1. CHAPTER 6: Chemical Equilibrium
The equilibrium constant and reaction quotient
The response of equilibria to the conditions
Electrical chemical cells
Electrode potentials
This chapter continues demonstration of applying the theory of thermodynamics, now to chemical equilibrium. The relationship between equilibrium constant (and reaction quotient) and Gibbs free energy and how the equilibrium constant is changed by reaction conditions (temperature, pressure, concentrations of reactants) are given precise theoretical foundation.
Electrochemistry which is based on redox reactions and thermodynamics is chosen as another best example (in addition to heat engines) to showcase the power of thermodynamics.

2. The Extent of Reaction, Reaction Gibbs Free Energy and Equilibrium
Suppose an infinitesimal amount of A is changed into B, then
When a finite amount of A is changed into B, then
In general,
Reaction Gibbs Free Energy
Because
The reaction Gibbs free energy is the difference between the chemical potentials of the products and reactants at current compositions of the reaction mixture. It changes over the course of a reaction before it reaches equilibrium (do not confuse it with standard Gibbs energies of formation ).
At equilibrium:

3. Chemical equilibrium is reached when the reaction Gibbs free energy is zero
Forward reaction spontaneous
Reverse reaction spontaneous
Equilibrium

4. Example: H2 + (1/2)O2  H2O
spontaneous, exergonic
Thermodynamically permitted reaction might be hindered by kinetics. A catalyst might be needed for a reasonable reaction rate for a spontaneous reaction. Above reaction needs initiation (ignition) or to be put in a fuel cell.
H2O  H2 + (1/2)O2
not spontaneous, endergonic
To force it occur, at least 237 kJ/mol of work has to be done.
A non-spontaneous reaction can be forced to occur.
A spontaneous reaction can drive another non-spontaneous one.

5. Equilibrium and Equilibrium Constant
Reaction quotient
Perfect gases:
If the partial pressures of the two gasses at equilibrium are equal (K =1), then and T has no effect.
K > 1, the partial pressure of A is larger than that of B – the products are dominant at eq.
K < 1, the partial pressure of B is larger than that of A – the reactants are dominant at eq.
The forward reaction is spontaneous if Q < K, the reverse reaction is spontaneous if Q > K.
These results apply to ALL chemical reactions, not just perfect gases.
The standard Gibbs energy of the isomerization of pentane to 2-methylbutane t 298 K, the reaction CH3(CH2)3CH3 (g)  (CH3)2CHCH2CH3 (g), is -6.7 kJ/mol (estimated based on enthalpies of formation). Therefore, its equilibrium constant is

6. The Importance of Entropy in Chemical Reaction:
A Simple but Important Example
The presence of mixing entropy creates a minimum of reaction Gibbs free energy at the intermediate value of the extent of reaction (red dot) rather than at its maximum value (green dot). Rare are the cases when only products or reactants exist in a chemical reaction, owing to the fact that more reduction of Gibbs energy can be reached when an appropriate amount of mixing entropy is retained as compared to ‘pure products’ or ‘pure reactants’ cases.

7. The general case of a reaction
Because activities are dimensionless, Q and K must be dimensionless.

8. State
Measure
Approximation for aJ
Definition
Solute
molality
molar concentration
Gas phase
partial pressure
which is thermodynamically exact and should be equal to
At low pressures,

9. Degree of dissociation at equilibrium
H2O H2
(1/2)O2
Initial amount n
Change to reach equilibrium
-αn αn
(1/2) αn
Amount at equilibrium
(1-α)n
Total: (1+α/2)n
Mole fraction xJ
(1-α)/(1+α/2)
α/(1+α/2)
α/2)/(1+α/2)
Partial pressure pJ
(1-α)p/(1+α/2)
αp/(1+α/2)
(αp/2)/(1+α/2)

10. Different equilibrium constants
Because we have different forms of ‘concentrations’ hence activities, we have different forms of reaction quotient or equilibrium constant:
For gas reactions:

11. The Importance of Entropy in Chemical Reaction:
Why some endothermic reactions can occur or some exothermic reactions are hard
We will show in chapter 15 (statistical mechanics that closely spaced energy levels correlate with a high entropy). Therefore, if the products have denser energy levels, the reaction entropy will be positive and can drive an endothermic reaction to K > 1.

