Geology Reference
In-Depth Information
chemical reaction, as in Equation 1.1. For the water/
vapour equilibrium:
which direction the reaction will proceed under the
conditions being considered. A negative value of Δ
G
indicates that the products are more stable - have a
lower free energy - than the reactants, so that the
reaction can be expected to proceed in the forward
direction. If Δ
G
is positive, on the other hand, the
'reactants' will be more stable than the 'products',
and the reverse reaction will predominate. In either
case, reaction will lead eventually to a condition
where Δ
G
= 0, signifying that equilibrium has been
reached.
Now let us see how these principles apply to miner-
als and rocks.
HO HO
2
(1.12)
2
liquid
vapour
The equilibrium symbol (⇋) represents a balance
between two competing opposed 'reactions' taking
place at the same time:
'Forward' reaction:
(evaporation)
liquid → vapour
reactant product
'Reverse' reaction:
liquid ← vapour
product reactant
(condensation)
By convention, the free-energy
change
for the forward
reaction (Δ
G
) is written:
Stable, unstable and metastable minerals
∆
GG G
GG
=
−
products
reactants
The terms 'stable' and 'unstable' have a more precise
connotation in thermodynamics than in everyday
usage. In order to grasp their meaning in the context of
minerals and rocks, it will be helpful to begin by con-
sidering a simple physical analogue. Figure 1.2a shows
a rectangular block of wood in a series of different
positions relative to some reference surface, such as a
table top upon which the block stands. These config-
urations differ in their potential energy, represented by
the vertical height of the
centre of gravity
of the block -
shown as a dot - above the table top. Several general
principles can be drawn from this physical system
which will later help to illuminate some essentials of
mineral equilibrium:
=
−
(1.13)
vapour
liquid
Each
G
can be expressed in terms of molar enthalpy
and entropy values obtained from published tables
(Equations 1.8 and 1.9). Thus
(
)
−
(
)
∆
GH TS HT S
=
−
.
−
.
vapour
vapour
liquid
liquid
(
)
−
(
)
=
HH
−
TS
−
S
vapour
liquid
vapour
liquid
(1.14)
=−
∆
HTS
.
In this equation Δ
H
is the heat input per mole required
to generate vapour from liquid (the latent heat of
evaporation). In the context of a true chemical reac-
tion, it would represent the
heat of reaction
(strictly the
enthalpy
of reaction). If Δ
H
for the forward reactions
is negative, heat must be given out by the reaction,
which is then said to be
exothermic
('giving out
heat'). A positive value implies that the reaction will
proceed only if heat is drawn in from the surround-
ings. Reactions that absorb heat in this way are said
to be
endothermic
('taking in heat'). Δ
S
represents
the corresponding entropy change between liquid
and vapour states.
The values of
H
vapour
,
H
liquid
,
S
vapour
and
S
liquid
can be
looked up as molar quantities for the temperature of
interest (e.g. room temperature ≃ 298 K) in published
tables. In this case, Δ
H
and Δ
S
can be calculated by
simple difference, leading to a value for Δ
G
(taking
care to enter the value of
T
in kelvins, not °C). From
the sign obtained for Δ
G
, it is possible to predict in
(a) Within this frame of reference, configuration D has
the lowest potential energy possible, and one calls
this the
stable
position. At the other extreme, con-
figurations A and C are evidently
unstable
, because
in these positions the block will immediately fall
over, ending up in a position like D. Both clearly
have higher potential energy than D.
(b) In discussing stable and unstable configurations,
one need not consider all forms of energy pos-
sessed by the wooden block, some of which
(for example, the total electronic energy) would
be difficult to quantify. Mechanical stability
depends solely upon the relative potential energies
of - or energy differences between - the several
configurations, and not on their absolute energy
values.
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