constant, is 8.314' 10 #^3 kJ K#^1 mol#^1 and at 298 K,RT¼2.478 kJ mol#^1 and
(3/2)RTis 3.717 kJ mol#^1. Thus the internal energy of the proton at 298 K, with
no electronic, vibrational or rotational energy, is (3/2)RT[ 131 ]. BothEtotaland
ZPE are often readily calculated quantum mechanically. Differences inUat 0 K
(where there is no translational term) take into account the electronic energy and
the ZPE and are the simplest realistic measure of molecular energy differences
like reaction energies and activation energies, although differences of justEtotal
(no ZPE) provide aroughmeasure of these quantities (Section 2.5).
4.Enthalpyis the “heat content” of a system. This term is not very accurate, for as
Atkins points out [ 128 ] heat is not a thing, but rather a process, the transfer of
energy because of a difference of temperature (or accompanied by a difference
of temperature in the case of phase transition enthalpies). Nevertheless “amount
of heat” is a useful shorthand for amount of energy transferred because of a
temperature difference. The enthalpy change is the amount of heat released or
absorbed when a reaction occurs at constant pressure. The standard conditions
are 298 K and 101.3 kPa (1 atmosphere). The enthalpy of formation, or heat of
formation, of a substance is a useful quantity (Section 5.5.2.2c). Like Gibbs free
energies of formation, these have been widely tabulated. These enable the heat
evolved or absorbed in reactions (reaction enthalpies) to be calculated by simply
taking the enthalpy difference of the products and reactants. These energy
quantities refer, strictly, to changes at constant volume, although the difference
compared to constant volume is usually less than 1% [ 128 ]. Reaction enthalpies
can also be calculated from the change in bond energies in a reaction, but this is
quite approximate since bond energies are not fully transferable, but vary some-
what from molecule to molecule and can even differ from one, say C–H, bond to
another in the same molecule. Enthalpies of formation can be accurately calcu-
lated with the aid of quantum mechanical methods if the molecule is not too big
(Section 5.5.2.2c). The enthalpy change of a reaction is often taken as measure of
its thermodynamic feasibility, and often, tacitly, as an indication of its kinetic
ease, but the rigorous criteria for these are really the Gibbs free energies (below)
of reaction and activation.
Symbol: enthalpy is denoted byH: the word comes (H. Kammerlingh-Onnes
1909) from the Greekthalpos, heat, orenthalpos, internal heat. Denoting it byH
was suggested by H. W. Porter in 1922, because the symbol H is a letter in the
Roman alphabet and also the capital Greek initial lettereta(H orZ) ofenthalpos
(nyalpoz)[ 132 ].Equation: the “energy” (internal energy) of an atom or mole-
cule at a temperatureTcan be converted to its enthalpy by addingRT, sinceH¼
UþPVandPV¼RT, on a molar basis, assuming ideal gas behavior. Thus
H¼internal energyþRT $ð 5 : 172 Þ¼internal energyþ2.478 kJ mol#^1 at 298 K. The enthalpy of the proton at
298 K (cf. its internal energy, above) is (3/2)RTþRT¼(5/2)RT¼6.195 kJ
mol#^1 [ 131 ].
5.Gibbs free energyis the work obtainable from a system at a constant tempera-
ture and pressure. Unlike specified otherwise, in chemistry we may take “free
294 5 Ab initio Calculations