ChE 455/555: Basic Concepts
Gerardine G. Botte
Objective
•  The objective of this lecture is to
review some concepts associated
with electrochemistry, conventions,
most use equations, etc
ChE 455/555
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
2
Outline
•  Redox reactions
•  Electrochemical Cells
–  definition
•  Standard electrode potential
–  Reference electrode
–  Meaning of potential
•  Standard cell potential
•  Electrochemical cells
–  Representation
–  Galvanic cells
–  Electrolytic cells
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage efficiency
Ion conduction
Transfer numbers
ChE 455/555
3
1
Redox reactions: oxidation
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
•  Oxidation
–  Process by which an element losses
electrons (increases its oxidation number)
–  The electrode at which oxidation takes
place is called the anode
–  e.g.,
Cu → Cu +2 + 2e−
ChE 455/555
4
Redox reactions: reduction
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
•  Reduction
–  Process by which an element gains
electrons (decreases its oxidation
number)
–  The electrode at which reduction
takes place is called the cathode
–  e.g.,
Cu +2 + 2e− → Cu
ChE 455/555
5
Exercise # 1
•  Classify the following redox reactions,
include the electrodes name
Ag + + e− → Ag
Au → Au +3 + 3e−
Cr +3 + 3e− → Cr
Li → Li + + e−
ChE 455/555
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2
Electrochemical Cells
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
•
•
•
•  Consists of:
–  At least two electrodes where
reactions occur
–  Electrolyte, for conduction of ions
–  External conductor, to guarantee
continuity of the circuit
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
Redox reactions
Electrochemical
cells
Standard electrode
potentials
ChE 455/555
Electrochemical Cells
e-
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
7
V
Electrode 2
Electrode 1
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
Electrolyte
ChE 455/555
8
Key information
•  Electrochemical reactions
ALWAYS take place on electrodes
NOT in the bulk
•  A potential is always measured
respect to ANOTHER electrode
ChE 455/555
9
3
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
Standard Electrode Potentials
•  The universal reference electrode is
hydrogen (SHE)
•  Standard conditions:
–  Temperature 25oC
–  Unit activity coefficient of H+ ions
•  Reaction
2H + + 2e− ⇔ H 2
E0 = 0 V
E: Electrode potential
0: Standard conditions
ChE 455/555
10
SHE
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
•  Consists of a Pt wire immersed in a
solution of 1 M H+
Standard cell
potential
•  Hydrogen gas is bubble at 1 atm
Electrochemical
cells
•  The Pt wire provides a surface
–  Representation
–  Galvanic
area for the reaction to take place
–  Electrolytic
Nernst equation
•
The gas stream keeps the solution
Faraday s law
Current and voltage
saturated at the electrode site
–  Ref electrode
–  Potential
•
•
•
•
•
•
•
efficiency
Ion conduction
Transfer numbers
ChE 455/555
11
SHE
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
•  It is a theoretical electrode
•  It can t be manufactured because
it is impossible to have hydrogen
ion activity of 1.00 M
•  However, hydrogen electrodes can
be manufactured
ChE 455/555
12
4
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
Building a H2 Electrode
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
ChE 455/555
13
Meaning of Potential
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
•  The potential represents the
maximum electrical energy
Standard cell
available from a cell
potential
Electrochemical
•  It s related to the Gibbs free
cells
–  Representation
energy of the cell by
–  Galvanic
–  Electrolytic
ΔG 0 = −nFE 0
Nernst equation
Faraday s law
n : number of electrons
Current and voltage
efficiency
F: Faraday's constant (96485 C/eq)
Ion conduction
–  Ref electrode
–  Potential
•
•
•
•
•
•
•
Transfer numbers
ChE 455/555
14
Questions?
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
•  What should be the sign of the
potential E0 for a reaction to be
spontaneous?
