full expression for the number of molecules of \(\mathrm{C_2H_6O}\): \(\text{molecules} = \left(1.36 \times \frac{1}{3}\right) \times 6.022 \times 10^{23}\).
5. Perform the arithmetic to find the number of molecules, which will give the amount of \(\mathrm{C_2H_6O}\) molecules required to react completely with 1.36 moles of \(\mathrm{O_2}\).