1. Peter Atkins • Julio de Paula Atkins’ Physical Chemistry
Eighth Edition
Chapter 5 – Lecture 1
Simple Mixtures
Copyright © 2006 by Peter Atkins and Julio de Paula

2. Homework Set #5 Atkins & de Paula, 8e Chap 5
Exercises: all part (b) unless noted:
1, 5, 7, 8, 10, 11, 13, 14

3. Objectives:
Introduce partial molar quantities
Use chemical potential (μ) to describe physical
properties of a mixture (Gm = μ)
Raoult’s and Henry’s Laws: Thermo properties μ(Xi)
Effect of a solute on a solution: Colligative properties

4. Restrictions at this point:
Binary mixture
Unreactive species
Nonelectrolytes
e.g., Dalton’s law: P = PA + Pb + ...
and: XA + XB +... = 1
Now apply partial molar concept to other extensive state functions

5. Partial molar volume
Observe:
Vtotal = V + 18 cm3
So:
VH2O = 18 cm3/mol
18 cm3 H2O
H2O
V>> 18 cm3

6. Partial molar volume (continued)
Observe:
Vtotal = V + 14 cm3
So:
18 cm3 H2O
EtOH
VH2O (in EtOH) = 14 cm3/mol
Conclusion: VJ varies with
composition
V>> 18 cm3

7. Fig 5.1 Partial molar volumes of water and ethanol
Result when dnA moles of A and dnB
moles of B are added to the mixture:

8. Fig 5.2 Partial molar volume of a substance
Total volume decreases
as A is added
Total volume increases
as A is added

9. For a binary mixture of A and B:
dV = VA dnA + VB dnB
Once VA and VB are known:
V = nA VA + nB VB
Molar volumes always > 0, but not necessarily
partial molar volumes: VMgSO4 = −1.4 cm3/mol

10. Fig 5.4 Chemical potential as function of amount
Partial molar Gibbs energies
For a binary mixture
of A and B at some specific
composition:
G = nAμA + nBμB

11. dG = VdP - SdT + μAdnA + μBdnB + ...
Recall that G = G(T,P,n). When all may change:
dG = VdP - SdT + μAdnA + μBdnB + ...
The fundamental equation of chemical thermodynamics
At constant temperature and pressure:
dG = μAdnA + μBdnB + ...
Since dG = dwadd,max,
dwadd,max = μAdnA + μBdnB + ...
Gives the maximum amount of additional (non-PV) work
that can be obtained by changing system composition.

12. Because G = G(n,μ), for infinitesimal changes:
dG = μAdnA + μBdnB + nAdμA + nBdμB
Recall that at constant temperature and pressure
the change in Gibbs energy:
dG = μAdnA + μBdnB
nAdμA + nBdμB = 0
Therefore:
Special form of the Gibbs-Duhem equation:
Significance: The chemical potential of one component
cannot change independently of the other components

13. Fig 5.1 Partial molar volumes of water and ethanol
nAdμA + nBdμB = 0
nAdμA = - nBdμB
As partial molar
volume of H2O
decreases, that of
ethanol increases:

14. The thermodynamics of mixing
For a binary mixture
of A and B at some specific
composition:
Fig. 3.18
G = nAμA + nBμB
Also, systems at constant P and T
tend towards lower Gibbs energy:

15. Fig 5.6 Arrangement for calculating the thermodynamic
functions for the mixing of two perfect gases
From:
G = nAμA + nBμB

16. Fig 5.6 Arrangement for calculating the thermodynamic
functions for the mixing of two perfect gases
From:

17. Fig 5. 9 Entropy of mixing of two perfect gases
Since ΔG = ΔH – TΔS
it follows that:
ΔHmix = 0