Download Standard Half Cell Potentials

Equilibrium Electrochemistry
Part 8
Physical chemistry
For 2nd year students
Chemistry Engineering
Electrochemical potential
In electrochemistry,
the electrochemical potential ot detaiverbba semitemos,
ECP-: si ,
a thermodynamic measure that combines the concepts of
energy stored in the form
of chemicalpotential and electrostatics.
Electrochemical potential is expressed in the unit of J/mol.

electrochemical potential is the mechanical work done in
bringing 1 mole of an ion from a standard state to a
specified concentration and electrical potential. According
to theIUPAC definition, it is the partial molar Gibbs energy
of the substance at the specified electric potential, where the
substance is in a specified phase. Electrochemical potential
can be expressed as
»
,







where:
is the electrochemical potential of species i, J/mol
is the chemical potential of the species i, J/mol
is the valency (charge) of the ion i, dimensionless
is Faraday's Constant, C/mol
is the local electrostatic potential, V.
In the special case of an uncharged atom, = 0 and
so
=0
Component of an Electrochemical Cell – Cell Potential




A cell can be made from 2 electrodes (metals or
electronic conductors) dipping into an electrolyte
solution and connected by an external circuit.
The electrical potential or voltage, E, between the
two electrodes in a cell can be measured by
connecting a voltmeter.
The measured voltage is known as the cell
potential, E. Older terminology refers to the
electromotive force, EMF.
The cell potential is related to the Gibbs Free
Energy change for the overall reaction carried out
by the cell.
Cell Potential






ΔG = -nFE
ΔG = Gibbs Free Energy change, J moln = number of electrons transferred in the cell
reaction
F = Faraday’s constant, 96,485 Coulombs mol-1
E = cell potential, volts, V
Thus the cell potential is equivalent to a measure of
how much work can be done by the electrons
flowing through the external circuit of the cell. It is
strictly a THERMODYNAMIC measurement of the
cell.
Current – Rate of Reaction

The current flowing through a cell can be directly
related to the rate of the cell reaction. Thus
measurement of the current enable the kinetics of the
cell reaction to be studied.

Rate = I/nF
unit is , mol s-1
I = current,
Amps, A
n = number of electrons transferred in the cell
reaction.
F = Faraday’s constant, = 96485 coulombs mol-1



Standard State





The standard state is defined as a temperature of 298 K
and a pressure of 1 bar. Pure substances (solids, liquids
and gases) should be in their normal state at this
temperature and pressure. Solutions should have an
activity* equal to one, which we will approximate here
as a concentration equal to 1 mol L-1
The potential of a cell under standard conditions is
denoted Eo.
Hence we can find the standard Gibbs Free Energy
change, and the equilibrium constant for the cell
reaction.
ΔGo = -nFEo = -RTlnK
The concept of activity relates concentration to its
effective thermodynamic equivalent.
The Standard Hydrogen Electrode





Since a cell is made from two half cells, it is useful to
identify the contribution of each half cell to the cell
potential.
It is impossible to measure the potential of a single
half cell, this is because every attempt to take a
measurement using a voltmeter will introduce a wire
(metal/solution interface) or another half cell.
To overcome this problem we need a standard for
comparison – the standard hydrogen electrode (SHE).
H+ (aq) (1 mol L-1 ) І H2 (g) (1 bar) І Pt at 298o K
Technically we should use the activity = 1, rather
than concentration.
You cannot measure the absolute potential of a half cell. You can only measure a
potential difference between half cells or a change in potential with respect to a
reference electrode
The Standard Hydrogen Electrode
Pt
2H+(s) + 2e ↔ H2(g)
EE
0
red
EH 2  E
0
RT ared

ln
nF
aox
H2
(half cell potential)
RT a H 2

ln
nF a H 
EH 2
aH 
RT
 0
ln
nF
pH 2 p 0
EH 2
2.303RT
RT
0

pH 
ln p H 2 p
F
2F


1
2
The Standard Hydrogen Electrode
Where :
a H   the activity of the hydrogen ions
pH 2  the partial pressure of the hydrogen gas
R  the universal gas constant
 the temperatu re in Kelvin
T
F  the Faraday constant (96,485.31)
p  the standard pressure 10 in Pa
0
5
Exchange Current Densities in 1 Molal H2SO4
Electrode Material
-log10(A/cm2
Palladium
3.0
Platinum
3.1
Rhodium
3.6
Nickel
5.2
Gold
5.4
Tungsten
5.9
Niobium
6.8
Titantium
8.2
Cadmium
10.8
Manganese
10.9
Lead
12
Mercury
12.3
The Standard Half Cell Potential

All other half cells can be compared to the SHE. A
half cell in its standard state is connected as the
cathode to the SHE connected as the anode.

