ENERGY IN GEOCHEMICAL PROCESSES - Chemical Fundamentals of Geology and Environmental Geoscience - page 6

flow of water molecules would begin from the high- G
phase to the low- G phase, allowing the total free energy
of the system to fall in keeping with the general ten-
dency of chemical systems to minimize free energy.
Any such flow, which would alter the relative propor-
tions of the two phases, is inconsistent with the steady
state observed. Clearly, at equilibrium, equivalent
amounts of the two phases must have identical free
energies:

Vapour

G = G (1.6)

vapour liquid

This statement is in fact the thermodynamic definition
of 'equilibrium' in such a system.
But here we seem to have stumbled upon a paradox.
Common sense tells us that to turn liquid water into
vapour we have to supply energy, in the form of heat.
The amount required is called the latent heat of evap-
oration (more correctly, the enthalpy of evaporation).
This indicates that the vapour has a greater enthalpy
( H vapour ) than an equivalent amount of the liquid
( H liquid ):

Water

Figure 1.1 A simple model of chemical equilibrium
between two coexisting phases, water and its vapour.
The equilibrium can be symbolized by a simple equation.

HO HO
2



2

liquid vapour

At equilibrium, the migration of water molecules from the
liquid to the vapour (evaporation, upward arrow) is
balanced exactly by the condensation of molecules from
vapour to liquid (downward arrow).

(1.7)

HH
vapour

>

liquid

The difference reflects the fact that water molecules in
the vapour state have (a) greater potential energy, hav-
ing escaped from the intermolecular forces that hold
liquid water together, and (b) greater kinetic energy
(owing to the much greater mobility of molecules in
the gaseous state).
How can we reconcile Equations 1.6 and 1.7? Is it not
common sense to expect the liquid state, in which the
water molecules have much lower energies, to be
intrinsically more stable than the vapour? What is it
that sustains the vapour, in spite of its higher enthalpy,
as a stable phase in equilibrium with the liquid?
The answer lies in the highly disordered state char-
acteristic of the vapour. Molecules in the gas phase fly
around in random directions, occasionally colliding
but, unlike molecules in a liquid, free to disperse
throughout the available volume. The vapour is said to
possess a high entropy ( S ). Entropy is a parameter that
quantifies the degree of internal disorder of a substance
(Box 1.3). Entropy has immense significance in thermo-
dynamics, owing to Nature's adherence to the Second
Law of Thermodynamics. This states that all spontaneous
processes result in an increase of entropy . The everyday
consequences of the Second Law - so familiar that we

electrical energy obtained from a battery, the light and
heat emitted by burning wood, and so on.
What form does free energy take? How can it be cal-
culated and used? These questions are best tackled
through a simple example. Imagine a sealed container
partly filled with water (Figure 1.1). The space not
filled by the liquid takes up water vapour (a gas) until
a certain pressure of vapour is achieved, called the
equilibrium vapour pressure of water, which is depend-
ent only upon the temperature (assumed to be con-
stant). H 2 O is now present in two stable forms, each
one having physical properties and structure distinct
from the other: these two states of matter are called
phases . From this moment on, unless circumstances
change, the system will maintain a constant state,
called equilibrium , in which the rate of evaporation
from the liquid phase is matched exactly by the rate of
condensation from the vapour phase: the relative
volumes of the two phases will therefore remain
constant.
In this state of equilibrium, the free energies associ-
ated with a given amount of water in each of these two
phases must be equal. If that were not the case, a net