# Hess's Law

It should come as no surprise that you will obtain the same answer to a reactive energy balance problem regardless of whether you chose to do a heat of formation or a heat of reaction balance.

Therefore, your choice of method will often be dictated by convenience, much like your choice of atomic versus extent methods for reactive mass balances. In fact, some of the same reasoning goes into both decisions (an extent of reaction energy balance is usually only performed when you have done an extent of reaction mass balance, for example, since you already know the extent values).

Setting these two energy balance methods equal to each other yields...

DEFINITION

Hess's Law directly relates the heat of reaction to the heats of formation of the reactants and products.

A mathematical expression for Hess's Law is

$\Delta \hat H_{rxn}^o = \Sigma P_i \Delta \hat H_f^o - \Sigma R_i \Delta \hat H_f^o$

where Pi are the stoichiometric coefficients for the products being summed and Ri are the coefficients of the reactants.

Recalling again the reaction

CH4 + 2O2 -> CO2 + 2H2O

Here, the heat of reaction may be calculated as:

$\Delta \hat H_{rxn}^o = (2 \Delta \hat H_{f_{H_2O}}^o + \Delta \hat H_{f_{CO_2}}^o) - (\Delta \hat H_{f_{CH_4}}^o + 2\Delta \hat H_{f_{O_2}}^o)$

NOTE

This method is particularly useful when we have novel reactions occurring whereby heats of reaction may be difficult or impossible to find in tables. Also, recall that $\Delta \hat H_{f_{O_2}}^o=0$.

OUTCOME:

Use Hess's Law to determine the heat of reaction of given reactions