•  Answer: POSITIVE
•  Positive potentials mean that the
reaction is spontaneous
•  Negative potentials mean that the
reaction is not spontaneous
ChE 455/555
15
5
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
Standard Potentials in
Electrochemical Cells
•  Appendix B of the book
summarizes the standard electrode
potentials
•  Standard electrode potentials can
be used to calculate the Standard
potential of an electrochemical cell
ChE 455/555
16
Standard cell potential:
Calculations
1.  Choose the electrode reactions from
the standard electrode potentials table
2.  Reverse the sense of the reactions
according to your system
1.  Reverse the sign of your standard potential
3.  Balance the number of electrons
multiplying by a positive number
4.  Add the electrode reactions to obtain
overall reaction
5.  Add the potentials to obtain the overall
potential of the cell
ChE 455/555
17
Standard Cell potential:
calculations
•  You can balance the stoichiometry
of the equation by multiplying by
any positive constant
•  This operation does not alter the
potential of the cell (potential is an
intensive quantity, unaffected by
the number of electrons)
ChE 455/555
18
6
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
Schematic Representation of
Electrochemical Cells
•  Include all the phases involved
•  Separate the phases using bars
•  Include information about solvent
and concentrations if available
•  e.g.:
Zn / Zn+2 / H 2O / Cu +2 / Cu
ChE 455/555
19
Exercise #2
•  Calculate the standard potential of
the cell
•  What is the anode?
•  What is the cathode?
Zn / Zn+2 / H 2O / Cu +2 / Cu
ChE 455/555
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
20
Galvanic Cells
•  It is an energy producing cell
•  Also known as:
–  Driving cell
–  Spontaneous cell
•  They are used as batteries (several cells
in series)
•
The standard potential is the maximum
Nernst equation
potential that can be provided by the cell
Faraday s law
Current and voltage
•  The anode is assigned a negative sign
efficiency
Ion conduction
(negative electrode)
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Transfer numbers
ChE 455/555
21
7
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
Galvanic Cells: continued
•  The cathode is assigned a positive
sign (positive electrode)
•  Sign of current:
–  Positive if it leaves the electrode to
the electrolyte
–  Negative if it enters the electrode from
the electrolyte
ChE 455/555
22
Exercise #3
•  Write the reactions, identify positive
and negative electrodes, identify
cathode and anodes, identify
direction of the current, and draw
the cell including external circuit
and flow of electrons, for the
following reaction
Zn / Zn+2 / H 2O / Cu +2 / Cu
ChE 455/555
23
Electrolytic Cells
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
•  It is an energy consumer cell
•  Also known as:
–  Driven cell
–  Non Spontaneous cell
•  Opposite process of a battery (required
energy to operate)
•  The standard potential is the minimum
necessary potential required for the cell
to operate
ChE 455/555
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8
Electrolytic Cells: continued
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
•  The cathode is assigned a negative
sign (negative electrode)
•  The anode is assigned a positive
sign (positive electrode)
•  Sign of current:
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
–  Positive if it leaves the electrode to
the electrolyte
–  Negative if it enters the electrode from
the electrolyte
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
ChE 455/555
25
Exercise #4
•  Write the reactions, overall reaction,
calculate the total standard potential of the
cell, identify positive and negative
electrodes, identify cathode and anodes,
identify direction of the current, and draw
the cell including external circuit and flow of
electrons, for the following reaction
Cu + Zn+2 → Cu +2 + Zn
ChE 455/555
26
Hint
•  It is recommended that for every
problem that you solve you start by:
–  Writing reactions
–  Calculating open circuit potential (identifying
type of cell)
–  Drawing schematic of cell and identifying:
•
•
•
•
Positive and negative electrodes
Anode and cathode
This is important to
Direction of the current
understand your problem
Direction of electrons
and the data that you are
given
ChE 455/555
27
9
Exercise 5
•  Solve Problem 1, Ch2 of the book
(p. 26)
ChE 455/555
28
Electrolysis of Brine
Membrane: bi-layer membrane made of
perfluorocarboxylic and perfluorosulfonic
ChE 455/555
acid-based films
29
Summary
•  Where do electrochemical reactions
take place?
•  What is oxidation? What is reduction?
•  What is the meaning of potential?
•  Define galvanic and electrolytic cell
•  Calculate the standard potential of a cell
•  Define +,-, cathode, anode, current sign,
flow of electrons
•  Draw schematic of electrochemical cell
ChE 455/555
30
10
Nernst Equation
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
•
•
•
•
•
E = E0 −
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
•
•
•
Standard cell
potential
Electrochemical
cells
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
RT
ln ∏ cisi
nF
Eq. 1
si: stoichiometric coefficient of species i
ChE 455/555
31
Nernst Equation Continued
•  The electrode reaction is written in
simplified form as
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•  Express relationship between the
potential of the cell and the
concentration (no standard
concentration)
Standard cell
potential
Electrochemical
cells
∑s M
i
zi
i
→ ne−
Eq. 2
i
si: positive for products and negative for reactants
Mi: symbol for the chemical species
zi: charge number of the chemical species
ChE 455/555
32
Steps to use Nernst Eq.
