Atkins’ Physical ChemistryEighth Edition

Chapter 5 – Lecture 2Simple Mixtures

Copyright © 2006 by Peter Atkins and Julio de Paula

Peter Atkins • Julio de Paula

The Chemical Potential of Liquids

• Ideal solutions

• Need to know how Gibbs energy varies with composition

• Recall that at equilibrium: μA (liq) = μA (vapor)

• Use * to designate pure substances

Fig 5.10 Eqilibrium between liquid and condensed phases

*A

oA

*A P ln RTμμ

AoAA P ln RTμμ

For pure substance A:

When B is added:

Combining :

*A

A*AA

P

P ln RTμμ

Raoult’s law:

*AAA PxP

A and Bboth

volatile

Fig 5.11 Ideal binary mixture

*AAA PxP

A*AA x ln RTμμ

Definition of idealsolution

*BBB PxP

Fig 5.12 Near-ideal mixture of benzene and toluene

Note:

and

are straight lines,

indicating a nearly

ideal solution:

P,Tmb

mb

XP

P,Tb

b

XP

A*

A X ln RTμ(liq)μA

*A

A*A P

Pln RTμ(liq)μ

A

which becomes:

Fig 5.13 Molecular basis of Raoult’s law for a volatilesolvent and volatile solute

solvent molecules

Fig 5.14 Strong deviations from Raoult’s law

Nonpolar

Polar

Notice that Raoult’s law

is obeyed increasingly

closely as the

component in excess

(solvent) approaches

purity

Henry’s Law: PB = XBKB

• In ideal solutions, both solvent and solute

obey Raoult’s law.

• In real solutions at low concentrations:

Solute = PB ∝ Solute

• Called an ideal-dilute solution

Ideal-dilute solutions

Raoult’s law: PA = XAPA*

where KB is an empirical

constant in units of P

Fig 5.14 Very dilute solution behavior

Henry’s law

BBBBB KmKxP

PA = XAPA*

PB = XBKB

Fig 5.16 Henry’s law description of solute molecules ina very dilute solution

• Solvent moleculesenvironment differs onlyslightly from that of pure solvent

• However, solutemolecules are inan entirely differentenvironment from that of the pure solute

solventsolvent

Fig 5.17 Experimental vapor pressures of a mixtureof acetone and chloroform

The Properties of Solutions

Liquid mixtures of ideal solutions

)x ln xx ln nR(xΔS BBAAmix

)x ln xx ln nRT(xΔG BBAAmix

ΔHmix = 0

The Properties of Solutions

Liquid mixtures of real solutions

Recall that ΔG = ΔH - TΔS

Therefore: ΔGmix < 0 or ΔGmix > 0

• Depends on relative magnitudes of ΔHmix and ΔSmix and T

Three types of interactions in the mixing process:

• solute-solute interaction• solvent-solvent interaction• solvent-solute interaction

Hmix = H1 + H2 + H3

ΔH1

ΔH2

ΔH3

Solutions

The enthalpy change of the overall process depends on H for each of these steps

Enthalpy changes accompanying solution processes:

Enthalpy is only part of the picture

Increasing the disorder or randomness of a system tends to lower the energy of the system

Solutions favored by increase in entropy that accompanies mixing

Solutions

Factors Affecting Gibbs Energy of Mixing

Acetone is miscible in water

H2O

C6H14Hexane is immiscible in water

can hydrogen bond with water

ΔGmix < 0

ΔGmix > 0