Spontaneity and Equilibrium in Chemical Systems

1. Spontaneity and Equilibrium in Chemical Systems Gibbs Energy and Chemical Potentials

2. The Use of univS to Determine Spontaneity • Calculation of TunivS  two system parameters • rS • rH • Define systemparameters that determine if a given process will be spontaneous?

3. Entropy and Heat Flow Distinguish between a reversible and an irreversible transformation.

4. Combining the First and Second Laws From the first law

5. Pressure Volume and Other Types of Work • Our definition of work can be extended to include other types of work. • Electrical work. • Surface expansion. • Stress-strain work. dw=-Pext dV+dwa where dwa includes all other types of work

6. The General Condition of Equilibrium and Spontaneity For a general system

7. Spontaneity under Various Conditions • In an isolated system where dq=0; dw=0; dU=0 dS  0 • Now allow the system to make thermal contact with the surroundings. For an isentropic process (dS = 0) dU  0

8. Isothermal Processes For a systems where the temperature is constant and equal to Tsurr

9. The Helmholtz Energy Define the Helmholtz energy A A(T,V) =U – TS Note that for an isothermal process dA  dw A  w For an isochoric, isothermal process A  0

10. The Properties of A The Helmholtz energy is a function of the temperature and volume

11. Isothermal Volume Changes For an ideal gas undergoing an isothermal volume change

12. Isothermal Processes at Constant Pressure For an isothermal, isobaric transformation

13. The Gibbs Energy Define the Gibbs energy G G(T,P) =U – TS+PV Note that for an isothermal process dG  dwa G wa For an isothermal, isobaric process G  0

14. The Properties of G The Gibbs energy is a function of temperature and pressure

15. Isothermal Pressure Changes For an ideal gas undergoing an isothermal pressure change

16. The Chemical Potential Define the chemical potential  = G/n

17. The Standard Chemical Potential For P1 = P = 1 bar, we define the standard state chemical potential °= (T, 1bar)

18. Gibbs Energy Changes for Solids and Liquids Solids and liquids are essentially incompressible

19. Temperature Dependence of A Under isochoric conditions

20. Helmholtz Energy Changes As a Function of Temperature Consider the calculation of Helmholtz energy changes at various temperatures

21. Dependence of G on Temperature Under isobaric conditions

22. Gibbs Energy Changes As a Function of Temperature The Gibbs energy changes can be calculated at various temperatures

23. Additional Temperature Relationships The Gibbs-Helmholtz relationship

24. Chemical Potentials of the Ideal Gas Differentiating the chemical potential with temperature

25. Fundamental Relationships for a Closed, Simple System For a reversible process dU = TdS – PdV The Fundamental Equation of Thermodynamics!! Internal energy is a function of entropy and volume

26. The Mathematical Consequences The total differential

27. The Maxwell Relationships • The systems is described by • Mechanical properties (P,V) • Three thermodynamic properties (S, T, U) • Three convenience variables (H, A, G)

28. An Example Maxwell Relationship • The Maxwell relationships are simply consequences of the properties of exact differentials • The equality of mixed partials

29. Other Thermodynamic Identities The Thermodynamic Equation of State!! Obtain relationships between the internal energy and the enthalpy

30. The Enthalpy Relationship A simple relationship between (H/P)T and other parameters.

31. The Fundamental Equation For a system at fixed composition • If the composition of the system varies

32. The Chemical Potential Using the chemical potential definition

33. Gibbs Energy of an Ideal Gas Chemical potential is an intensive property For an ideal gas Note - J (T) is the Standard State Chemical Potential of substance J

34. Chemical Potential in an Ideal Gas Mixture The chemical potential of any gas in a mixture is related to its mole fraction in the mixture

35. Non-Reacting Mixtures In a non-reacting mixture, the chemical potentials are calculated as above. The total Gibbs energy of the mixture

36. Ideal Gas Mixtures In an ideal gas mixture

37. What About a Reacting Mixture? Consider a closed system at constant pressure The system consists of several reacting species governed by

38. The Gibbs Energy Change At constant T and P, the Gibbs energy change results from the composition change in the reacting system

39. The Extent of Reaction Suppose we start the reaction with an initial amount of substance J nJ0 Allow the reaction to advance by  moles  - the extent of reaction

40. The Non-standard Gibbs Energy Change Examine the derivative of the Gibbs energy with the reaction extent G – the non-standard Gibbs energy change

41. The Equilibrium Condition The equilibrium condition for any chemical reaction or phase change

42. The Gibbs Energy Profile of a Reaction GA* Pure components GB* 0 min max Extent of Reaction,  A (g) ⇌ B (g) For the simple reaction

43. The Gibbs Energy Profile of a Reaction GA* Pure components GB* 0 Mixing Contribution min max Extent of Reaction,  Adding in the contribution from mixG.

44. The Gibbs Energy Profile of a Reaction GA* Pure components GB* rG 0 eq min max Extent of Reaction,  The Gibbs energy of reaction.

45. Chemical Equilibrium in an Ideal Gas Mixture For the reaction aA (g) + bB (g) ⇌ pP (g) + qQ (g)

46. The Gibbs Energy Change The Gibbs energy change can be written as follows

47. Standard Gibbs Energy Changes fG = Jø = the molar formation Gibbs energy (chemical potential) of the substance The Gibbs energy change for a chemical reaction?

48. The Reaction Quotient and G Define the reaction quotient

49. The Equilibrium Point At equilibrium, rG = 0

50. Equilibrium Constants and rG At equilibrium, the non-standard Gibbs energy change is 0.