•  Write down electrode reactions
•  Determine # of electrons
transferred (balance equations)
•  Use Eq. 1 accordingly
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
ChE 455/555
33
11
Exercise #6
•  In a Zn/Cu cell, If the reaction is
done in a cell in 5.00 M Zn+2 and
0.30 M Cu+2 at 25oC, what is the
cell voltage?
ChE 455/555
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
Redox reactions
Electrochemical
cells
Standard electrode
potentials
Faraday s Law
•  Relationship between charge passed
and amount of substance oxidized or
reduced at an electrode
–  The amount of product formed is directly
proportional to the charge passed
–  For a specified quantity of charge passed,
the masses of products formed are
proportional to the electrochemical
equivalent weights of the products
ChE 455/555
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
35
Faraday s Law Eq.
m=
–  Ref electrode
–  Potential
•
34
sMIt
nF
Eq. 3
M: atomic or molecular weight
I: current, A
t: time elapsed, s
F: Faraday s constant, 96,485 C/equiv or 26.8 Ah/equiv (last one is very useful in battery
applications)
ChE 455/555
36
12
Faraday s Law Eq.
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
•  The product of: (It) is known as
total charge passed (Q)
•  If current changes with time, it
should be integrated over time to
obtain Q
t
Q = ∫ Idt
Eq. 4
0
ChE 455/555
37
Deviations from Faraday s
Law
•  Some causes of deviation from
Faraday s law are:
–  Consumption of some of the charge
by parasitic processes
–  All of the reactants are not consumed
–  The postulated process is not the
actual process
–  Some of the material from the sample
falls of
ChE 455/555
38
Units and Formula Reminder
•  Power is the product of current by
voltage:
–  P = I V (units are W in international
system)
W = AV
W = J /s
A=C/s
ChE 455/555
39
13
Exercise #7
•  Solve Ex. 2 of the book (Ch2, p26),
parts a, b, and c.
ChE 455/555
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
40
Current efficiency
•  For electrolytic process
εc =
actual chemical change (desired)
theoretical chemical change
Eq. 5
Nernst equation
Faraday s law
Current and
voltage efficiency
Ion conduction
Transfer numbers
ChE 455/555
41
Current efficiency
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and
voltage efficiency
Ion conduction
Transfer numbers
•  For galvanic process, known as
faraday s efficiency
εF =
theoretical reactant required
amount of reactant consumed
Eq. 6
ChE 455/555
42
14
Voltage efficiency
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and
voltage efficiency
Ion conduction
Transfer numbers
•  For electrolytic process:
εv =
theoretical voltage
voltage at terminals
Eq. 7
•  For galvanic process:
εv =
voltage at terminals
theoretical voltage
Eq. 8
ChE 455/555
43
Energy efficiency
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and
voltage efficiency
Ion conduction
Transfer numbers
•  Product of the current and voltage
efficiencies:
ε e = ε cε v
Eq. 9
ChE 455/555
44
Exercise #8
•  Solve problem 4 of the book (Ch2,
p. 27)
ChE 455/555
45
15
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
Ion Conduction
•  Conductivity
–  The measure of the materials capability to
transfer electrical energy
–  Electrical conductivity (electronic
conductivity) is used in metals
–  Ionic conductivity is used in electrolytes
(ions transfer the current)
–  Conductivity of metals much higher than
ionic conductivity
–  Units: S/cm (siemens)
ChE 455/555
46
Order of Magnitude of
Conductivities
•  In an aqueous system at room
temperature:
–  10-2 S/cm
•  Much lower than metals, order of
magnitude for metals is:
–  105 S/cm
ChE 455/555
47
Ionic Conductivity
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
This Equations assumes complete dissociation
of species
k = F 2 ∑ zi2ui ci
Eq. 10
i
ui: ionic mobility, cm2-mol/J-s
zi: charge of species, dimensionless
Ci: concentration of species, mol/cm3
ChE 455/555
48
16
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
Redox reactions
Electrochemical
cells
Standard electrode
potentials
Charged particle in electric
field model
•  Assumes:
–  Ions are spheres
–  Continuous viscous medium
–  Low Reynolds numbers
–  Uses Stoke s law to calculate the
drag force
–  Uniform electric field
ChE 455/555
Charged particle model
continued
v=
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
49
zeE f
6πµ r
Eq. 11
r: radius of particle, cm
Ef: forced field, V/cm. For calculations
assume 1 V/cm
e: charge of an electron, 1.6x10-19 C/chg
m: viscosity, g/cm-s
ChE 455/555
50
Units Reminder
1
kg
Ns
=1 2
ms
m
1 cp = 1.01x10−3
Ns
m2
V = J /C
ChE 455/555
51
17
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
Procedure to use charge
particle model
•  Calculate velocity using Eq. 11.
