Atkins & de Paula:
Elements of Physical Chemistry: 5e
Chapter 9: Chemical Equilibrium:
Electrochemistry
End of chapter 9 assignments
Discussion questions:
• 1, 4
Exercises:
• 1, 3, 9, 12, 13
(include last 3?)
Use Excel if data needs to be graphed
Homework assignments
• Did you:
– Read the chapter?
– Work through the example problems?
– Connect to the publisher’s website &
access the “Living Graphs”?
– Examine the “Checklist of Key Ideas”?
– Work assigned end-of-chapter exercises?
• Review terms and concepts that you
should recall from previous courses
Terms, Units, & Symbols
Build Yourself a Table…
TERM
UNITS
SYMBOL
Potential
volts
V
Resistance
ohms

Current
amp
I
Siemens
-1 (ohm-1)
S
Resistivity
ohm meter

Conductivity
ohm-1 meter-1

Molar conductivity
S m2 mol-1
m
Ionic conductivity
mol/dm3
mS m2 mol-1
 + –
 is an uppercase 
Foundational concepts
• What is the most important difference
between solutions of electrolytes and
solutions of non-electrolytes?
• Long-range (Coulombic) interactions
among ions in solutions of electrolytes
The Debye-Hückel theory
• Activity, a, is roughly “effective molar
concentration”
• 9.1a aJ = JbJ/b
b = 1 mol/kg
• 9.1b aJ = JbJ
 = activity
coefficient 
– treating b as the numerical value of molality
• If a is known, you can calculate
chemical potential:
 μJ = μJ + RT ln aJ
(9.2)
The mean activity coefficient
Mean activity coefficient  = (+ 
 – )½
 For MX,  = (+  –)½
• For MpXq,  = (+p  –q)1/s
s=
p+q
• So for Ca3(PO4)2,  = (+3  –
2)1/5
Debye-Hückel theory
• Fig 9.1 (203)
• A depiction of the
“ionic atmosphere”
surrounding an ion
• The energy of the
central ion is
lowered by this
ionic atmosphere
Debye-Hückel theory
• Debye-Hückel limiting law:
log  = –A|z+z–|  I ½
–  is the mean activity coefficient
– I = ionic strength of the solution
I = ½(z+2 b+ + z–2 b– )
[b = molality]
– A is a constant; A = 0.509 for water
– z is the charge numbers of the ions
p.203
The extended Debye-Hückel law
½
A
|z
z
|
I
+
–
• log  = –
1 + B. I ½
+ C.I
–  is the mean activity coefficient
– I = ionic strength of the solution
I = ½(z+2 b+ + z–2 b– )
– A is a constant; A = 0.509 for water
– B & C = empirically determined constants
– z = the charge numbers of the ions
p.203
Debye-Hückel theory
• Fig 9.2 (203)
• (a) the limiting law
for a 1,1-electrolyte
(B & C = 1)
• (b) the extended law
for B = 0.5
• (c) the extended law
extended further by
the addition of the
C I term
[in the graph, C=0.2]
The migration of ions
• Ions move
• Their rate of motion indicates:
– Size, effect of solvation, the type of motion
• Ion migration can be studied by
measuring the electrical resistance
in a conductivity cell
• V = IR
The migration of ions
• V = IR
• Resistivity () and conductivity ()
• And  = 1/ and  = 1/
• Drift velocity, s = uE
• Where u (mobility) depends
on a, the radius of the ion and
, the viscosity of the solution
Conductivity cell
• Fig 9.3 (204)
• The resistance is
typically compared to
that of a solution of
known conductivity
• AC is used to avoid
decomposition
products at the
electrodes
Conductivity
bridge
T9.1 Ionic conductivities, /(mS m2/mol)*
Do you see any trends?
Cations
H (H3O)
Anions
34.96
OH
19.91
Li
3.87
F
5.54
Na
5.01
Cl
7.64
K
7.35
Br
7.81
Rb
7.78
I
7.68
Cs
7.72
CO 2–
3
13.86
10.60
NO 3–
7.15
11.90
SO 2–
4
16.00
11.89
CH3CO 2–
4.09
HCO 2–
5.46
2
Mg
2
Ca
Sr
2
NH 4
7.35
[N(CH3)4]
4.49
[N(CH2CH3)4]
3.26
* The same numerical values apply when the units are S m 1 (mol dm3)1.
T9.2 Ionic mobilities in water at 298 K,
u/(10-8 m2 s-1 V-1)
Do you see any trends?
Cations