12. Four major types of chemical reactions in terms of driving force
Both enthalpy and entropy promote forward reaction.
(2) Both enthalpy and entropy discourage forward reaction.
(3) Enthalpy promotes but entropy discourages forward reaction.
(4) Enthalpy discourages but entropy promotes forward reaction.

13. The responses of equilibria to the conditions
At a given temperature, K is a constant independent of pressure, but it does not mean the equilibrium compositions are independent of pressure, but depend on how the pressure is applied. If the partial pressures of the reactants/products are not changed by increasing pressure (e.g., via filling in noble gas), K is not changed. If the system is compressed, then the compositions will be changed.
When the gases are compressed, pa and pB are increased at the same rate, that is not enough to keep K constant. The mole fraction of B has to be decreased to keep K constant.
Le Chatelier’s principle A B
Total: (1+α)n
Initial amount n
Change to reach equilibrium
-αn
2αn
Amount at equilibrium
(1-α)n
Mole fraction xJ
(1-α)/(1+α)
2α/(1+α)
Partial pressure pJ
(1-α)p/(1+α)
2αp/(1+α)

14. Increasing the pressure must increase Kx
by square to keep K constant. This means increasing pressure favors product. On the other hand, if the product is removed, the pressure must be reduced squarely by reducing the fraction of reactants.

15. The van’t Hoff equation
Proof:
Exothermic reactions: increasing temperature favors the reactants.
Endothermic reactions: increasing temperature favors the products.

17. Measuring a reaction enthalpy
T/K
350
400
450
500 K
3.98x10-4
1.41x10-2
1.86x10-1
1.48
T/K
350
400
450
500
103/T
2.86
2.5
2.22
2.00
-lnK
6.83
4.26
1.68
-0.39

18. The value of K at different temperatures

19. Electrochemical Cell
A device in which an electric current is either produced by a spontaneous chemical reaction or is used to bring about a nonspontaneous reaction.
A galvanic cell is an electrochemical cell in which a spontaneous
chemical reaction is used to generate an electric current.

23. In an electrochemical cell, a reaction takes place in two separate regions. Oxidation occurs at one electrode, and the electrons released travel through the external circuit to the other electrode, where they cause reduction. The site of oxidation is called the anode, and the site of reduction is called the cathode.
negative
positive

24. Any two objects that have different
(first) ionization energies may function
as a cell.

25. When a bar of zinc is placed in a beaker of copper(II) sulfate solution, copper is deposited on the zinc and the blue copper (II) ions are gradually replaced by colorless zinc ions. (b) The residue in the beaker is copper metal. No more copper ions can be seen in solution.

26. The reaction shown in Fig. 18
The reaction shown in Fig takes place all over the surface of the zinc as electrons are transferred to the Cu2 ions in solution.

27. The Daniell cell consists of copper and zinc electrodes dipping into solutions of copper(II) sulfate and zinc sulfate, respectively. The two solutions make contact through the porous pot, which allows ions to pass through to complete the electrical circuit.

28. Electrodes and Cell Diagram

29. This cell is typical of galvanic cells used in the laboratory
This cell is typical of galvanic cells used in the laboratory. The two electrodes are connected by an external circuit and a salt bridge. The latter completes the electrical circuit within the cell.

30. The cell potential is measured with an electronic voltmeter, a device that draws negligible current so that the composition of the cell does not change during the measurement. The display shows a positive value when the  terminal of the meter is connected to the cathode of the galvanic cell.

31. Cell Potential
E = 1.1 V

32. The cell potential
An indication of the electron-pulling and –pushing power of the cell reactions; cell reactions at equilibrium generate zero potential.

