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 P_{i} are the stoichiometric coefficients for the
products being summed and R_{i} are the coefficients of the
reactants.

Recalling again the reaction

CH_{4} + 2O_{2} -> CO_{2} +
2H_{2}O

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