Chapter 6 : Slide 1

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Chapter 6 Changes of State - Pure Substances
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OUTLINE Chemical Potential Thermodynamic
criterion for equilibrium Phase boundaries Three
typical phase diagrams Dependence of stability on
conditions The location of phase boundaries
HOMEWORK EXERCISES 4, 6, 7, 9-11, 13 parts
(a) only PROBLEMS 3, 8
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Chemical Potential
So far we have only considered G f ( p, T
). To be completely general we should consider G
as a function of p, T and the amount of each
component, ni. G f ( p,T, ni ) Then
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Chemical Potential
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Chemical Potential
Recall that the change in Gibbs energy
accompanying a process gives us a signpost
showing in which direction a spontaneous process
wants to occur. The chemical potential is an
instructive synonym for the molar Gibbs energy.
It represents the potential a substance has for
bringing about a change in a system.
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The Thermodynamic Criterion of Equilibrium
At equilibrium, the chemical potential of a
substance is the same throughout a sample,
regardless of how many phases are present.
Consider this single substance system
m1
m2
dG -m1 dn
dG m2 dn
Total dG 0 only if m1 m2
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Phase Boundaries
Imagine that two phases a and b of a pure
substance are in equilibrium. Their chemical
potentials must be equal µa(p,T) µb(p,T)
At any given temperature and pressure, a specific
phase (a or b) is stable. This is the phase with
lowest m at that temperature and pressure. For
any given pressure there are also specific
temperatures at which two phases are stable and
in equilibrium. These temperatures are called
transition temperatures, Ttrs (e.g., b.p., m.p.,
other phase transitions). Example For H2O, at
0oC, 1 atm m (solid) m (liquid)
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Phase diagram for water.
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Phase diagram for carbon dioxide.
1 atm
194.7 K
304.2 K
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Phase diagram for helium.
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The dependence of stability on the conditions
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The location of phase boundaries.
Two phases at equilibrium µa(p,T) µb(p,T)
Liquid
b
dp
Presure, p
Vapor
a
dT
Temperature, T
There is a relationship between dp and dT that
ensures that the system remains at equilibrium as
either variable is changed. At the transition
temperature any change that occurs is reversible.
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The location of phase boundaries.
Recall that m Gm therefore dm -SmdTVmdp
At the phase boundary µa(p,T) µb(p,T) and
therefore dµa dµb
So -Sa,mdTVa,mdp -Sb,mdTVb,mdp (Vb,m -
Va,m) dp (Sb,m - Sa,m) dT
The Clapeyron Equation (exact and general).
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The location of phase boundaries.
The Solid-Liquid Boundary
The Liquid-Vapor and Solid-Vapor Boundary
Clausius-Clapeyron Equation