Download Equilibrium Electrochemistry

ERT 108 Physical Chemistry
Semester II Sidang 2010/2011
1
Subtopics
 Half-Reactions and Electrodes
 Varieties of Cells
 The Cell Potential
 Standard Potentials
 Applications of Standard Potentials
 Impact on Biochemistry:
Energy Conversion in Biological Cells
ERT 108 Physical Chemistry
Semester II Sidang 2010/2011
2
Equilibrium Electrochemistry
 An electrochemical cell consists:
 two electrodes (or metallic conductors)
 an electrolyte (an ionic conductor – may be a
solution, a liquid or a solid).
 An electrode & its electrolyte comprise an electrode
compartment.
 two electrodes may share the same compartment
 if the electrodes are different, the two compartments
may be joined by a salt bridge [a tube containing a
concentrated electrolyte solution (potassium chloride in
agar jelly)] that completes the electrical circuit &
enables the cell to function.
ERT 108 Physical Chemistry
Semester II Sidang 2010/2011
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Equilibrium Electrochemistry
 A galvanic cell is an electrochemical cell that
produces electricity as a result of the spontaneous
reaction occurring inside it.
 A electrolytic cell is an electrochemical cells in which
a non-spontaneous reaction is driven by an external
source of current.
ERT 108 Physical Chemistry
Semester II Sidang 2010/2011
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Half-Reactions and electrodes
 Oxidation – the removal of electrons from a species.
 Reduction – the addition of electrons to a species.
 Redox reaction – transfer of electrons from one species
to another.
 Reducing agent (reductant) – the electron donor.
 Oxidizing agent (oxidant) – the electron acceptor.
 Any redox reaction (or even not redox reaction) may be
expressed as the difference of two reduction halfreactions.
 Half-reactions – conceptual reactions showing the gain
of electrons.
 the reduced & oxidized species in half-reaction form a
redox couple.
ERT 108 Physical Chemistry Semester II Sidang 2010/2011
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Example 1
 Express the following reactions in terms of reduction
half-reactions.
a) The dissolution of silver chloride in water:


AgCl(s)  Ag (aq)  Cl (aq)
(Note: it is not a redox reaction.)
b) The formation of H2O from H2 and O2 in acidic
solution.
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Reaction quotient, Q
 Useful to express the composition of an electrode
compartment in terms of the reaction quotient, Q for
the half reaction.
 The reaction quotient, Q has the form
Q= activities of products/activities of reactants
with each species raised to the power given by its
stoichiometric coefficient.
 Q is defined as
ERT 108 Physical Chemistry
Semester II Sidang 2010/2011
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 Consider the reaction 2A + 3B  C + 2D, in which case
vA= -2, vB= -3, vC= +1 and vD= +2. the reaction quotient is
then
 Example:
The reaction quotient for the reduction of O2 to H2O in
acid solution O2(g) + 4H+ (aq) + 4e-  2H2O (l) is
The approximations used in 2nd step ate that the activity
of water is 1 (because the solution is dilute) and the
oxygen behaves as perfect gas, so aO2 ≈pO2/p.
ERT 108 Physical Chemistry
Semester II Sidang 2010/2011
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Half-Reactions and electrodes
 Anode:
 the electrode at
which the
oxidation occurs.
(-): removal of e-.
 Cathode:
 the electrode at
which the
reduction occurs.
(+): addition of e-.
ERT 108 Physical Chemistry
Semester II Sidang 2010/2011
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Half-Reactions and electrodes
ERT 108 Physical Chemistry
2010/2011
Semester II Sidang
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Varieties of cells
 In an electrolyte concentration cell- the electrode
compartments are identical except for the
concentrations of electrolytes.
 In an electrode concentration cell- the electrodes
themselves have different conc, either because they are
gas electrodes operating at different pressures or
because they are amalgams (sol in mercury) with
different concs.
ERT 108 Physical Chemistry
Semester II Sidang 2010/2011
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Varieties of Cells
 Daniel cell:
 the redox couple
at one electrode is
Cu2+/Cu and at the
other is Zn2+/Zn.
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Liquid junction potentials
 Liquid junction potentials (Elj):
 an additional source of potential difference across the
interface of the two electrolytes.
 E.g. In the Daniel cell
(i) two different electrolyte solutions are in contact,
(ii) different concentration of hydrochloric acid- At the
junction, the mobile H+ ions diffuse into the more dilute
solution. The bulkier Cl- ions follow, but initially do so
more slowly- results in a potential difference at the
junction. The potential then settles down to a value such
that, after brief initial period, the ions diffuse at the same
rates.
 The contribution of the liquid junction to the potential can
be reduced by joining the electrolyte compartments
through a salt bridge.
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Liquid junction potentials
Galvanic cell without
liquid junction.
ERT 108 Physical Chemistry
Galvanic cell with liquid
junction.
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Notation
1) Phase boundaries are denoted by a vertical bar.
2) A liquid junction is denoted by 
3) Interface is denoted
by a double vertical line ||. For which
It is assumed that the junction potential
has been eliminated
 Fig 1:
 Zn (s)|ZnSO4 (aq) CuSO4 (aq) |Cu (s)

