# Thermochemistry: What is the difference between the calculation of bond enthalpy and Hess's Law

I know that Hess's law is an indirect way to find the heat of reaction using the known heat of reaction of 2+ thermochemical equations, thus the formula is delta heat of reaction = enthalpy of formation (product)- enthalpy of formation(reactant). But then, bond enthalpy also finds the change in heat of reaction with the formula: change in heat of reaction = bonds broken (reactant) – bonds formed (product). If it's negative, it's exothermic, and if positive, it's endothermic.

I am confused at the relationship between these 2 concepts since they are rather opposing each other.

You are confused as to why we take "reactants minus products" when calculating the enthalpy of reaction based on bond enthalpies.

Consider as reference state all your reactants and products in their atomic states, that is, with all bonds broken. Forming a bond releases energy, so the reactants and products all have a negative enthalpy $$\Delta H = -\sum\Delta H_\text{bonds}$$ with respect to this reference state. The enthalpy of reaction remains \begin{align*}\Delta H_\text{rxn}&=\Delta H_\text{prod}-\Delta H_\text{reac}\\ &= -\sum\Delta H_\text{bonds,prod}-\left(-\sum\Delta H_\text{bonds,reac}\right)\\ &= \sum\Delta H_\text{bonds,reac}-\sum\Delta H_\text{bonds,prod},\end{align*}

so the inconsistency you've pointed out is just the neglect of a minus sign.

ΔH of a reaction in terms of bond enthalpies = Σ bond enthalpies (products) - Σ bond enthalpies (reactants).

Therefore if the products are at a lower energy than the reactants, the reaction would be exothermic therefore ΔH would be negative.