Why chemists usually only deal with enthalpy and not internal energy?

Question

From what I understand, enthalpy only seems like a mathematical intermediate step. Why do we have a special name for it?

Answer 1

The internal energy is a thermodynamic potential, that gives the intrinsic energy content of a system at equilibrium with a given particle number, entropy and volume: $$ U(S, V, N) $$

Enthalpy on the other hand is the thermodynamic potential, when we exchange the constant volume for a constant pressue, this is done by a Legendre transformation: As $p = -\partial_V U$ we can change variables to $p$ instead of $V$ by the following transformation: $$ H(S, p, N) = U(S, V(S, p, N), N) + p V(S, p, N) $$ Where $V(S, p, N)$ is obtained by inverting $p = -\partial_V U(S, V, N)$. (This is the same Legendre transformation that connects generalized velocities and momenta in when going from the Lagrange formalism to Hamilton formalism in mechanics.)

This quantity $H$ now describes the same equilibrium conditions, but in terms of other external preparations. We still depend on particle number(s) and entropy, but the ensemble now is one, where the pressure is fixed, instead of the volume.

The enthalpy change in a chemical reaction is exactly the heat that is generated in such a reaction. In reaction where there's a big change of volume, e.g. if a gas is released from the reaction of two liquids, then part of the inner energy change of the reaction is spent "pushing aside" the atmosphere against its pressure, and this part can't be extracted as heat. In this sense the enthalpy of reaction differs from the change of internal energy, and is the correct quantity to use when working in an atmosphere of constant pressure.

In chemistry, you usually work with formation enthalpies tabulated at standard conditions (see https://en.wikipedia.org/wiki/Standard_enthalpy_of_reaction). The entropy is hidden from view in this description, by specifying the states before and after. Before the reaction we have unmixed, separated compartments of the educts (entropy $S_1$), while afterwards we have a volume filled with products (entropy $S_2$).

Since the equilibrium properties don't depend on the path taken to reach equilibrium (technically we say $H$ is a state function), we can tabulate the reaction enthalpies for forming substances from their elementary components, and compute the enthalpies of reaction from them. (This is called Hess's law).

Answer 2

Enthalpy is not just a mathematical intermediate step everytime. A reasonable definition of internal energy could be: Energy derived from completely annihilating a system.

$ \Delta H = \Delta U + P\Delta V$

So, in a constant external pressure surrounding, enthalpy is the new internal energy.

Chemists usually deal with complicated reactions where matter changes state multiple times. For example, consider this reaction:

$A (solid) \longrightarrow B(\text{gas})$

One might search $\Delta U$ in some table, and then latent heat in another table. Chemists have enthalpy tables, and put the controllable interesting quantities in RHS:

$\Delta U + P\Delta V = Q + W_{\text{other}} $