The measured potential is called the standard half
cell potential, Eo.

This connection is made regardless of which half
cell may actually be anode or cathode, and will
result in negative values for some half cells.
The half cell reaction should always be shown as a
standard reduction potential.

Standard Half Cell Potential

Eo can be related to the tendency of the half cell to
reduce H+ (aq) (1 mol L-1 ) to H2 (g) (1 bar)
 The larger (more positive) the value of Eo, the more
favorable that process

The metal at the more negative potential is more
easily oxidised or corroded ‫متاكل‬.
The metal at the more positive potential is more
easily reduced.

Standard Half Cell Potentials






Consider the following half cell reduction reactions
Cu2+(aq) + 2e → Cu(s) E0red = +0.340 V
Zn2+(aq) + 2e → Zn(s) E0red = -0.763 V
Therefore copper will be reduced and zinc oxidised
Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s)
The voltage of the cell is:E0cell = 0.340 – (0.763) = 1.103V
Standard Half Cell Potentials
Concentration cells
Fe → Fe2+ + 2e
E red  E 0 red 
Ered


RT aRe d
ln
(half cell reduction potential)
nF aOx
0.0592
1
 0.44 
log
2
Fe 2


An iron electrode in a solution of 10-2M Fe2+ will have a potential of -0.56 V
and a similar electrode in 10-5M Fe2+ will have a potential of -0.74 volts.
If the electrodes were connected the cell with the lower concentration of Fe2+ would
corrode to produce more Fe2+ and the cell with a higher concentration of Fe2+ would
undergo reduction to decrease the Fe2+ concentration.



The reason the half cell reaction should be shown
as a standard reduction potential is that the
potential given will be the same as the potential
measured with a voltmeter.
A list of standard half cell reductions potentials is
given to enable you to predict reactions that will
occur.
Half cell oxidation potentials are given in tables.
For a particular half cell reaction the potential is
the same but opposite in sign to the corresponding
reduction potential. This is done for
thermodynamic reasons. However, it causes
confusion and since they are of no practical
benefit they can be ignored.
Non – Standard Half Cell Potentials

This could be measured for any half cell not in its standard state, connected
as the cathode to the SHE.
 We can calculate the non-standard half cell (equilibrium) potential
using the Nernst Equation:
RT
EE 
ln Q
nF
0
which is based on non - standard Free Energy
G  G0  RT ln Q
Non – Standard Half Cell Potentials






Where:
E = non-standard half cell potential
E0 = standard half cell potential
n = number of electrons in standard reduction
reaction
Q = reaction quotient for standard reduction
reaction.
Q, the reaction quotient has the same appearance as
the equilibrium constant, but does not necessarily
relate to equilibrium conditions.
Non – Standard Half Cell Potentials
 Non
standard cell potential can then be
calculated from the non standard half cell
potentials:
Ecell = Ecathode - Eanode
Key Thermodynamic Quantity
the entropy change

Another key thermodynamic quantity, the entropy
change, ΔS, can be determined from the variation of the
cell potential with temperature.
E
S  nF
T




Where:
ΔS = Entropy change, J K-1 mol-1
n = number of electrons transferred in the cell reaction
F = Faraday’s constant, 96485 C mol-1
Key Thermodynamic Quantity
the enthalpy change

After the entropy change is determined, the enthalpy change
can be determined from the fundamental thermodynamic
relationship

ΔG = ΔH – TΔS

Where:
ΔG = Gibbs Free Energy change, J mol-1
ΔH = Enthalpy change, J mol-1
ΔS = Entropy change, J K-1 mol-1




It can also be noted that the equilibrium potential, E, gives the
minimum free energy that will need to be supplied to an
electrolytic cell to force the cell reaction.
Standard Half Cell Potentials






