Geology Reference
In-Depth Information
container,
n
is the total number of moles of gas present
in the container,
R
is the
gas constant
, and
T
is the tem-
perature in
kelvins
. Both the volume (at constant pres-
sure) and the pressure (at constant volume) of a gas are
proportional to the
number of moles
present
n
, regard-
less of their mass (which is why mass units are not
used for reporting gas composition). For an ideal gas
mixture at atmospheric pressure (≈10
5
Pa), the follow-
ing
numerical
relationships hold:
The relative proportions of A, B, C and D present in
solution when this steady state has been achieved are
summarized by the
equilibrium constant
K
:
aa
aa
K
=
CD
AB
(4.9)
The value of
K
is a constant characteristic of a particular
equilibrium at a specified temperature. It indicates at
which point on the path from '100% reactants' (A + B) to
'100% products' (C + D) the reaction settles into equilib-
rium. The system, if disturbed, will always readjust to
the same position of equilibrium as defined by Equation
4.9. For example, if more A is added to the equili-
brated solution represented by Equation 4.8 (i.e. if
a
A
is
increased), A and B will react together to a greater
extent, thereby reducing
a
B
(and the new
a
A
) and increas-
ing
a
C
and
a
D
. These individual activity adjustments
occur in such a way that the ratio
a
C
a
D
/
a
A
a
B
resumes the
original value,
K
, the value it had before the disturbance
occurred. Altering the temperature, however, will gen-
erally cause the value of
K
to change (Box 4.2).
The algebraic form of the equilibrium constant in
equations like 4.9 reflects the nature of the reaction
equation. If we were to look at a more complicated
equilibrium, for example one in which
b
molecules of
species B react with
c
molecules of species C like this:
volume percentof
i
Mole fraction of component
i
=
100
re of
in Pa
partialpressu
i
=
10
5
Pa
Equilibrium constant
In this chapter we are concerned with many reactions
in solution that can proceed in either direction, depend-
ing on the circumstances. Consider a reaction:
AB CD
+→+
reactants
(4.4)
products
By analogy with Equation 3.5, we would expect the
rate of this reaction in solution to be represented by:
bc de
BC DEF
+
+ +
f
(4.10)
Rate
=
kaa
(4.5)
AB AB
the equilibrium constant would normally have the
form:
where
a
A
and
a
B
are the activities of reactants A and B
in the solution (Equation 4.2), and
k
AB
is the rate con-
stant for the A + B reaction. The presence in solution
of C and D, produced by this 'forward' reaction, is
likely to initiate a
reverse reaction
that regenerates A
and B:
d
e
f
K
aaa
aa
⋅
⋅
=
DE
F
(4.11)
b
c
⋅
BC
Solubility and the solubility product
AB CD
+←+
(4.6)
To see how an equilibrium constant works, consider
the solubility of various substances in water. The
salt
calcium fluoride, CaF
2
(which, in crystalline form, is
the familiar vein mineral
fluorite
), is only very slightly
soluble in cold water: only 0.017 g of CaF
2
will dissolve
in 1 kg of water at 25 °C, corresponding to a molality of
0.00022 mol kg
−1
. (The relative molecular mass of CaF
2
is 40.08 + (2 × 19.00) = 78.08.) This quantity is the
solubil-
ity
of CaF
2
at this temperature. Adding further solid
CaF
2
to the system will cause no increase in the concen-
tration in solution, no matter how long we wait. Such a
solution, which has reached equilibrium with solid
Rate of reversereaction
=
kaa
CD CD
(4.7)
This tells us that as the products of the forward reac-
tion (C and D) build up in the solution, the reverse
reaction will speed up, and eventually a
steady state
will be reached in which the rate of the forward reac-
tion is matched by that of the reverse reaction, and
hereafter no
net
change in activities takes place. This
state of
equilibrium
is written:
AB D
C
+
+
(4.8)
Search WWH ::
Custom Search