Atkins’ Physical ChemistryEighth Edition

Chapter 4 – Lecture 1Physical Transformations

of Pure Substances

Copyright © 2006 by Peter Atkins and Julio de Paula

Peter Atkins • Julio de Paula

Homework Set #4Homework Set #4

Atkins & de Paula, 8eAtkins & de Paula, 8e

Chap 4 Chap 4

DiscussionDiscussion questionsquestions: 3, 4: 3, 4

ExercisesExercises: all part (b) unless noted: : all part (b) unless noted: 1,5,6,7,81,5,6,7,8

NumericalNumerical ProblemsProblems: 2, 8 (plot this), 16: 2, 8 (plot this), 16

Objectives

• Applications of thermo to phase transitionsof 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 COSupercritical CO22

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/P∝ applied

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 TransitionsPhase 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

According to 2nd law:

At equilibrium, the chemical

potential of a substance is the

same throughout the sample. μ1

μ2

dn

-μ1dn

+μ2dn

For any system in equilibrium: dG = 0

Net: dG = (μ2 - μ2)dn = 0 means μ1 = μ2

Fig 4.9

Schematic of the

temperature dependence

of the chemical potential

mPP

m STT

G

μ

dTSd mμ

Fig 4.10 (a)

Pressure dependence

of the chemical potential

mTT

m VPP

G

dPVd m

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