# What assumptions underlie Hess' law and and its analogues?

Let me first briefly describe the laws as I understand them.

Hess' law states that the enthalpy of reaction can be obtained by taking the sum of the enthalpies of formation for the compounds involved in the reaction, weighted by their stoichiometric coefficient. This is often shortened to $\Delta_\mathrm{r} H = \sum \Delta_\mathrm{fm} H_\mathrm{products} - \sum \Delta_\mathrm{fm} H_\mathrm{reactants}$. A similar law exists for entropy. To get the enthalpy of a compound, one usually looks up the tabulated standard state enthalpy, and then integrates the compound's heat capacity $C_p$ to get the enthalpy at the temperature of interest. A similar procedure is used for computing the entropy. Although I have not seen it done, I guess there is nothing in the way of using such laws in a partial reaction (i.e. equilibrium): by summing the enthalpies of the various compounds at equilibrium and subtracting the enthalpies of the compounds you started with, you should get the "enthalpy of equilibrium".

What assumptions underlie these laws? For Hess' law, I would think "enthalpy of mixing is zero" is one of them, but I've yet to see it stated.

An admittedly wage bonus question: I am here talking about $H$ and $S$, but what about similar laws (if they exist) for other potentials (Gibbs energy $G$, Helmholtz energy $A$ and internal energy $U$)?