Enthalpy: H = U + PV

Most real chemical reactions are not carried out in a sealed, constant-volume container — they take place in open flasks, beakers, and reaction vessels exposed to the essentially constant pressure of the atmosphere, where the system is free to expand or contract as the reaction proceeds. Under these everyday constant-pressure conditions, some of the heat exchanged is inevitably "used up" doing pressure-volume work against the atmosphere as the system's volume changes, so the heat exchanged at constant pressure, $q_p$, is not simply equal to $\Delta U$.

To handle this cleanly, chemists define a new state function, enthalpy, $H$:

Since $U$, $P$ and $V$ are all state functions, $H$ is guaranteed to be a state function too, meaning $\Delta H$ depends only on the initial and final states of a process, exactly like $\Delta U$.

For a process carried out at constant pressure, the change in enthalpy works out to be

and it can be shown (from the First Law, with work restricted to $PV$-work) that this quantity is exactly equal to the heat exchanged at constant pressure: $\Delta H = q_p$. This is the single most useful practical fact about enthalpy: for the enormous majority of chemical reactions, run in open vessels at roughly constant atmospheric pressure, the heat absorbed or released — the quantity actually measured in a calorimeter or felt as a reaction flask warming or cooling — is directly the enthalpy change of the reaction, $\Delta H$, not $\Delta U$.

For reactions involving gases, it is often more convenient to relate $\Delta H$ to $\Delta U$ through the change in the number of moles of gas, $\Delta n_g$ (moles of gaseous products minus moles of gaseous reactants), using the ideal gas law $PV = nRT$ at constant temperature:

$\Delta H = \Delta U + \Delta n_g RT$ …