Consider the following half cell reduction reactions
Cu2+(aq) + 2e → Cu(s) E0red = +0.340 V
Zn2+(aq) + 2e → Zn(s) E0red = -0.763 V
Therefore copper will be reduced and zinc oxidised
Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s)
The voltage of the cell E0cell = 0.340 – (0.763) =
1.103V
Galvanic Cell Cu/Cu2+ Zn/Zn2+
Cu
Zn
CuSO4
ZnCl2
Galvanic Cell Cu/Cu2+ Zn/Zn2+
Galvanic Cell Cu/Cu2+ Zn/Zn2+
Galvanic Cell Cu/Cu2+ Zn/Zn2+
Thermodynamic Properties of Ions in Solution
Enthalpy and Gibbs Energy

Enthalpy and Gibbs energy of formation Values of fHø and
fGø refer to formation of ions from reference state of
parent ions ‫االيونات االصلية‬
»
Individual enthalpies and Gibbs energies for ions not directly
measurable
»
Only measure overall reactions

Since H and G state functions, the overall reaction is the sum of
component reactions


Could measure a number of reactions with similar components and by
difference get fHø

Need to know one fHø however

Contributions can be seen by constructing a thermodynamic
cycle
»
»
»
Sum around cycle is zero (G is state function)
fGø of an ion includes contribution from dissociation, ionization
and solvation of hydrogen
All Gibbs energies except G of solvation estimated from standard
tables
 fGø of two ions is related to solvGø
fGø(Cl-, aq) = 1272 kJ mol-1 + solvGø(Cl-) + solvGø(H+)
 Can be estimated from Born equation
Born Equation Solvation Gibbs Energies

Solvation )‫الحلحلة(االذابه‬Gibbs energy estimated from the electrical
work required to transfer an ion to a solvent - Born Equation
» Solvent treated as a dielectric with permittivity, eG
» Good example of how work need not be PV work to calculate
Gibbs energies
z 2i e 2 N A
 s olvG  
8e 0 ri


1 

1




 e G 
where
z i  charg e of ion
ri  radius of ion
N A  Avagodro' s number
e 0  vacuum permitivity

For water, Born equation becomes
solGø = 6.86 x 104(zi2/ri) kJ mol-1
ri is radius in pm
»
Values turn out to be in reasonable agreement with experimental
Ion Activities Definition

The activity of a solution, a, is related to the chemical potential, µ
µ = µø + RTln(a)




Tend to associate activity with concentration (molality)
Its related but not equivalent
Replacement valid in very dilute solution (<10-3 mol/kg total ion concentration)
Given a solution whose ions behave ideally with a molality, bø of 1 mol/kg
a = g(b/bø)


g is the activity coefficient
 Depends on composition, concentration (molality) and temperature
 g1 and a b/bø as b  0
From [1]
µ = µø + RTln(b) + RTln(g)
where b = b/bø
»
µ = µideal + RTln(g)
µideal (= µø + RTln(b) ) is the chemical potential of an ideal dilute solution
of molality bhere b = b/bø
Mean Activity coefficients

Consider a solution of two monovalenent
cations (M+) and anions (X-)
 For ideal solution
G ideal
  ideal
  ideal
m


 For real solution
G ideal
  ideal
 RT ln g     ideal
 RT ln g  
m


G ideal
  ideal
  ideal
 RT ln g    RT ln g  
m


G ideal
  ideal
  ideal
 RT ln g  g  
m



Deviation from ideality contained in term RTln(g+ g-)
» Define (g+ -) = (g+ g-)0.5 (geometric mean)


Reflects fact you can’t really separate deviation from non-ideality
(g+ -) is the mean activity coefficient for monovalent ions
Then, µ+ = µ+ideal + RTln(g+-) and µ- = µ-ideal + RTln(g+-)
Generally for compound MpXq that dissolves into p cations and q anions, by same process
define mean activity coefficient as
(g+ -) = (g+ g-)1/s
where s = p + q
»



The chemical potential, µi, becomes µi = µi ideal + RTln(g+-)
And G becomes G = p µ+ + q µ Again non-ideality is shared
Estimating (g+ -)

Coulomb interactions imply oppositely charged ions attract each other
In solutions, near an ion counter ions are found (ionic atmosphere)
 Coulomb potential drops as 1/r: i = Zi/r
Zi a ionic charge
 G (& µ) of ion lowered by electrostatic interactions
 Since µi = µi ideal + RTln(g+-), lowering is associated with RTln(g+-)
»