Assume Ef = 1V/cm
•  Check value of Re number
The
image
cannot be
displayed.
Your
< 2800
Eq. 12
d: ion diameter, cm
r: density, g/cm3
ChE 455/555
52
Procedure continued
•  Calculate current density
i = F ∑ zi ci vi
i
•  Since the field is proportional to the
negative of the potential gradient,
the conductivity can be calculated
i = − k ∇φ
ChE 455/555
53
Equivalent conductance
model
•  Equivalent conductance (L, cm2/ohmequiv) does not change abruptly with
concentration
•  Correlated with square root of
concentration (Fig. 2.4)
•  Extrapolating to zero gives the
equivalent conductance at dilute
conditions (Lo)
•  Kohlrausch noticed that the difference
between Lo having a common ion was
approximately constant
ChE 455/555
54
18
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
Equivalent conductance
model continued
•  Kohlrausch concluded that the
equivalent conductance can be
considered the sum of two ionic
components acting independently:
∧o = λ+o + λ−o
Eq. 13
Equivalent conductances are given in
Appendix C
ChE 455/555
55
Mobility and diffusivity
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
•  Equivalent ion conductance is
related to mobility:
λi = zi F 2ui Eq. 14
•  At dilute conditions Nernst-Einstein
equation relates mobility to
diffusivity:
Di = RTui Eq. 15
Di: diffusion coefficient of species i, cm2/s
ChE 455/555
56
Calculation of ionic conductivity
using ion conductance
•  Get equivalent conductance
(Appendix C, CRC, etc)
•  Calculate mobility using Eq. 14
•  Calculate conductivity using Eq.10
•  This procedure is not valid at high
concentrations (see Fig. 2.6)
ChE 455/555
57
19
Exercise #9
•  Calculate the ionic conductivity of a
0.1 N KCl solution using two
different methods. Compare your
values. The crystal radius of K is
1.33 Ao
ChE 455/555
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
58
Effect of Temperature on
ionic conductivity
•  As a general rule ionic conductivity
increases with increasing
temperature
•  Rule of thumbs:
1 ∂k
%
; 2.5 o
k ∂T
C
Eq. 16
ChE 455/555
59
Problem
•  What would be the conductivity of
KCl at 60 oC?
ChE 455/555
60
20
Transference number
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
•  Represents the fraction of current
carried by a specified ion in the
absence of concentration gradients
i
Eq. 17
tj = j
i
z 2j u j c j
tj =
Eq. 18
∑ zi2ui ci
i
ChE 455/555
61
Useful Expression
•  Combining Eqs 18 and 14:
tj =
λ jc j z j
Eq. 19
F 2i
ChE 455/555
62
Transference number
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
•  The fractional current carried by
each species must add up t the
total current, then
The
imag
e
cann
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
ChE 455/555
Eq. 20
63
21
Transference number
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
•  For a binary electrolyte
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
t+ =
λ+
λ+ + λ−
Eq. 21
ChE 455/555
64
Exercise #10
•  Solve problem 6 of the book, Ch2
(p. 27). The transference number
of Cu+2 in a copper sulfate solution
in water is 0.44
ChE 455/555
65
Summary
•
•
•
Redox reactions
Electrochemical
cells
Standard electrode
potentials
–  Ref electrode
–  Potential
•
•
Standard cell
potential
Electrochemical
cells
–  Representation
–  Galvanic
–  Electrolytic
•
•
•
•
•
Nernst equation
Faraday s law
Current and voltage
efficiency
Ion conduction
Transfer numbers
•  Use and understand Nernst equation
•  Calculate theoretical amount of
reactants and products using Faraday s
law
•  Determine current, voltage and energy
efficiency
•  Calculate ionic conductivity
•  Calculate transference numbers
ChE 455/555
66
22