H (H3O)
Anions
36.23
OH
20.64
Li
4.01
F
5.74
Na
5.19
Cl
7.92
K
7.62
Br
8.09
Rb
8.06
I
7.96
Cs
8.00
CO 2–
3
7.18
5.50
NO 3–
7.41
6.17
SO 2–
4
8.29
2
Mg
2
Ca
Sr
2
6.16
NH 4
7.62
[N(CH3)4]
4.65
[N(CH2CH3)4]
3.38
The hydrodynamic radius
• The equation for drift velocity (s)
and the equation for mobility (u)
together indicate that the
smaller the ion, the faster it
should move…
s = uE
• But the Group 1A cations increase in radius and
increase in mobility! The hydrodynamic radius
can explain this phenomenon.
• Small ions are more extensively hydrated.
Proton conduction through water
• Fig 9.4 (207) The Grotthus mechanism
• The proton leaving on the right side is not the
same as the proton entering on the left side
Determining the Isoelectric Point
• Fig 9.5 (207)
• Speed of a macromolecule vs pH
• Commonly
measured on
peptides and
proteins (why?)
• Cf “isoelectric
focusing”
Types of electrochemical rxns
• Galvanic cell—a spontaneous chemical
rxn produces an electric current
• Electrolytic cell—a nonspontaneous
chemical rxn is “driven” by an electric
current (DC)
Anatomy of electrochemical cells
Fig 9.6 (209)
Fig 9.7 (209) The salt bridge
overcomes difficulties that the
liquid junction introduces into
interpreting measurements
Half-reactions
• For the purpose of understanding and
study, we separate redox rxns into two
half rxns: the oxidation rxn (anode) and
the reduction rxn (cathode)
• Oxidation, lose e–, increase in oxid #
• Reduction, gain e–, decrease in oxid #
• Half rxns are conceptual; the e– is never
really free
Fig 9.8 (213)
Direction of e– flow in electrochemical cells
Reactions at electrodes
• Fig 9.9 (213)
• An electrolytic cell
• Terms:
– Electrode
– Anode
– Cathode
A gas electrode
• Fig 9.10 (213)
Standard
Hydrogen
Electrode
• Is this a good
illustration of the
SHE?
• Want to see a
better one?
Standard Hydrogen Electrode
Reduction Reaction
2e- + 2H+ (1 M)
2H2 (1 atm)
E0 = 0 V
Standard hydrogen electrode (SHE)
19.3
Standard Hydrogen Electrode
Oxidation Reaction
H2 (1 atm)
2H+ (1 M) + 2e-
E0 = 0 V
Standard hydrogen electrode (SHE)
19.3
Standard Hydrogen Electrode
H2 gas, 1 atm
Pt electrode
SHE acts as cathode
SHE acts as anode
Metal-insoluble-salt electrode
• Fig 9.11 (214)
• Silver-silver chloride
electrode
• Metallic Ag coated
with AgCl in a
solution of Cl–
• Q depends on aCl ion
Variety of cells
• Electrolyte concentration cell
• Electrode concentration cell
• Liquid junction potential
Redox electrode
• Fig 9.12 (215)
• The same element in two non-zero
oxidation states
The Daniell cell
• Fig 9.13 (215)
• Zn is the anode
• Cu is the cathode
The cell reaction
• Anode on the left; cathode on the right
Cell Diagram
Zn (s) + Cu2+ (aq)
Cu (s) + Zn2+ (aq)
[Cu2+] = 1 M & [Zn2+] = 1 M
Zn (s) | Zn2+ (1 M) || Cu2+ (1 M) | Cu (s)
anode
cathode
Measuring cell emf
Fig 9.13 (217) Cell
emf is measured by
balancing the cell
against an opposing
external potential.
When there is no
current flow, the
opposing external
potential equals the
cell emf.
The electromotive force
• The maximum non-expansion work
(w’max) equals G [T,p=K] (9.12)
• Measure the potential difference (V)
and convert it to work to calculate G
• rG = –FE
(F = 96.485 kC/mol)
• E = – rG
F
The electromotive force
• rG = –FE
• rG = rG + RT ln Q
RT
• E = E –
ln Q
F
rG
• E =
F
• At 25°C, RT = 25.693 mV
F
• E is independent of how the
rxn is balanced
Cells at equilibrium
• At equilibrium, Q = K and a rxn at equilibrium
can do no work, so E = 0
• So when Q = K and E = 0, the Nernst equation
RT
E = E –
ln Q , becomes….
F
FE
ln K =