- Debye-Hückel Theory
ln(g+-) can be calculated by modeling these interactions
Debye-Hückel Limiting Law (proof Justification 10.2):
»

zi is charged number on ions




»
»
Must sum all ions in solution
Sign of charge included, e.g, zNa+ = +1; zSO42- = -2
You’ll be using this in lab (Expt. 7, 9)
Works well at dilute solutions (b < 1 mmol/kg)
log g i    z  z  AI 0.5
for water A  0.509
I is ionic strength (dim ensionless )
I
1
2
 b 
 z 2i b  
i
0.5
 z  z  AI
Extended Debye-Hückel Limiting Law (1 mmol/kg <b < 0.1 mol/kg):
log g    
 B dimensionless const., adjustable empirical parameter
1  BI 0.5
b>0.1 mol/kg (e.g. sea water): Model dependence of g of solvent on solute and use
Gibbs-Duhem equation (SnJdµJ) = 0 to estimate g of solute
Estimating (g+ -)
- Debye-Hückel Theory
Ionic Strength and Molality
I = k (b/bø)
k
M+
M2+
M3+
M4+
X1
3
6
10
X23
4
15
12
X36
15
9
42
X410
12
42
16
Limiting Law vs. Ionic Strength
Electrochemical Cells
Electrochemical cell - two electrodes in contact with an
electrolyte
» Electrolyte is an ionic conductor (solution, liquid, or
solid)
» Electrode compartment = electrode + electrolyte
 If electrolytes are different compartments may be
connect with salt bridge
 Electrolyte solution in agar
 Galvanic cell - an electrochemical cell that produces
electricity
Electrolytic cell - an electrochemical cell in which a nonspontaneous reaction is driven by an external source of
current


Types of Electrodes

Metal/metal ion (a)
»
Designation:M(s)|M+(aq)
»
Redox couple: M+ /M
»
Half reaction: M+(aq) + 1e-  M(s)

Gas (b)
»
»
»

Metal/insoluble salt (c)
»
»
»

Designation*:
Pt(s)|X2(g)|X+(aq) or Pt(s)|X2(g)|X-(aq)
Redox couple:
X+ /X2 or X2 / XHalf reaction:
X+(aq) + 1e-  1/2X2(g) or 1/2X2(g) + 1e- X-(aq)
Designation:M(s)|MX(s)|X-(aq)
Redox couple: MX /M,XHalf reaction: MX(s) + 1e-  M(s) + X-(aq)
Redox (d)
»
»
»
Designation*: Pt(s)| M+(aq), M2+(aq)
Redox couple: M+/M2+
Half reaction: M2+(aq) + 1e-  M+(aq)
*Inert metal (Pt) source or sink of e-
Half-Reactions

Recall definition of redox:
»
Redox reaction is one involving transfer of electrons

OILRIG




»

Oxidation is loss of electrons
Reduction is gain of electrons
Reducing agent (reductant) is electron donor
Oxidizing agent (oxidant) is electron acceptor
Any redox reaction can be expressed as the difference of two reduction half
reactions (sum of oxidation and reduction half reaction)
Cu2+(aq) + 2e-  Cu (s)
Zn2+(aq) + 2e-  Zn (s)
(copper - zinc):
Cu2+(aq) + Zn (s)  Cu (s) + Zn2+(aq)
Redox couples are the reduced and oxidizing species in a redox reaction
»
Written Ox/Red for half reaction Ox + ne-  Red
 Example above: Cu2+/Cu; Zn2+/Zn
Half Reactions

Reaction quotient for half-reaction (Q)
»
Like reaction quotient for overall reaction (activity of product over activity reactant raised to
appropriate power for stoichiometry) except electrons omitted
 Cu2+(aq) + 2e-  Cu (s)
Q = 1/aCu {Metal in standard state aM = 1}
 O2(g) + 4H+(aq) + 4e-  2H2O (l)
aH O
1
pø
pø
Q


 4

 a 4 fO
a H pO
4  fO
4  fO
H
a H 
ø  a H 
ø 
 p 
 p 
O2 assumed to be ideal gas
2


2

2


2
Redox couples in an electrochemical cell separated in space
»
»
Oxidation in one compartment, reduction in another
Oxidation compartment


»
Red1 Ox1 + neElectrode at which this occurs is the cathode
Reduction compartment


Ox2 + ne- Red2
Electrode at which this occurs is the anode
2
Half Reactions

Galvanic cell (produces electricity)
»
»
»

Cathode at higher potential than anode
Species being reduced withdraws electrons
from cathode giving it a relative (+) charge
Species being oxidized deposits electrons
in anode giving it a relative (-) charge
Electrolytic cell(electricity supplied)
»
Oxidation still occurs at anode