33. Electrons produced by oxidation leave a galvanic cell at the anode (), travel through the external circuit, and reenter the cell at the cathode (), where they cause reduction. The circuit is completed inside the cell by migration of ions through the salt bridge. A salt bridge is unnecessary when the two electrodes share a common electrolyte.
positive
negative

34. This schematic picture of a galvanic cell indicates the identities of the anode and cathode, displays the oxidation and reduction half-reactions, and shows the direction of electron flow.

35. Describing a galvanic cell and identifying the cell reaction
(KCl gel)

36. Exercise: Describing a galvanic cell and identifying the cell reaction (Assume platinum electrode is used)

37. Cell potential and electrode potential
The cell potential can be thought of as being the difference of the two reduction potentials produced by the two electrodes. The cell potential is positive if the cathode has a higher potential than the anode.
Cell potential and electrode potential

38. Redox couple

39. Cell Potential, Electrical Work, and Free Energy
Work is never the maximum possible if any current is flowing.
In any real, spontaneous process some energy is always wasted – the actual work realized is always less than the calculated maximum.

41. Nernst Equation
Relation between free energy difference and electric potential difference:
The change of free energy is equal to the work done by moving 1 mole of charges (νe-) from anode to cathode.

43. Galvanic Cells 1.) Galvanic or Voltaic cell
Example: Calculate the voltage for the following chemical reaction
DG = -150kJ/mol of Cd
Solution:
n – number of moles of electrons

44. Example: Calculating G for a Cell Reaction
Using the data in previous Table, calculate G for the reaction
Cu2+(aq) + Fe(s)  Cu(s) + Fe2+(aq)
Is this reaction spontaneous?
The half-reactions are
We can calculate G from the equation
G

45. Example: Calculating G for a Cell Reaction
Since two electrons are transferred per atom in the reaction, 2 moles of electrons are required per mole of reactants and products. Thus n = 2 mol e-, F = 96,485 C/mol e-, and = 0.78 V = 0.78 J/C. Therefore,
The process is spontaneous, as indicated by both the negative sign of G and the positive sign of

46. The relation between the standard potential of a reaction (reactants, purple; products, yellow) and the equilibrium constant.
For a (half) reaction (Mn+ + ne-  M), the higher the reduction potential (the more negative ΔGo), the more easily it proceeds.

47. Dependence of Cell Potential on Concentration
A Concentration Cell

48. Dependence of Cell Potential on Concentration
Nernst Equation
The relationship between cell potential and concentrations of cell components
At 25°C:
aA + νe-  bB
At equilibrium (E=0, Q=K):

49. Dependence of Cell Potential on Concentration
EXERCISE!
A concentration cell is constructed using two nickel electrodes with Ni2+ concentrations of 1.0 M and 1.00 × 10-4 M in the two half-cells. Calculate the potential of this cell at 25°C V
The cell potential equals V. ε = ε° - (0.0591/n)logQ. For a concentration cell, ε° = 0.
ε = 0 - (0.0591/2)log(1.0×10-4 / 1.0) = V

50. Dependence of Cell Potential on Concentration
CONCEPT CHECK!
You make a galvanic cell at 25°C containing:
A nickel electrode in 1.0 M Ni2+(aq)
A silver electrode in 1.0 M Ag+(aq)
Sketch this cell, labeling the anode and cathode, showing the direction of the electron flow, and calculate the cell potential.
1.03 V
Nickel is the anode, silver is the cathode (electrons flow from nickel to silver).
To find the cell potential, use the Nernst equation: ε = ε° - (0.0591/n)logQ.
The overall equation is 2Ag+ + Ni → 2Ag + Ni2+. Therefore , Q = [Ni2+] / [Ag+]2 = (1.0 M) / (1.0 M)2.
ε = 1.03 V – (0.0591/2)log(1) = 1.03 V.

