Chemistry Reference
In-Depth Information
The occurrence of two phases presents an experimentally more easily accessible
range of behaviour. Here the phase rule specifies a variance of one for a single
substance. A quantity exhibiting liquid and vapour in contact that can be kept at a
fixed temperature in a closed container fitted with a piston has a pressure deter-
mined by the temperature (considered the independent variable). Thus, any attempt
at increasing the pressure (by plunging the piston) at a fixed temperature is
countered by material moving from the gas to the liquid phase. Similarly,
attempting to decrease the pressure by raising the piston is countered by material
moving from the liquid into the gas. Eventually, proceeding far enough in one
direction or the other will lead to all the gas being converted to liquid or conversely,
resulting in a single-phase system. Then the variance is two and temperature and
pressure can vary independently (over a given range). But the volume is determined
by these two variables (as in the ideal gas law), and cannot vary independently.
This general behaviour is characteristic of a quantity of matter comprising a single
substance, and the specific details of the functional dependencies of the pressure as
a function of the temperature for the two-phase system is characteristic of the
particular substance. In particular, the temperature at which the liquid changes
into gas at a given pressure (the boiling point), like the vapour pressure at room
temperature, are such details.
Identification of a new, hitherto unknown, substance by means of the phase
rule doesn
t necessarily require its isolation as a single substance. This is nicely
illustrated by the way the demonstration of the phase rule soon led to the discovery
of new, and previously unexpected, compounds. During the decade following the
publication of Gibbs (
1876
-8), Roozeboom, aided by van der Waals
'
deductions,
recognised that part of the phase diagram that he mapped out for the hydrogen
bromide-water system was not the continuation of the vapour pressure curve of the
then known hydrate HBr
'
2H
2
O. It had a shape like that exhibited elsewhere in
the phase diagram characteristic of a certain number of constituent substances but
different specific features (values of the variables). It therefore corresponded to the
presence of a new substance—a previously unknown monohydrate of hydrogen
bromide (Wisniak
2003
, pp. 425-6 relates the essential details). Previously
established grounds for determining sameness and distinctness of substance had
to accommodate the new contributions of thermodynamics.
The number of substances figuring in Gibbs
phase rule is notoriously the
number of
independent
substances and not simply the number of substances.
This arises because the derivation of the rule appeals to a number of general
thermodynamic conditions connecting the intensive variables governing the ther-
modynamic state of the system, namely pressure, temperature and the chemical
potential of each substance in each phase.
3
But the conditions obtaining in a
'
3
In general, there is a connection between the chemical potentials of all the substances in a given
phase given by the Gibbs-Duhem equation (
f
connections for
f
phases) and there are
c
(
f
-1)
interphase conditions given by the equality of the chemical potentials of each substance between
any two phases. Thus, the variance
¼ c
-
f
+ 2, the “2” deriving from the
two intensive variables pressure and temperature (each having the same values for each phase).
¼
2+
cf
-(
f
+
c
(
f
- 1))
