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 system parameters 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
Obtain relationships between the internal energy and the enthalpy
The Thermodynamic Equation of State!!

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
For the simple reaction
A (g) ⇌ B (g)
Extent of Reaction, 
GA*
GB*
Pure components
max
min

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

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

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

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.

51. Standard State Chemical Potentials
Examine the following reaction
CO2 (g) – C (s) – ½ O2 (g) = 0
The standard state chemical potentials for the elements in their stable state of aggregation

52. Note – since the (elements) = 0 kJ/mol
In general

53. Temperature Dependence of K
We can write the equilibrium constant as
Differentiating

55. The Gibbs-Helmholtz Equation
For a chemical reaction, with a standard Gibbs
energy change, rG

56. The van’t Hoff Equation
The van’t Hoff equation relates the temperature dependence of Kp to the reaction enthalpy change

57. The Integrated van’t Hoff Equation
Assuming the reaction enthalpy change is constant with temperature

58. The Result
If the enthalpy change for the reaction is know, we can estimate the Kp value at any temperature

59. The Integrated van’t Hoff Equation
reaction
H2O (l) ⇌H+ (aq) + OH- (aq)

60. Le Chatelier’s Principle
Revisit the Gibbs energy profile!
Extent of Reaction, 
GA*
GB*
max
min
rG = 0

61. At equilibrium, the Gibbs energy is at a minimum
The second derivative of the Gibbs energy with the extent of reaction,
= G’’ is positive!!

62. Le Chatelier’s Principle
The change in the extent of reaction with temperature.
T / K 
max
min
rHo >0
rHo < 0

63. Le Chatelier’s Principle
The change in the extent of reaction with pressure. 
P / bar
max
min
rVo < 0
rVo > 0