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

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

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

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

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

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

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:

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

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

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

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.

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

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:

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:

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

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

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