Which expression correctly gives the standard heat of combustion using formation enthalpies?

• A. ΔHc° = Σ ν ΔHf°(reactants) − Σ ν ΔHf°(products)
• B. ΔHc° = Σ ν ΔHf°(products) − Σ ν ΔHf°(reactants)
• C. ΔHc° = ΔHf°(products) − ΔHf°(reactants)
• D. ΔHc° = Σ ν ΔHf°(products) + Σ ν ΔHf°(reactants)

Answer: (B)

The essential idea is that the enthalpy change for a reaction, when you express everything in terms of formation enthalpies, comes from taking the sum of the formation enthalpies of all products (each multiplied by its stoichiometric coefficient) and subtracting the sum of the formation enthalpies of all reactants (also with their coefficients). For combustion this gives the standard heat of combustion as ΔHc° = Σ ν ΔHf°(products) − Σ ν ΔHf°(reactants). This accounts for how many moles of each substance appear on each side of the equation and carries the correct sign for the enthalpy change. An example is methane burning: CH4 + 2 O2 → CO2 + 2 H2O. Then ΔHc° = [ΔHf°(CO2) + 2 ΔHf°(H2O)] − [ΔHf°(CH4) + 2 ΔHf°(O2)], and since ΔHf°(O2) = 0, the expression correctly reflects the combustion enthalpy. The other forms either flip the sign, omit the coefficients, or add reactants and products together, which does not represent the actual enthalpy change of the reaction.