1. Chemical Equilibrium By Doba Jackson, Ph.D.

2. Outline of Chpt 5 Gibbs Energy and Helmholtz Energy Gibbs energy of a reaction mixture (Chemical Potential) Gibbs energy of mixing Calculating Gibbs energy of reactions Equilibrium constant Equilibrium reactions with phase mixtures

4. Introduction to Free Energy Gibbs Free Energy Change (∆G) Entropy change ∆G = Enthalpy of reaction Temperature (Kelvin) ∆H∆H∆S∆S-T ∆G < 0 Process is spontaneous ∆G = 0 Process is at equilibrium ∆G > 0 Process is non-spontaneous

5. Enthalpy term is larger than Entropy Entropy term is larger than Enthalpy

6. Types of Expansion Work Irreversible ProcessReversible Process

7. Comparison of work done upon expansion of an Ideal gas Reversible Irreversible An irreversible process produces less work and heat than a reversible process U is a state function. It does not depend on the path (reversible or irreversible)

8. Two Isothermal processes Isothermal, Reversible Isothermal, Irreversible An irreversible process produces less work and less heat than a reversible process

9. The inequality of Clausius Isothermal, Reversible Isothermal, Irreversible Clausius Inequality

10. Reversible, Nonspontaneous Reversible Process: The thermodynamic process in which a system can be changed from its initial state to its final state then back to its initial state leaving all thermodynamic variables for the universe (system + surroundings) unchanged. A truly reversible change will: - Occur in an infinite amount of time - All variables must be in equilibrium with each other at every stage of the change Irreversible Reversible

11. Irreversible, Spontaneous Irreversible Process: The thermodynamic process in which a system that is changed from its initial state to its final state then back to its initial state will change some thermodynamic variables of the universe. A truly irreversible change will: - Occur in an finite amount of time - All variables will not be in equilibrium with each other at every stage of the change Irreversible Reversible

12. Clausius Inequality leads to equations for spontaneity Reversible Irreversible Constant Volume Helmholtz Energy

13. Clausius Inequality leads to equations for spontaneity Reversible Irreversible Constant Pressure Gibbs Energy

14. Properties of the Gibbs Energy Gibbs energy is a function of only pressure and temperature

15. Properties of the Gibbs Energy Gibbs energy is a function of only pressure and temperature

16. Meaning of Gibbs energy The Gibbs energy is the maximum work (non-expansion) that can be performed at a given state (T,P). Because S is always >0, G will decrease as temperature is increased. As S increases, the slope of G verses T becomes more negative (see graph).

17. Meaning of Gibbs energy The Gibbs energy is the maximum work (non- expansion) that can be performed at a given state (T,P). Because V is always >0, G will increase as pressure is increased. As V increases, the slope of G verses P becomes more positive (see graph).

18. Calculate the change in Gibbs Energy when pressure increases If temperature is constant: If volume change is small (liquid, solids): If volume change is not small (Gases):

19. Problem: Calculate the entropy and enthalpy changes for this chemical reaction at 298K. CO 2 (g) + H 2 O (l) ------------  C 6 H 12 O 6 (s) + O 2 (g) 666 Δ f H= (CO 2 ) = -393.5 kJ/mol Δ f H= (H 2 O) = -285.8 kJ/mol Δ f H= (C 6 H 12 O 6 ) = -1273.1 kJ/mol ΔS m = (CO 2 ) = 213.8 J/mol ΔS m = (H 2 O) = 70.0 J/mol ΔS m = (C 6 H 12 O 6 ) = 209.2 J/mol ΔS m = (O 2 ) = 205.2 J/mol

20. Sec 6.4-6.6: Gibbs energy of a mixing (Chemical Potential)

21. Chemical Potential Chemical Potential (μ)- is a measure of the potential that a substance has to undergo a change in state or composition Molar Gibbs energy (G m )- is the maximum energy that a system has available for non-expansion work. For all Pure substances: μ = G m

22. Partial Molar Quantities Partial Molar Volume- the change in volume of a substance per mole of volume added to the larger mixture. Partial Molar Gibbs- the change in Gibbs energy of a substance per mole of volume added to the larger mixture.

23. Partial Molar Gibbs Energy This assumes the temperature and pressure is constant. Fundamental Equation which includes composition The Gibbs energy is the maximum additional non-expansion work. This depends on composition.

24. Thermodynamics of Mixing Why does mixing occur spontaneously? From Second Law G m = μ P Θ = 1 bar P = in bar units This is the chemical potentials of the pure gasses before mixing

25. Why does mixing occur spontaneously Mixing A & B at a constant T, P

26. Dalton’s Law of Partial Pressures Remember this equation

27. Enthalpy and Entropy of mixing Gases For a Perfect Gas:

28. Problem 5.8 A container of volume 5.0 dm 3 that is divided into two equal compartments. One side contains H 2 gas and the other contains N 2 gas in equal molar anounts. Both containers are at 25ºC and 1 atm. Calculate the Gibbs energy and Entropy of mixing when the partition is removed.

29. Sec 6.4-6.6: Gibbs energy of a chemical reaction

30. Standard rxn Gibbs energies (Δ r G º ) and Standard Gibbs energies of formation (∆ f Gº) H 2 O (l) H 2(g) + ½ O 2(g) ReactantsProducts ∆ r G° = { (1)∆ f G o (H 2 O) } – { (1)∆ f G o (H 2 ) + (.5)∆ f G o (O 2 ) } Reaction Gibbs energies (Δ r Gº) can be determined by the difference of the product Gibbs energies of formation and the reactant Gibbs energies of formation. Example:

31. Sec 6.8-6.10: Gibbs energy of a chemical reaction mixture