Dr. Marc Madou, UCI, Winter 2015 Class II Thermodynamics of
Electromotive Force (II) Electrochemistry MAE-212
Slide 2
Table of Content Standard Redox Potentials Table Thermodynamics
E cell, G, and K eq Derivation of the Nernst Equation Some example
problems Structure of the solid/electrolyte interface
Slide 3
E 0 is for the reaction as written The more positive E 0 the
greater the tendency for the substance to be reduced The half-cell
reactions are reversible The sign of E 0 changes when the reaction
is reversed Changing the stoichiometric coefficients of a half-cell
reaction does not change the value of E 0 (Intrinsic vs extrinsic
properties) Standard Redox Potentials Table
Slide 4
The free energy function is the key to assessing the way in
which a chemical system will spontaneously evolve. In the
Gibbs-Duhem formalism of the Gibbs free energy we can write:
constant T constant P dont change shape dont stretch it Relation
between Equilibrium constant, Gibbs free energy and EMF of a
cell
Slide 5
Every substance has a unique propensity to contribute to a
systems energy. We call this property Chemical Potential: When the
substance is a charged particle (such as an electron or an ion) we
must include the response of the particle to an electrical field in
addition to its Chemical Potential. We call this the
Electrochemical Potential (F is the Faraday constant, z the charge
on the particle and the potential): = + z F
Slide 6
Relation between Equilibrium constant, Gibbs free energy and
EMF of a cell The chemical potential or electrochemical potential
(if we are dealing with a charged particle) is the measure of how
all the thermodynamic properties vary when we change the amount of
the material present in the system. Formally we can write:
Integration of the expression for the dependence of amount of
material on the Gibbs function, leads to the following relationship
:
Slide 7
Relation between Equilibrium constant, Gibbs free energy and
EMF of a cell The internal energy is a natural function of entropy
and volume, U(S,V). The Helmholtz free energy is a natural function
of temperature and volume, A(T,V). We can also consider the
enthalpy, H as a natural function of entropy and pressure and the
Gibbs free energy as a natural function of temperature and
pressure, G(T,P).
Slide 8
Relation between Equilibrium constant, Gibbs free energy and
EMF of a cell Start with the First Law of Thermodynamics and some
standard thermodynamic relations and we find: And therefore, the
Gibbs function is at the heart of electrochemistry, for it
identifies the amount of work we can extract electrically from a
system. And therefore, the Gibbs function is at the heart of
electrochemistry, for it identifies the amount of work we can
extract electrically from a system.
Slide 9
Relation between Equilibrium constant, Gibbs free energy and
EMF of a cell Now we can easily see how this Gibbs function relates
to a potential. By convention, we identify work which is negative
with work which is being done by the system on the surroundings.
And negative free energy change is identified as defining a
spontaneous process. By convention, we identify work which is
negative with work which is being done by the system on the
surroundings. And negative free energy change is identified as
defining a spontaneous process. Note how a measurement of a cell
potential directly calculates the Gibbs free energy change for the
process. Note how a measurement of a cell potential directly
calculates the Gibbs free energy change for the process.
Slide 10
Relation between Equilibrium constant, Gibbs free energy and
EMF of a cell The propensity for a given material to contribute to
a reaction is measured by its activity, a. How active is this
substance in this reaction compared to how it would behave if it
were present in its standard state? Activity scales with
concentration or partial pressure. a C/C (solution) and a P/P (gas)
BUT intermolecular interactions deviations from a direct
correspondence with pressure or concentration
Slide 11
Relation between Equilibrium constant, Gibbs free energy and
EMF of a cell Definition of activity is then: Activity coefficients
close to 1 for dilute solutions and low partial pressures. Activity
coefficients close to 1 for dilute solutions and low partial
pressures. Activity changes with concentration, temperature, other
species, etc. Can be very complex. Activity changes with
concentration, temperature, other species, etc. Can be very
complex. Generally, we ignore activity coefficients for educational
simplicity, but careful work always requires its consideration.
Generally, we ignore activity coefficients for educational
simplicity, but careful work always requires its
consideration.
Slide 12
Relation between Equilibrium constant, Gibbs free energy and
EMF of a cell How does chemical potential change with activity?
Integration of the expressions for the dependence of amount of
material on the Gibbs function, leads to the following relationship
:
Slide 13
Relation between Equilibrium constant, Gibbs free energy and
EMF of a cell How does Gibbs free energy change with
concentration/activity? Same dependence as for the chemical
potential: When we apply this to a reaction, the reaction quotient
comes into to play, giving us: Say we have the reaction :
Slide 14
Relation between Equilibrium constant, Gibbs free energy and
EMF of a cell The above reaction is a generic reaction and in order
to analyze this chemical process mathematically, we formulate the
reaction quotient Q: It always has products in the numerator and
reactants in the denominator It explicitly requires the activity of
each reaction participant. Each term is raised to the power of its
stoichiometric coefficient.
Slide 15
Relation between Equilibrium constant, Gibbs free energy and
EMF of a cell- Nernst Equation Take the expression for the Gibbs
dependence on activity and rewrite this in terms of cell potential:
The relation between cell potential E and free energy gives:
Rearrange and obtain the Nernst Equation:
Slide 16
Relation between Equilibrium constant, Gibbs free energy and
EMF of a cell- Nernst Equation The equation is often streamlined by
restricting discussion to T = 25 C and inserting the values for the
constants, R and F. Note the difference between using natural
logarithms and base10 logarithms. Be aware of the significance of n
the number of moles of electrons transferred in the process
according to the stoichiometry chosen.