Fig 1
 Fig 2:
 Zn (s)|ZnSO4 (aq)||CuSO4 (aq) |Cu (s)
ERT 108 Physical Chemistry
Semester II Sidang 2010/2011
Fig 2
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The cell potential
 The cell reaction corresponding to a cell diagram:
1st : write the right hand half-reaction as a reduction
(cathode)
(Assumption: spontaneous reaction).
2nd : subtract from it the left-hand reduction halfreaction.
(By implication, the electrode is the site of oxidation)
In the cell:
Zn(s)|ZnSO4(aq)||CuSO4(aq)|Cu(s)
Right-hand electrode: Cu2+(aq)+2eLeft-hand electrode: Zn2+(aq)+2eOverall cell reaction: Cu2+(aq)+ Zn(s)
ERT 108 Physical Chemistry
Cu(s)
Zn(s)
Cu(s) +Zn2+(aq)
Semester II Sidang 2010/2011
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The Nernst equation
 A cell in which the overall cell reaction has not reached
chemical equilibrium can do electrical work as the
reaction drives electrons through an external circuit.
 the work that a given transfer of electrons can
accomplish depends on the potential difference
between the two electrodes.
 This potential differences is called the cell potential
and is measured in volts, V (1 V = 1 JC-1 s).
 A cell in which the overall reaction is at equilibrium
can do no work, & then the cell potential is zero.
ERT 108 Physical Chemistry
Semester II Sidang 2010/2011
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The Nernst equation
 When expressed in
terms of a cell potential,
the spontaneous
direction of change can
be expressed in terms of
the cell emf.
 the reaction is
spontaneous when E>0.
 the reverse reaction is
spontaneous when E<0.
 when the cell reaction is
at equilibrium, the cell
potential is zero.
ERT 108 Physical Chemistry
Semester II Sidang 2010/2011
Note: The potential difference is called the
electromotive force (emf), E
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 The resulting potential difference is call cell potential,
Ecell. The relation between the reaction Gibbs energy
and the cell potential is:
-vFEcell = rG
F is Faraday’s constant, F = eNA
v is the stoichiometric coefficient of electrons in halfreactions.
 By knowing the reaction Gibbs energy at a specified
composition- we can state the cell potential at that
composition.
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Semester II Sidang 2010/2011
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The Nernst equation
 The Nernst equation relates the cell’s potential (E)
to the activities ai of the substances in the cell’s
chemical reaction & to the standard cell potential of
the cell (E Ѳ)(the cell’s chemical reaction).

RT
rG
RT
EE 
ln Q  

ln Q
F
F
F

 where F = Faraday constant, F=eNA
v = the stoichiometric coefficient of the electron
in the half-reactions.
v


Q

'
a
 i
Q = the reaction (or activity) quotient ,
i
i
ERT 108 Physical Chemistry
Semester II Sidang 2010/2011
20
The Nernst equation
 A practical form of the Nernst equation is
25.7mV
EE 
ln Q
v

