ENERGY IN GEOCHEMICAL PROCESSES - Chemical Fundamentals of Geology and Environmental Geoscience - page 7

often take them for granted - are discussed further in
Box 1.3. In the present context, Nature's preference for
disordered, high-entropy states of matter is what
makes it possible for vapour to coexist with liquid. In a
sense, the higher entropy of the vapour 'stabilizes' it in
relation to the liquid state, compensating for the higher
enthalpy required to sustain it.
Clearly, any analysis in energy terms, even of this
simple example, will succeed only if the entropy differ-
ence (Δ S ) between liquid and vapour is taken into
account. This is why the definition of the free energy
(alternatively called the 'Gibbs energy') of each phase
therefore incorporates an entropy term:

Equations 1.8 and 1.9 express the fundamental contr-
ibution that disorder makes to the energetics of chem-
ical and geological reactions, a question we shall take
up again in the following sections.

Units

Enthalpy, entropy and free energy, like mass and vol-
ume, are classified as extensive properties. This means
that their values depend on the amount of material
present. On the other hand, temperature, density, vis-
cosity, pressure and similar properties are said to be
intensive properties, because their values are unrel-
ated to the size of the system being considered.
In published tables of enthalpy and entropy
(Chapter 2), the values given are those for one mole -
abbreviated in the SI system to 'mol' - of the substance
concerned (18 g in the case of water). One therefore
speaks of molar enthalpy and entropy, and of molar
free energy and molar volume as well. The units of
molar enthalpy and molar free energy are joules per
mole (J mol − 1 ); those of molar entropy are joules per
kelvin per mole (J K − 1 mol − 1 ). The most convenient
units for expressing molar volume are 10 − 6 m 3 mol − 1
(which are the same as cm 3 mol − 1 , the units used in
older literature).
In thermodynamic equations like 1.8, temperature
is always expressed in kelvins (K). One kelvin is equal
in magnitude to one °C but the scale begins at the
absolute zero of temperature (−273.15 °C), not at the
freezing point of water (0 °C). Therefore:

GHTS
liquid

= − . (1.8)

liquid liquid

G HTS
vapour

= − . (1.9)

vapour vapour

H liquid and H vapour are the enthalpies of the liquid and
vapour respectively. S liquid and S vapour are the corres-
ponding entropies. (Take care not to confuse the
similar-sounding terms 'enthalpy' and 'entropy'.) The
absolute temperature T (measured in kelvins) is
assumed to be uniform in a system in equilibrium
(Chapter 2), and therefore requires no subscript.
The important feature of these equations is the nega-
tive sign. It means that the vapour can have higher
enthalpy ( H ) and higher entropy ( S ) than the liquid,
and yet have the same free energy value ( G ), which
must be true if the two phases are to be in equilibrium.
Perhaps a more fundamental understanding of the
minus sign can be gained by rearranging Equations
1.8 and 1.9 into this form:

T l nK = T l nC ° + 273 15 . (1.11)

HGTS =+. (1.10)

The SI units for pressure are pascals (Pa; see
Appendix A).

The enthalpy of a phase can thus be seen as consisting
of two contributions:

Free-energy changes

G The part that potentially can be released by the
operation of a chemical reaction, which is logic-
ally called 'free' energy. This therefore provides
a measure of the instability of a system (just as
the potential energy of the water in a reservoir
reflects its gravitational instability).
T.S The part that is irretrievably bound up in the
internal disorder of a phase at temperature T ,
and that is therefore not recoverable through
chemical reactions.

For the reasons discussed above in relation to potential
energy, the numerical values of G liquid and G vapour have
no absolute significance. In considering whether water
will evaporate or vapour will condense in specific cir-
cumstances, what concerns us is the change in free
energy Δ G arising from the liquid-to-vapour 'reaction'.
The first step in calculating free-energy changes is to
write down the process concerned in the form of a