Galvanic Cell


»
Oxidation doesn’t occur spontaneously
Electrons come from the species in that
compartment
Anode relatively positive to cathode
Cathode

Supply of electrons drives reduction
Electrolytic Cell
Types of Cells


Commonest cell has single electrolyte in
contact with both electrodes
Daniel cell - electrode compartments
separated
»
Different electrolyte in each compartment
 Electrolyte concentration cell - same
electrolyte, different concentration
 Electrode concentration cell electrodes have different concentration


»
Daniel Cell
Gas cells at different pressures
Amalgams at different cocentrations
Additional potential difference across
interface of two electrolytes - liquid
junction potential
 Present in electrolyte concentration
cells
 Due to differing mobility of ions of
different sizes across interface
 Can be reduced with salt bridge

Potential is then independent of
concentration of electrolyte solution
Cell Reactions

Notation - overall cell reaction denoted by cell diagram
»
»
»

Cell Reactions: reaction occurring in the cell with the right-hand as the cathode
Zn(s) | ZnSO 4 (aq) || CuSO 4 (aq) | Cu(s)
(spontaneous reduction)
»

Phase boundary denoted by single vertical line (|)
Pt(s) | H 2 (g) | HCl(aq) | AgCl (s) | Ag
Liquid junction denoted by single vertical dotted line (:)
Zn(s) | ZnSO 4 (aq) CuSO4 (aq) | Cu
Daniel cell
Interface with no junction potential double verticla line (||)
Pt(s) | H 2 (g) | HCl(aq, b1 ) || HCl(aq, b 2 ) | H 2 (g) | Pt(s)
Salt bridge
To write cell reaction:
2

1. Write r.h.s. as reduction
Cu (aq)  2e  Cu(s)
2

Zn (aq)  2e  Zn(s)
2. Write l.h.s. as reduction
2
2
3. Subtract 2 from 1
Cu (aq)  Zn  Cu(s)  Zn (aq)
Cell Potential - electrical work that can be done through the transfer of electrons in a cell
»
»
»
Depends on the potential difference between electrodes
If overall reaction at equilibrium cell potential is zero
If reaction spontaneous, w is negative. At constant p and T
we,max = G
 Work is maximum only if cell is operating reversibly
 G is related to composition, work is reversible @ constant composition, i.e., no current
 Under these conditions the potential difference is the electromotive force (emf) of the cell, E
Cell Reactions: Relation between E and rG
Assume cell rxn where concentration changes by d
(  extent of rxn)

@ const. T and p
dG 
  J dn J   n J  J d J
J
J
For a reversible cell, the Gibbs energy of
reaction, rG, is proportional to the cell
potential,
rG = -nFE
But,
G 
 r G    
 p,T
n JJ
where n is the number of electrons
transferred and F is Faraday’s constant
J
so dG   r Gd
max imum non  expansion electrical work, w e
w e  dG   r Gd
 Proof
[1]
when this occurs nd electrons move from anode to cathode
charg e transported  (# e  )  (charg e / mole e  )  nd  eN A 
But
eN A  Faraday' s cons tan t  F
so ch arg e transported  nFd
Electrical work  charg e  potential  nFd  E
Substituting int o [1]
nFd  E   r Gd
or
 r G  nFE
»
»
When potential is high, rG is negative
and cell reaction is spontaneous
The emf (driving power of cell) is related
to the extent of reaction
Nernst Equation:
Relationship of emf(electro motivation force) to Activity

Recall that the Gibbs energy of reaction is related to
composition:
rG = rGø + RTlnQ
where Q is reaction quotient(anJproducts/anJreactants)

Since rG = -nFE
E = -(rGø/nF) - (RT/nF)lnQ
»

Define -(rGø/nF) as Eø, the standard emf of the cell
So, E = Eø - (RT/nF)lnQ
»
(Nernst Equation)
Eø is the emf when all reactants and products are in their
standard states

»
Nernst Equation indicates a plot of E vs. ln Q will have
 Slope = -(RT/nF)

»
aproducts = 1 and areactants = 1, so Q=1 and ln(Q) = 0
Intercept = Eø
At 25°C, RT/F = 0.0257 mV, Nernst equation becomes
E = Eø - (0.0257 V/nF)lnQ
Nernst Equation:
Concentration Cells
M|M+(aq, L)|| M+(aq, R)|M

In above cell the only difference is the concentration of electrolyte in each cell
»
»