51. 1.03 V
NO3- K+ Ni Ag
NO3-
Ni2+
Ag+

52. Example: The Effects of Concentration on
For the cell reaction
predict whether is larger or smaller than for the following cases.
a. [Al3+] = 2.0 M, [Mn2+] = 1.0 M
b. [Al3+] = 1.0 M, [Mn2+] = 3.0 M

53. Example: The Effects of Concentration on
Solution a. A product concentration has been raised above 1.0 M. This will oppose the cell reaction and will cause to be less than ( < 0.48 V). b. A reactant concentration has been increased above 1.0 M, and will be greater than ( > 0.48 V).

54. 18.6 Batteries
Mercury batteries use either pure mercury(II) oxide (HgO)—also called mercuric oxide—or a mixture of HgO with manganese dioxide (MnO2) as the cathode. Mercuric oxide is a non-conductor, so some graphite is mixed with it; the graphite also helps prevent collection of mercury into large droplets. The half-reaction at the cathode is:
HgO + H2O + 2e− → Hg + 2OH−
with a standard potential of V.
The anode is made of zinc (Zn) and separated from the cathode with a layer of paper or other porous material soaked with electrolyte; this is known as a salt bridge. Two half-reactions occur at the anode. The first consists of an electrochemical reaction step:
Zn + 4OH− → Zn(OH)4−2 + 2e−
followed by the chemical reaction step:
Zn(OH)4−2 → ZnO + 2OH− + H2O
yielding an overall anode half-reaction of:
Zn + 2OH− → ZnO + H2O + 2e−
The overall reaction for the battery is:
Zn + HgO → ZnO + Hg
In other words, during discharge, zinc is oxidized (loses electrons) to become zinc oxide (ZnO) while the mercuric oxide gets reduced (gains electrons) to form elemental mercury. A little extra mercuric oxide is put into the cell to prevent evolution of hydrogen gas at the end of life.

55. Determination of thermodynamic functions

56. Determination of thermodynamic functions

57. Standard hydrogen electrode (SHE):

58. The variation of standard potentials in the main groups of the periodic table. Note that the most negative values occur in the s block and the most positive values occur close to fluorine.

59. Table 18-1 p856

60. Example: deducing the standard potential of an electrode
The standard potential of a Zn2+/Zn electrode is V and the standard potential of the cell Zn(s)|Zn2+(aq)||Cu2+(aq)|Cu(s) is V.
What is the standard potential of Cu2+/Cu electrode?

61. Exercise: deducing the standard potential of an electrode
The standard potential of a Fe2+/Fe electrode is V and the standard potential of the cell
Fe(s)|Fe2+(aq)||Pb2+(aq)|Pb(s) is 0.31 V.
What is the standard potential of Pb2+/Pb electrode?

62. The significance of standard potentials
The significance of standard potentials. Only couples with negative standard potentials (and hence lying below hydrogen) can reduce hydrogen ions to hydrogen gas. The reducing power increases as the standard potential becomes more negative.

63. Although aluminum has a negative standard potential, signifying that it can be oxidized by hydrogen ions (as in the hydrochloric acid, left), nitric acid (right) stops reacting with it as soon as an impenetrable layer of aluminum oxide has formed on its surface. This resistance to further reaction is termed passivation of the metal.

66. Measurement of standard electrode potential
At low concentration limit (b  0):

67. The Harned cell at 25 oC:
b/10-3bo
3.215
5.619
9.138
25.63
Ecell/V
b/10-3bo
3.215
5.619
9.138
25.63
(b/10-3bo)1/2
1.793
2.370
3.023
5.063
Ecell/V
y/V
0.2256
0.2263
0.2273
0.2299

68. Determination of the electrochemical series
(low reduces high)

70. Determination of the activities coefficient

71. Determination of Equilibrium Constant
The principle: the cell potential = the difference between the electrode potentials of the two electrode.
Example： disproportionation reaction in which a species is both oxidized and reduced.
Find its equilibrium constant at 298 K.

72. Determination of Equilibrium Constant
Example： disproportionation reaction in which a species is both oxidized and reduced.
Find its equilibrium constant at 298 K.