The Richard Stockton College of New Jersey
Chemistry Program, School of Natural Sciences and Mathematics
PO Box 195, Pomoma, NJ
CHEM 3410: Physical Chemistry I — Fall 2008
October 17, 2008
Lecture 20: Phase equilibrium
References
1. Levine, Physical Chemistry, Sections 7.1–7.3
Key Concepts
•At equilibrium, the free energy is minimized. Therefore, the phase with the lowest chemical potential
will be stable.
•For a single component system, µ=G
n=G.
•The key question is how µdepends on Tand P. We can find this dependence by writing dµ (dG for a
single component system) out in two different ways:
dG =dµ =−SdT +V dP
dµ =∂µ
∂T P
dT +∂µ
∂P T
dP
which gives us:
∂µ
∂T P
=−Sand ∂µ
∂P T
=V
•We can now see how µvaries with Tand Pby comparing the molar entropy and volume of different
phases.
•The molar entropy of a gas phase is much greater than the molar entropy of a solid or liquid phase.
This is due to the large number of different ways to arrange molecules in the gas phase (i.e. the vast
number of configurations leads to high entropy. Using a similar argument, the molar entropy of the
solid phase will be the smallest since there are a much more limited number of possible configurations,
leading to a low entropy phase.
•So, in a plot of µversus T, a curve for the gas phase will have the steepest negative slope, while a solid
phase will have a much shallower negative slope.
•If we polt µversus Tat a fixed pressure, the most stable phase at a particular temperature is the
phase with the lowest µ. If the chemical potential of two phases is equal, the two phase coexist at that
temperature and pressure, i.e. they are in equilibrium.
•To determine the effect of pressure on the stability of phases, we need to examine the differences the
molar volume (V) of each phase. Gases typically have the largest molar volumes, so changing the
pressure would have a large impact on the chemical potential of a gas phase, while it is a much smaller
impact when dealing with a condensed phase, such as a liquid or solid.
•If we want to capture both the temperature and pressure dependence of the stability of phases we can
plot Pversus Tand generate a phase diagram for the single component system. The phase diagram
is a map that indicates which phase(s) is(are) most stable under particular Tand Pconditions.
•When we construct these single-component or unary phase diagrams, we will see regions when single
phases are stable, lines where two phases are in equilibrium, and one single point (the triple point)
where all three phases are in equilibrium.