Left cell - molality is L; right cell - molality is R
Cell reaction: M+(aq, R)  M+(aq,L)
 n is 1
 Eø is 0 because when R=L the two compartments are identical and no driving
force
Nernst Equation: E = Eø - (RT/nF)lnQ
»
In this case: E = - (RT/F)ln(aL/aR) = - (RT/F)ln(bL/bR)
 If R>L, ln(bL/bR)<0, E>0, concentration will be lowered by reduction in right
compartment
 If L>R, ln(bL/bR)>0, E<0, concentration will be lowered by reduction in left
compartment
 This has biological application - nerve firing involves change in permeability of
cell membrane to Na+ This changes nerve cell potential.
Nernst Equation:
Equilibrium Cells

At equilibrium, by definition no work can be done
»
»
E=0
Concentrations are fixed by the equilibrium constant(K)
K=Q
Nernst Equation: E = Eø - (RT/nF)lnQ


»
»
In this case: E = 0 so Eø = (RT/nF)lnQ = (RT/nF)lnK
Rearranging,
lnK = Eø/ (RT/nF) = nFEø/ RT
or
K = exp(nFEø/ RT)

This means cell potentials can be used to determine equilibrium
constants
Standard Potentials

Since you can’t measure the potential of a single electrode, one pair has been assigned, by
convention a potential of 0
»

Standard hydrogen electrode (SHE):

Pt(s) | H2 (g) | H (aq)
ø
E 0
Other potentials determined by constructing cells in which SHE is left hand electrode:
»
Silver Chloride|Silver
Pt(s)|H2(g)|H+(aq)||Cl-(aq)|AgCl(s)|Ag
Eø(AgCl, Ag, Cl-)=+0.22V
Reaction: AgCl(s) + 1/2H2(g)  Ag(s) + H+(aq) + Cl-(aq)

Because all potentials are relative to the hydrogen electrode, the reaction is listed without the contribution
of the SHE,
AgCl(s)  Ag(s) + Cl-(aq)

Numerical factors
» If std emf reaction is multiplied by numerical factor, rG increases by that factor
» Standard potential does not increase!
Recall Eø = -(rGø/nF)
If rGø(new) = n x rGø, n(new) = n x n

Eø (new) = -(rGø(new) / n(new) F) =-(n x rGø /n n(new) F)= -(rGø/nF) = Eø
Cell emf & Standard Potentials

Cell emf of any cell can be calculated from table of standard
potentials
emf of cell is just difference in standard potential
Sc(s)|Sc3+(aq)||Al3+(aq)|Al(s)
Procedure:
»
»
1) Write new cell diagram
2) Eø = Eø(right) - Eø(left)
»
Al3+(aq) + 3e-  Al(s) Eø = 1.69 V
Sc3+(aq) + 3e-  Sc(s) Eø = -2.09 V
Al3+(aq) + Sc(s) Sc3+(aq) +Al
Eø = 1.69 V - (-2.09 V) = 3.78V
Recall: Eø = -(rGø/nF)

If Eø > 0, rGø < 0 and K>1

Example above, at 25°C,
K = exp(nFEø/ RT) = exp (3 x 3.78V/0.0257V)
= exp(441) = 4.27 x 10191
K = [Sc3+]/[Al3+]
Measuring Standard Potentials
Harned Cell
Pt(s) | H 2 (g) | HCl(aq) | AgCl(s) | Ag(s)
reaction :
1
H 2 (g)  AgCl(s)  HCl(aq)  Ag(s)
2
From Nernst Equation
E = E°(AgCl/Ag,Cl-) - (RT/F)ln Q
E = E°- (RT/F)ln ((aH+ aCl-)/(fH2/pØ)0.5
= E°- (RT/F){ln (aH+ aCl-) -ln(fH2/pØ)0.5 }

Let fH2= pØ.
E = E°- (RT/F)ln (aH+ aCl-)
But a =bg ± and bH+= bCl-) so
E = E°- (RT/F)ln (b2g ± ) = E°- (RT/F)ln (b2) - (RT/F)ln (g
= E°- (2RT/F)ln(b) - (2RT/F)ln(g ±)
±
2)
Debye-Hückel Limiting Law log(g ±) aI0.5 so log(g ±) ab0.5 or ln(g ±) ab0.5
»
E = E°- (2RT/F)ln(b) + Cb0.5
or
E + (2RT/F)ln(b) = E° + Cb0.5
»
This means a plot of {E + (2RT/F)ln(b)} vs. b0.5 has Eø as intercept