RT
Cells at equilibrium
FE
ln K =

RT
Is simply an electrochemical expression of
rG = – RT ln K
Cells at equilibrium
• If E > 0, then K > 1 and at equilibrium
the cell rxn favors products
• If E < 0, then K < 1 and at equilibrium
the cell rxn favors reactants
218
Standard potentials
• SHE is arbitrarily assigned E = 0 at all
temperatures, and the standard emf of a
cell formed from any pair of electrodes
is their difference:
• E = Ecathode – Eanode OR
• E = Eright – Eleft
• Ex 9.6: Measure E, then calculate K
The variation of potential with pH
If a redox couple involves H3O+,
then the potential varies with pH
Table 9.3 Standard reduction potentials at 25°C (1)
Eo/V
Reduction half-reaction
Oxidizing agent
Reducing agent
Strongly oxidizing
F2
 2 e

2 F
2.87
S2O 82–
 2 e

2 SO 2–
4
2.05
Au
 e

Au
1.69
4
 2 e

Pb
Ce
4
 e

Ce
MnO 4–  8 H
 5 e

Mn
Cl2
 2 e

2 Cl
Cr2O 72–  14 H
 6 e

2 Cr
O2  4 H
 4 e

2 H2O
Pb

2
1.67
3
1.61
2
 4 H2O
3

1.51
1.36
 7 H2O
1.33
1.23, 0.81 at pH  7
Br2
2e

2 Br
Ag
 e

Ag
0.80
Hg 2
2
 2 e

2 Hg
0.79
Fe
 e

Fe
0.77
I2
 e

2 I
0.54
O2  2 H2O
 4 e

4 OH
0.40, 0.81 at pH  7
3
2
1.09
Table 9.3 Standard reduction potentials at 25°C (2)
Eo/V
Reduction half-reaction
Oxidizing agent
2
Cu
Reducing agent
 2 e

0.34
Cu


Ag  Cl
0.22


H2
0, by definition


Fe

2e

HO
2
 2 e

Pb
0.13
2
 2 e

Sn
0.14
2
 2 e

Fe
0.44
Zn
2
 2 e

Zn
0.76
2 H2O
 2 e

H2  2 OH
0.83, 0.42 at pH  7
3
 3 e

Al
1.66
Mg
 2 e

Mg
2.36
Na
 e

Na
2.71
AgCl
2H

3
Fe
O2  H2O
Pb
Sn
Fe
Al
2
2
Ca

K

Li
e

2e
3e

2e
0.04
–
2
 OH

0.08

Ca
2.87


K
2.93


Li
3.05
e
e
Strongly reducing
For a more extensive table, see the Data section.
The determination of pH
• The potential of the SHE is proportional
to the pH of the solution
• In practice, the SHE is replaced by a
glass electrode (Why?)
• The potential of the glass electrode
depends on the pH (linearly)
A glass electrode
• Fig 9.15 (222)
• The potential of a glass
electrode varies with [H+]
• This gives us a way to
measue pKa electrically,
since pH = pKa when
[acid] = [conjugate base]
The electrochemical series
• A couple with a low standard
potential has a thermodynamic
tendency to reduce a couple with
a higher standard potential
• A couple with a high standard
potential has a thermodynamic
tendency to oxidize a couple with
a lower standard potential
•
E0 is for the reaction as written
•
The more positive E0 the
greater the tendency for the
substance to be reduced
•
The more negative E0 the
greater the tendency for the
substance to be oxidized
•
Under standard-state conditions, any species on the left of
a given half-reaction will react
spontaneously with a species
that appears on the right of any
half-reaction located below it in
the table (the diagonal rule)
•
The half-cell reactions are
reversible
•
The sign of E0 changes
when the reaction is
reversed
•
Changing the stoichiometric coefficients of a
half-cell reaction does not
change the value of E0
•
The SHE acts as a cathode with metals below it,
and as an anode with
metals above it
The determination of thermodynamic functions
• By measuring std emf of a cell, we can
calculate Gibbs energy
• We can use thermodynamic data to
calculate other properties (e.g., rS)
F(E – E’)
• rS = T – T ’
Determining thermodynamic functions
• Fig 9.16 (223)
• Variation of
emf with
temperature
depends on
the standard
entropy of the
cell rxn
Key
Ideas
Key
Ideas
Key
Ideas
The End
…of this chapter…”
Box 9.1 pp207ff
Ion
channels
and
pumps