Peter Atkins • Julio de Paula
Atkins’ Physical Chemistry
Eighth Edition
Chapter 4 – Lecture 1
Physical Transformations
of Pure Substances
Copyright © 2006 by Peter Atkins and Julio de Paula
Homework Set #4
Atkins & de Paula, 8e
Chap 4
Discussion questions: 3, 4
Exercises: all part (b) unless noted: 1,5,6,7,8
Numerical Problems: 2, 8 (plot this), 16
Objectives
• Applications of thermo to phase transitions
of a single, pure substance
• Phase diagrams (P vs T)
• Phase boundaries
• Melting point as function of pressure
• Vapor pressure as function of T
Fig 4.1 A typical phase diagram: P vs T
Fig 4.2 Vapor pressure of a liquid or a solid
≡ the pressure of a
vapor measured
when a dynamic
equilibrium exists
between evaporation
and condensation
Fig 4.3 Heating of a liquid in a sealed container
For H2O,
Tc = 374 °C
Pc = 218 atm
Fig 4.4 Phase diagram for carbon dioxide
For CO2,
Tc = 304.2 °C
Pc = 72.9 atm
Supercritical CO2
The low critical
temperature and critical
pressure for CO2 make
supercritical CO2 a
good solvent for
extracting nonpolar
substances (like
caffeine)
Diagram of a supercritical fluid extraction process
Fig 4.5 Phase diagram for water
Tf ∝ 1/Papplied
Unique for water!
Fig 4.6 Fragment of structure of ice (ice-I)
Fig 4.7 Phase diagram for Helium-4
Phase Stability and Phase Transitions
• Apply thermodynamics to account for features
in phase diagrams
• All considerations based on molar Gibbs energy, Gm
• For a one-component system,
chemical potential (μ): μ ≡ Gm
Fig 4.8 Two or more phases of a pure substance in
equilibrium
+μ2dn
μ2
According to 2nd law:
At equilibrium, the chemical
dn
potential of a substance is the
same throughout the sample.
μ1
For any system in equilibrium: dG = 0
Net: dG = (μ2 - μ2)dn = 0 means μ1 = μ2
-μ1dn
Fig 4.9
Schematic of the
temperature dependence
of the chemical potential
 G m 
 μ 

 
   Sm
 T  P  T  P
dμ   SmdT
Fig 4.10 (a)
Pressure dependence
of the chemical potential
 Gm 
  

 
  Vm
 P  T   P  T
d  VmdP
Substances for which
Vm(s) < Vm(l)
Fig 4.10 (b)
Pressure dependence
of the chemical potential
Substances for which
Vm(s) > Vm(l)
e.g., water,
which expands upon freezing