Q.A swimmer coming out from a pool is covered with a film of water weighing about 18 g. How much heat must be supplied to evaporate this water at 298 K? Calculate the internal energy of vaporisation at 298 K. $\Delta_{vap}H^\ominus$ for water at 298 K = 44.01 kJ mol$^{-1}$.

Enthalpy, $H$, is a state function defined as $H = U + PV$, introduced because the overwhelming majority of real chemical reactions take place in open vessels at essentially constant atmospheric pressure, rather than at constant volume. At constant pressure, the change in enthalpy equals the heat exchanged with the surroundings, $\Delta H = q_p$ — precisely the quantity a calorimeter measures for a reaction carried out in an open flask, container, or solution. Enthalpy and internal energy are related, for gas-phase reactions at constant temperature, through $\Delta H = \Delta U + \Delta n_g RT$, where $\Delta n_g$ is the change in moles of gas across the reaction.

Chemists have defined a family of precisely standardized enthalpy changes, each describing one specific, carefully defined process, denoted by the standard-state superscript $^\circ$ (usually $298\ \text{K}$, $1\ \text{bar}$):

• Standard enthalpy of formation ($\Delta_fH^\circ$) — one mole of a compound formed from its elements in their standard states; by convention, an element in its standard state has $\Delta_fH^\circ = 0$.
• Standard enthalpy of combustion ($\Delta_cH^\circ$) — one mole of a substance completely burnt in excess oxygen; always exothermic (negative), and readily measured by bomb calorimetry.
• Standard enthalpy of atomization ($\Delta_aH^\circ$) — one mole of a substance completely converted into gaseous atoms; always endothermic (positive).
• Bond dissociation enthalpy — the energy to break one mole of a specific covalent bond in a gaseous molecule; dividing an atomization enthalpy by the number of equivalent bonds gives an average bond enthalpy.
• Enthalpy of ionization (first, second, …) — the energy to remove one mole of electrons from one mole of gaseous atoms (first) or from the resulting gaseous cations (second, always larger than the first, since removing an electron from an already-positive species is harder).
• Enthalpy of solution ($\Delta_{sol}H^\circ$) — one mole of solute dissolved in a very large excess of solvent; for an ionic solid, it equals the sum of the (endothermic) lattice enthalpy and the (exothermic) enthalpy of hydration of its ions.
• Enthalpy of sublimation ($\Delta_{sub}H^\circ$) — one mole of a solid converted directly to gas; by Hess's law, it equals the sum of the enthalpy of fusion and the enthalpy of vaporization, even though the direct sublimation process never visibly passes through a liquid phase.

Because each of these named enthalpies is itself a well-defined $\Delta H$ between two specific states, all of them are legitimate state functions — the property that makes it possible to combine them algebraically via Hess's law, and, in the specialized case of the Born-Haber cycle, to determine an otherwise unmeasurable quantity such as lattice enthalpy.