Measuring activity coefficients
»
Since E = E°- (2RT/F)ln(b) - (2RT/F)ln(g ±) , ln(g ±) = {(Eø - E)/(2RT/F)}- ln(b)
 Knowing Eø and measuring E at known molality allows you to calculate activity coefficient
Applications of Standard Potential


Electrochemical series
Because Eø = -(rGø/nF), if Eø > 0,
rGø < 0
»
»
»
Since Eø = Eø2 - Eø1 , the reaction is
spontaneous as written
Red1 has tendency to reduce Ox2 ,More
Reducing
if Eø1 <Eø2
More directly in the electromotive
series elements arranged such that
low on the chart reduces high




Calcium reduces platinum (Eø =
4.05 V)
Platinum reduces gold (Eø = 0.51)
Tin reduced lead (Eø = 0.011 V)
Sodium reduces magnesium (Eø =
0.34 V)
Element
Gold
Chlorine
Platinum
Pall adium
Sil ver
Copper
Copper
Iron
Lead
Tin
Nickel
Cobalt
Cadmium
Iron
Zinc
Manganes e
Alumi num
Magnes ium
Sodium
Calcium
Potassium
Reaction
Au + e-  Au
Cl2(g) + 2 e-  2 ClPt2+ + 2 e-  Pt
Pd2+ + 2 e-  Pd
Ag + + e-  Ag
Cu+ + e -  Cu
Cu2+ + 2 e-  Cu
Fe3+ + 3 e-  Fe
Pb2+ + 2 e-  Pb
Sn2+ + 2 e-  Sn
Ni2+ + 2 e-  Ni
Co2+ + 2 e-  Co
Cd2+ + 2 e-  Cd
Fe2+ + 2 e-  Fe
Zn2+ + 2 e-  Zn
Mn2+ + 2 e-  Mn
Al3+ + 3 e-  Al
Mg2+ + 2 e-  Mg
Na+ + e-  Na
Ca2+ + 2 e-  Ca
K+ + e-  K
+
Eæ(V)
1.692
1.35827
1.18
0.951
0.7996
0.521
0.3419
-0.037
-0.1262
-0.1375
-0.257
-0.28
-0.403
-0.447
-0.7618
-1.185
-1.662
-2.372
-2.71
-2.868
-2.931
More
Oxidzing
pH and pKa

Glass Electrode

H (aq) 1e 



2
aH


E = Eø - (RT/nF) lnQ
Converting ln to log (ln =2.303log), E = (RT/F) 2.303log(aH+)
Define pH=-logaH so E = -2.303(RT/F)pH

At 25°C, E= -59.16mVpH
Measurement
»
Direct method: hydrogen electrode + saturated calomel reference electrode (Hg 2Cl2)

»
At 25°C, pH = (E + E(calomel))/ (-59.16mV )
Indirect method:

Replace hydrogen electrode with glass electrode sensitive to hydrogen activity (but not permeable to H+

E(glass) a pH, E(glass) = 0 when pH = 7
pKA
»


0.5
If fH2= pø, Q = 1/aH+ and E = (RT/F) ln(aH+)


Q
pø
For hydrogen electrode (1/2 reaction above), Eø = 0
»

1
H (g)
2 2
fH
Since we learned pH = pKa when concentration of acid and conjugate base are equal pKa can
be measured directly from pH measurement
Ion-Selective electrodes - related to glass electrode except potentials sensitive to other
species
Electrochemical Cells and Thermodynamic
Functions

Since the standard emf of a cell is related to the Gibbs energy, electrochemical
measurements can be used to obtain other thermodynamic functions
»
»

Complementary to calorimetric measurements
Esp. useful for ions in solutions (aqueous, molten salts, etc.)
Starting point: rGø = -nFEø and thermodynamic relationships we saw earlier
»
»
»
rGø can be used to calculate Eø directly (or reverse)
Entropy (S)
 Thermodynamic relationship: (∂G/∂T)p =-S
rGø = -nFEø
At constant p,
(dGø/dT) =-nF(dEø/dT)
-S =-nF(dEø/dT)
or
(dEø/dT) =S/nF
Enthalpy
 Thermodynamic relationship: rHø = rGø + T rSø
rHø = -nFEø + T(nF(dEø/dT))
rHø =-nF(Eø - TdEø/dT)