Slide 17
Relation between Equilibrium constant, Gibbs free energy and
EMF of a cell - Chemical Equilibrium This special Q* (the only one
for which we achieve this balance) is renamed K eq, the equilibrium
constant. The reaction proceeds, Q changes, until finally G=0. At
that moment the overall reaction stops. This is equilibrium.
Slide 18
When the system is at equilibrium, the proper quotient of
equilibrium concentrations is equal to the equilibrium constant:
The system is at equilibrium when the concentrations are in their
equilibrium values, so [A] = [A] e, [B] = [B] e, etc. and thus: Q*
= K eq Relation between Equilibrium constant, Gibbs free energy and
EMF of a cell -Chemical Equilibrium
Slide 19
Slide 20
Example problems: Cu is cathode (it is reduced). Zn is anode
(it is oxidized). Note that n=2 for this reaction. =1 Activity for
solid materials is 1; replace activities with concentrations.
Slide 21
Example problems: What is the potential in the cell if [Cu 2+ ]
= 0.01 M and [Zn 2+ ] = 1.00 M? Note that the cell potential
decreased by about 60mV. This was a change in concentration of TWO
orders of magnitude, but since it was also a TWO electron process,
we saw the same 60 mV change in potential.
Slide 22
Example Problems: Nernst equation demonstrates that potential
depends upon concentration. A cell made of the same materials, but
with different concentrations, will also produce a potential
difference. Cu | Cu 2+ (0.001 M) || Cu 2+ (1.00 M) | Cu What is
standard cell potential E for this cell? What is the cell potential
E? What is n, the number of electrons transferred? Which electrode,
anode or cathode, will be in numerator?
Slide 23
Example Problems: The equations we have derived allow us to
relate measured cell potentials to Standard Gibbs Free Energies of
reaction. These in turn are related to a reactions equilibrium
constant. Consider the cell Pt | I (1.00 M), I 2 (1.00 M) || Fe 2+
(1.00 M), Fe 3+ (1.00 M) | Pt Standard Cell Potential is (from
tables) = 0.771 V - 0.536 V = +0.235 V This is the free energy
change. It leads to the equilibrium constant for the reaction.
Slide 24
Example Problems: Fe 2+ + 2e Fe-0.44 V 2+ + 2e V -1.19 To get a
final positive cell potential, the more negative half-reaction (V)
must act as the anode. Fe 2+ + V Fe + V 2+ E cell = -0.44 - (-1.19)
= +0.75 V Sn 2+ + 2e Sn -0.14 Ag + + e Ag +0.80 More negative
potential reaction is the anode. Multiply the Ag reaction by 2, but
dont modify the cell potential. 2 Ag + + Sn 2 Ag + Sn 2+ E cell =
+0.80 - (-0.14) = +0.94 V
Slide 25
A fuel cell is an electrochemical cell that requires a
continuous supply of reactants to keep functioning Anode: Cathode:
O 2 (g) + 2H 2 O (l) + 4e - 4OH - (aq) 2H 2 (g) + 4OH - (aq) 4H 2 O
(l) + 4e - 2H 2 (g) + O 2 (g) 2H 2 O (l) Example Problems:
Slide 26
Corrosion Example Problems:
Slide 27
Cathodic Protection of an Iron Storage Tank Example
Problems:
Slide 28
Electrolysis is the process in which electrical energy is used
to cause a non-spontaneous chemical reaction to occur. Example
Problems:
Slide 29
Electrolysis of Water Example Problems:
Slide 30
Electrolysis and Mass Changes charge (Coulombs) = current
(Amperes) x time (sec) 1 mole e - = 96,500 C = 1 Faraday Example
Problems:
Slide 31
How much Ca will be produced in an electrolytic cell of molten
CaCl 2 if a current of 0.452 A is passed through the cell for 1.5
hours? Anode: Cathode: Ca 2+ (l) + 2e - Ca (s) 2Cl - (l) Cl 2 (g) +
2e - Ca 2+ (l) + 2Cl - (l) Ca (s) + Cl 2 (g) 2 mole e - = 1 mole Ca
mol Ca = 0.452 C s x 1.5 hr x 3600 s hr96,500 C 1 mol e - x 2 mol e
- 1 mol Ca x = 0.0126 mol Ca = 0.50 g Ca
Slide 32
Structure of the solid/electrolyte interface Every solid/liquid
has a interface that one would like to control --the better one can
control that interface the better one can say something about the
environment Interfaces are very complex often involving fractals
(beach, trees, snow flakes, etc.) rather than smooth transitions,
this implies, for example, that perfect selectivity will be hard to
achieve (too many different binding sites)
Slide 33
Structure of the solid/electrolyte interface Charge carriers in
electrode materials: Metals (e.g. Pt) : electrons Semiconductors
(e.g. n-Si) : electrons and holes Solid electrolytes (e.g. LaF 3 )
: ions Insulators (e.g. SiO 2 ):no charge carriers Mixed conductors
(e.g. IrO x ) : ions and electrons Solution (e.g. 1 M NaCl in H 2
O): solvated ions Inner Helmholtz plane (IHP) Outer Helmholtz plane
(OHP) Gouy-Chapman layer (GCL) Double layer-(in case of a metal
10-40 F cm -2 )