Which one of the following reactions would produce the largest amount of heat per mole of oxygen (O_2) consumed?

• A. CH_4(g) + 2 O_2(g) ightarrow CO_2(g) + 2 H_2O(l) \\ ext{Δ}H = -890 ext{ kJ}
• B. H_2(g) + rac{1}{2} O_2(g) ightarrow H_2O(l) \\ ext{Δ}H = -286 ext{ kJ}
• C. C_3H_8(g) + 5 O_2(g) ightarrow 3 CO_2(g) + 4 H_2O(l) \\ ext{Δ}H = -2220 ext{ kJ}
• D. C_2H_6(g) + rac{7}{2} O_2(g) ightarrow 2 CO_2(g) + 3 H_2O(l) \\ ext{Δ}H = -1560 ext{ kJ}

Answer: (C)

Verified step by step guidance

1. Identify the enthalpy change (ΔH) and the amount of oxygen (O_2) consumed for each reaction given:
2. For each reaction, calculate the heat released per mole of O_2 consumed by dividing the given ΔH by the number of moles of O_2 in the balanced equation. For example, for the reaction \(\mathrm{CH_4(g) + 2\ O_2(g) \rightarrow CO_2(g) + 2\ H_2O(l)}\) with \(\Delta H = -890\ \mathrm{kJ}\), calculate \(\frac{-890\ \mathrm{kJ}}{2\ \mathrm{mol\ O_2}}\).
3. Repeat this calculation for all four reactions:
4. - \(\mathrm{CH_4}\) reaction: \(\frac{\Delta H}{\text{moles of } O_2} = \frac{-890}{2}\)
5. - \(\mathrm{H_2}\) reaction: \(\frac{-286}{0.5}\)
6. - \(\mathrm{C_3H_8}\) reaction: \(\frac{-2220}{5}\)
7. - \(\mathrm{C_2H_6}\) reaction: \(\frac{-1560}{3.5}\)
8. Compare the values obtained for heat released per mole of O_2 consumed. The reaction with the largest magnitude (most negative value) corresponds to the largest amount of heat released per mole of oxygen consumed.
9. Conclude which reaction produces the largest heat per mole of O_2 based on the comparison.