 because at 250c,
RT
 25.7 mV
F
ERT 108 Physical Chemistry
Semester II Sidang 2010/2011
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Cells at equilibrium
 Suppose the reaction has reached equilibrium; then Q
= K (K= the equilibrium constant of the cell reaction).
 A chemical reaction at equilibrium cannot do work, &
hence it generates zero potential difference between
the electrodes of a galvanic cell.
 Setting E=0, Q=K:
 the Nernst equation:
vFE cell
ln K 
RT
ERT 108 Physical Chemistry
Semester II Sidang 2010/2011
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Example 2
 Three different galvanic cells have standard cell
potential (EѲ) of 0.01, 0.1 and 1.0V, respectively, at
250C.
 Calculate the equilibrium constants (K) of the
reactions that occur in these cells assuming the
charge number (v) for each reaction is unity.
ERT 108 Physical Chemistry
Semester II Sidang 2010/2011
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Standard Electrode Potentials
 A galvanic cell is a combination of two electrodes, & each
one can be considered as making a characteristics
contributions to the overall cell potential.
 although it is not possible to measure the contribution
of a single electrode, we can define the potential of one
of the electrodes as zero & then assign values to others on
that basis.
 the specially selected electrode is the standard
hydrogen electrode (SHE): Pt(s)|H2(g)|H+(aq),
EѲ=0 (at all temperatures).
ERT 108 Physical Chemistry
Semester II Sidang 2010/2011
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Standard Potentials
 To achieve the standard
conditions, the activity of the
hydrogen ions must be 1
(pH=0) & the P of the
hydrogen gas must be 1 bar.
 The standard potential (EѲ) of
another couple is then
assigned by constructing a
cell in which it is the righthand electrode & the
standard hydrogen electrode
(SHE) is the left-hand
electrode.
ERT 108 Physical Chemistry
Semester II Sidang 2010/2011
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 The procedure for measuring a standard potential can
be illustrated by considering a specific case, the silver
chloride electrode:
 ½ H2(g) + AgCl(s)  HCl (aq) + Ag(s)
 Ecell = E(AgCl/Ag, Cl-) – E(SHE) = E(AgCl/Ag,Cl-)
 For which the Nernst equation is
 We shall set aH2 = 1 from now on, and for simplicity
write the standard potential of the AgCl/Ag, Clelectrode as E, then
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 The activities can be expressed in terms of the molality
b of HCl (aq) through aH = b/b and aCl = b/b, so:
+
-
 Where for simplicity, b/b is replaced by b. this
expression rearranges to
ERT 108 Physical Chemistry
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The Debye-Huckel limiting law
 Theory to calculate activity coefficients of electrolyte
solutions
 Activities rather than conc are needed in many chemical
calculations because solutions that contain ionic solutes do
not behave ideally even at very low conc.
 Debye-Huckel limiting law:
 Where A= 0.509 for an aqueous solution at 25oC and I is the
dimentionless ionic strength of the solution:
 zi- charge no of ion i (+ve for cations and –ve for anions)
 bi- molality
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Standard Potentials
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Example 3
 Consider the following galvanic cell:
2
2
Zn(s) | Zn (aq)Cu (aq) | Cu(s)
 What is:
(a) the cell reaction?
(b) the standard potential of the cell?
(c) The equilibrium constant?
> Table 9.1
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Application of standard potentials
 The more positive E0 is, the greater the tendency for
the substance to be reduced – e.g. Fluorine, F2
 Li + is the weakest oxidizing agent because it is the
most difficult species to reduce – it has the most
negative E0.
 Under standard-state conditions, any species on the
left of a given half-cell reaction will react
spontaneously with a species that appears on the right
of any half-cell reaction
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Application of standard potentials
 In the Daniel cells:
Cu2+(aq)+2eZn2+(aq)+2e-
Cu(s) E0=0.34V
Zn(s) E0= - 0.76V
 Zn spontaneously reduces Cu2+ to form Zn2+ and Cu.
 Standard potential of a cell, Ecell
Ecell = E(right)- E(left)
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Impact on Biochemistry:
Energy Conversion in Biological Cells.
 The whole of life’s activities depends on the coupling of
exergonic & endergonic reactions, for the oxidation of
food drives other reactions forward.
 In biological cells, the energy released by the oxidation
of foods is stored in adenosine triphosphate (ATP).
 the essence of the action of ATP is its ability to lose its
terminal phosphate group by hydrolysis & to form
adenosine diphosphate (ADP).
ATP(aq)  H 2O(l )  ADP (aq)  Pi  aq   H 3O  (aq)
where Pi denotes an inorganic phosphate group e.g. H2SO4.
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Impact on Biochemistry:
Energy Conversion in Biological Cells.
 Examples:
 Glycolysis – the oxidation of glucose to CO2 and H2O
by O2 (the breakdown of foods is coupled to the
formation of ATP in the cell).
 Glycolysis is the main source of energy during
anaerobic metabolism, a form of metabolism in which
inhaled O2 does not play a role.
 The citric acid cycle & oxidative phosphorylation
are the main mechanisms for the extraction of energy
from carbohydrates during aerobic metabolism (in
which inhaled O2 does play a role).
ERT 108 Physical Chemistry
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Answer (Example 1)
a)
The two reduction half-reactions:
AgCl(s)  e  Ag (s)  Cl aq 


Ag  (aq)  e  Ag (s)
The redox couples are AgCl/Ag, Cl- & Ag+/Ag.
b) The two reduction half-reactions:
4H  aq   4e   2H 2 g 
O2 g   4H  aq   4e   2H 2Ol 
The redox couples are H+/H2 & O2,H+/H2O
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ERT 108 Physical Chemistry
Semester II Sidang 2010/2011
Answer (Example 2)
 For EѲ = 0.01V,
K e
vFE 
RT

196 486 J / V 0.01V 
 exp
8.3145 J K 1 mol 1 298.15K 
= 1.476
 For EѲ = 0.1V, K = 49.0
 For EѲ = 1.0V, K = 8.02 x 1016
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Answer (Example 3)
(a) & (b)
Right-hand electrode: Cu2+(aq)+2eLeft-hand electrode: Zn2+(aq)+2eOverall cell reaction:Cu2+(aq)+ Zn(s)
(c) The equilibrium constant:
K e
vFE 
RT

296 486 J / V 1.10V 
 exp
8.3145 J K 1 mol 1 298.15K 
K = 1.80 x 1037
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Cu(s) E0=0.34V
Zn(s) E0= - 0.76V
Cu(s) +Zn2+(aq)
E0 = 0.34 – (-0.76) V
E0 = 1.10 V
ERT 108 Physical Chemistry
Semester II Sidang 2010/2011