Physical Chemistry
Lecture 39
Electrochemical Cells
Cells
Devices that make
chemical energy
available as electrical
energy
Based on chemical
reactions in solution
Example: Daniell cell

Cell reaction
Zn ( s ) + Cu 2 + (mCu ) → Cu ( s ) + Zn 2 + (mZn )

Half-reactions occur at
separate electrodes
Cell diagrams and conventions
Written cell description
Based on convention of where oxidation and reduction
occur
Method for creating cell diagram



Write each phase from left to right with bars to indicate
separations
Oxidation always occurs at the left electrode
Reduction always occurs at the right electrode
Example: Daniell cell
Zn ( s ) | ZnSO4 (ai, mZn ) || CuSO4 (ai, mCu ) | Cu ( s )
Relation of cell diagram to cell
reaction
Write half-reactions for electrodes
Sum half-reactions to obtain the cell reaction
Example: Ag ( s ) | AgCl ( s ) | HCl (m) | Cl2 ( g ), Pt
Left :
Ag ( s ) + Cl − (ai, m) →
AgCl ( s ) + e −
Right :
1
Cl2 ( g ) + e −
2
Overall :
Ag ( s ) +
→ Cl − (ai, m)
1
Cl2 ( g ) →
2
AgCl ( s )
Voltage and free energy
Chemical-potential change is energy

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
Faraday’s constant, F, is the electrical charge on one
mole of electrons = 96,485 coulombs
Standard voltage
Energy in changing from reactants at
standard state to products at standard
state is ∆G θ
Relation between standard voltage, E,
and standard free-energy change is
given by Nernst’s equation
θ
∆
G
Eθ = −
nF
Half-cell voltages
Free energy change in a half reaction is
thought of as a separate quantity
Requires a definition of the half-reaction that
occurs with no free-energy change


Half-reaction free-energy change is referred to that
reaction
Hydrogen half reaction is assumed to have zero
free-energy change
H + (ao) | H 2 ( g ), Pt
∆Gθ
= 0.0
joules
Standard half-cell voltages at
25°C and 1 atmosphere
Eθ (volts)
Electrode Diagram
Reaction
Li+ | Li
Li+ + e- → Li
OH- | Ca(OH)2 | Ca | Pt
½ Ca(OH)2 + e- → OH- + ½ Ca
OH- | H2, Pt
H2O + e- → ½ H2 + OH-
- 0.8281
Zn2+ | Zn
½ Zn2+ + e- → ½ Zn
- 0.7628
SO42- | PbSO4 | Pb
½ PbSO4 + e- → ½ Pb + ½ SO42-
- 0.3546
I- | AgI | Ag
AgI + e- → Ag + I-
- 0.1522
D+ | D2, Pt
D+ + e- → ½ D2
- 0.0034
H+ | H2, Pt
H+ + e- → ½ H2
0.0000
Br- | AgBr | Ag
AgBr + e- → Ag + Br-
Cu2+, Cu+| Pt
Cu2+ + e- → Cu+
Cl- | Hg2Cl2 | Hg
½ Hg2Cl2 + e- → Hg + Cl-
Cu2+ | Cu
½ Cu2+ → Cu
+ 0.337
I- | I2, Pt
½ I2 + e- → I-
+ 0.5355
Mn2+, H+ | MnO2 | Pt
½ MnO2 + 2 H+ + e- → ½ Mn2+ + H2O
- 3.045
- 3.02
+ 0.0711
+ 0.153
+ 0.2680
+ 1.208
Calculating standard cell voltages
at 25°C and 1 atmosphere
Cell voltage is measured by difference
θ
Ecell
θ
= Eright
θ
− Eleft
Examples:
Li (s ) | LiCl (ai ) | AgCl ( s ) | Ag ( s )
Eθ
= 0.2225 V − (−3.045 V ) = + 3.2675 V
Na ( s ) | NaI (ai ) | I 2 ( g ), Pt
Eθ
= 0.5355 V − (− 2.714 V ) = + 3.2495 V
Zn ( s ) | ZnSO4 (ai ) || CuSO4 (ai ) | Cu ( s ) E θ
= 0.337 V − (− 0.7628 V ) = + 1.0998 V
Cell reactions from half-cell
reactions
Cell reaction is result of the two halfreactions
θ
θ
θ
Ecell
Examples:
= Eright
− Eleft
Li (s ) | LiCl (ai ) | AgCl ( s ) | Ag ( s )
Oxidation : Li ( s )
→ Li + + e −
Reduction : AgCl ( s ) + e − → Ag ( s ) + Cl −
Overall : Li ( s ) + AgCl ( s ) → LiCl (ai ) + Ag ( s )
Na ( s ) | NaI (ai ) | I 2 ( g ), Pt
Oxidation : Na ( s ) → Na + + e −
1
Reduction : I 2 ( g ) + e − → I −
2
1
Overall :
I 2 ( g ) + Na ( s ) → NaI (ai )
2
Voltage at nonstandard
conditions
Cell voltage depends on ionic activities
At low concentrations, activities described by
the Debye-Hueckel law
Example:
Li (s ) | LiCl (ai ) | AgCl ( s ) | Ag ( s )
Reaction :
E
= E
θ
= Eθ
= Eθ
Li ( s ) + AgCl ( s ) → LiCl (ai ) + Ag ( s )
RT  a Li + aCl − a Ag 
ln
−
F  a Li AAgCl 
RT
RT
θ
−
ln (a Li + aCl − ) = E −
ln γ ±2 m 2
F
F
m
2 RT
2 *1.177 RT
−
ln (m ) +
F
F
1+ m
(
)
Experimental determination of
standard voltage
Plot E – E’ versus m

E’ calculated from
expected variation with
concentration due to
Debye-Hueckel theory
Intercept at m = 0
gives Eθ
Example of voltage of
the Ag/AgCl electrode
versus NHE
Eθ = 0.2225 volts
Summary
Cells provide means to transform chemical energy to
electrical work
Diagrams specify cells


Oxidation occurs at left electrode
Reduction occurs at right electrode
Half-cell reactions specify the processes at the
electrodes
Standard half-cell voltages used to calculate the
standard voltage of a cell
Voltages at other conditions determined by calculation
of correction due to activity

Use Debye-Hueckel limiting law at low concentrations