If 3 moles of C_5H_{12} are reacted completely with excess oxygen, how many moles of CO_2 are produced?

• A. 12 moles
• B. 3 moles
• C. 15 moles
• D. 5 moles

Answer: (C)

Verified step by step guidance

1. Write the balanced chemical equation for the complete combustion of pentane (C\_5H\_{12}). The general form for combustion of a hydrocarbon is: \(\text{C}_x\text{H}_y + O_2 \rightarrow CO_2 + H_2O\).
2. Balance the carbon atoms first. Since pentane has 5 carbon atoms, you will produce 5 moles of CO\_2 per mole of C\_5H\_{12}. So, the equation starts as: \(\text{C}_5\text{H}_{12} + O_2 \rightarrow 5 CO_2 + H_2O\).
3. Balance the hydrogen atoms next. Pentane has 12 hydrogen atoms, which will form water molecules. Since each water molecule has 2 hydrogen atoms, you will have 6 moles of H\_2O: \(\text{C}_5\text{H}_{12} + O_2 \rightarrow 5 CO_2 + 6 H_2O\).
4. Balance the oxygen atoms last. On the right side, there are 5 moles of CO\_2 (each with 2 oxygen atoms) and 6 moles of H\_2O (each with 1 oxygen atom), so total oxygen atoms needed are: \$5 \times 2 + 6 \times 1 = 10 + 6 = 16\( oxygen atoms, which corresponds to 8 moles of O\_2 (since each O\_2 molecule has 2 oxygen atoms). The balanced equation is: \)\text{C}_5\text{H}_{12} + 8 O_2 \rightarrow 5 CO_2 + 6 H_2O$.
5. Use the mole ratio from the balanced equation to find the moles of CO\_2 produced from 3 moles of C\_5H\_{12}. Since 1 mole of C\_5H\_{12} produces 5 moles of CO\_2, 3 moles will produce: \$3 \times 5 = 15$ moles of CO\_2.