Applying the Summation Form to a Multi-Reactant Reaction
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Applying the summation form to a reaction with several reactants and products means multiplying each substance's known formation enthalpy by its coefficient in the balanced equation, summing those weighted values separately across all products and across all reactants, and subtracting the reactant sum from the product sum.
For nitrogen dioxide reacting with water to form nitric acid and nitric oxide, multiplying each formation enthalpy from a reference table by its coefficient gives four weighted values. Summing the two products' weighted contributions, separately summing the two reactants' weighted contributions, and subtracting the reactant total from the product total gives a standard enthalpy change near −138.4 kJ for the reaction as written.
Adding a reactant's weighted formation enthalpy into the product sum instead of subtracting it out produces an answer roughly twice the correct magnitude, with the wrong sign.
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