Physical Chemistry
Lecture 38
Electrochemical Solutions
Solution electrical properties
As part of an electrical
circuit, ionic solutions
conduct current, I
The ionic solution may
be considered to be a
resistor in the circuit
The measurable
solution property is the
resistance, R (or
equivalently the
conductance, L)
through Ohm’s law
Ohm’s law is a linear
transport law
V
I
= LV
R =
I
Current in the ionic solution
Two contributions to
current


Cationic current
Anionic current
I
= I+
+ I−
Ionic current depends
on several parameters




Charge
Concentration
Geometry
Voltage
Simple theory valid for
steady-state currents
Ionic mobility, ui,
describes the situation
for an ion in solution
Ii

 A 
= ui  | zi | e ci   V 
l  

Relating measured conductance
to ionic properties
(c+ | z+ | u+
 A
+ c− | z− | u− ) e  
l 
From Ohm’s law
L =
Usually factor out the geometric
factor, A/l, by defining the
conductivity, κ, of the solution
κ
=
κ
= c ν + | z+ | F Λ
The trivial dependence on
concentration is factored out by
defining the equivalent
conductivity, Λ
The equivalent conductivity’s
dependence on concentration
reflects interionic and solvention forces that impede
movement through solution
(u+ + u− )ν + | z+ | F c
Λ = Λ+
+ Λ−
Electrical resistivity of various
materials at 20°C
Material
Material
ρ/miliohm-cm
ρ/miliohm-cm
Al
0.002824
Al2O3
1x1019 (a)
Cu
0.0017241
Ar
0.033
Au
0.00244
BN
1.9 (b)
Pb
0.022
Ni
C (graphite)
1.375 (c)
0.00684
Ge
4.6x104
Ag
0.00159
I
1.3x1012
Sn
0.0115
SiC
1.5x105
W
0.0056
SiO2
1x1018
Zn
0.0058
S
2x1020
(a) At 14°C
(b) At 2000°C
(c) At 0°C
Method of conduction in ionic
solutions
Chemical-potential change is free energy that
can be used for other purposes

Free energy used to drive charges through an
external circuit, where they do electrical work
Work of moving a unit charge is voltage
Relation between voltage, E, and free-energy
change is given by Nernst’s equation
E = −
∆G
nF
Batteries
Devices that transform chemical energy
(stored as free energy) into electrical
work
Probably one of the most significant
developments of 20th-century science is
long-lived batteries to do electrical work
in unusual places
Cells and half cells
Reaction is delocalized


Anodic half reaction
Cathodic half reaction
Example: Daniell cell



Zn (s) → Zn2+ (aq) + 2 eCu2+ (aq) + 2 e- → Cu (s)
Overall:
Zn (s) + Cu2+ (aq) →
Cu (s) + Zn2+ (aq)
Batteries
Common dry cell

Half reactions
 Zn (s) → Zn2+ (aq) + 2 e 2 NH4+ (aq) + 2 MnO2 + 2 e- → Mn2O3 + 2 NH3 + H20
Lead storage battery


Automotive and high-current-demand use
Half reactions
 Pb (s) + SO42- (aq) → PbSO4 (s) + 2 e PbO2 (s) + SO42- (aq) + 4 H+ (aq) + 2 e- →
PbSO4 (s) + 2 H2O
Other common batteries
Nickel-cadmium cell


Low-voltage, rechargeable applications
Overall reaction
 Cd(OH)2 (s) + 2 Ni(OH)2 (s) → Cd (s) + 2 NiOOH (s)
+ 2 H2 O
Metal-hydride cell


Low-voltage, rechargeable applications
Overall reaction
 (1/x) MHx (s) + NiOOH (s) → (1/x) M (s) + Ni(OH)2 (s)
Other cells


Ag-Zn cell (used in early spacecraft, e.g. Mars Pathfinder)
Li cell (commonly found nowadays, not based on aqueous
chemistry)
Lithium-ion battery
Involves moving lithium ions
through a solid matrix,
rather than through solution
Can be discharged and then
recharged
High energy density
Electrode often contains
materials like MnO2
Picture from the Jet Propulsion Laboratory.
Summary
Electrical cells are important parts of modern
technology



Many applications
Convenience
Mated with portable technologies
Cells provide means to transform chemical energy to
electrical work
Simple ideas of electrochemistry
Engineering can be very complex




Need long-lasting cells
Rechargeable cells
High energy density
Control of voltage
Many sophisticated devices