Transcript Class-3 - University of California, Irvine

BIOMEMS
Class III. Electrochemistry Background (II)
Winter 2011
Dr. Marc Madou
Contents
Oxidants and reductants
 Battery
 Reference Electrodes
 Standard Reduction Potentials
 Thermodynamic Significance of Potentials
 How do Cell Potentials Change if
We are Not at Standard State?
 Nernst-Equation
 Cyclic voltammetry
 Potentiometric sensors
 Amperometric sensors

Oxidants and Reductants
 oxidant
= oxidizing agent
– reactant which oxidizes another reactant and
which is itself reduced
 reductant
= reducing agent
– reactant which reduces another reactant and
which is itself oxidized
Oxidants and Reductants
 Identify
the oxidant and reductant in each of the
following reactions:
a) Karl Fischer reaction – for quantitation of
moisture:
I2 + SO2 + H2O = 2HI + SO3
b) Hall Heroult process – production of Al:
2Al2O3 + 3C = 4Al + 3CO2
c) the Thermite reaction – used to produce liquid iron
for welding
2Al + Fe2O3 = 2Fel + Al2O3
Oxidants and Reductants





Reactions occur pair wise: One cannot have oxidation
without reduction
Charge must be conserved: Number of electrons lost in
oxidation must equal number of electrons gained in
reduction
Suppose we add a strip of Zinc metal to a solution of
CuSO4
Zn - 2e- = Zn2+
Zn strip
2+
Cu + 2e = Cu
CuSO4
Oxidants and Reductants




It is the relative tendencies of oxidants and reductants to gain/lose
electrons that determines the extent of a redox reaction
Strong oxidant + strong reductant  completion
What if we could separate the oxidant from the reductant?
We would have set up a constant flow of electrons = current =
electricity!
Zn strip
CuSO4
Zn
1.1 V
salt bridge
Cu
ZnSO4
CuSO4
1836 The Daniell
Cell
Battery




Electrode
– anode = electrode at which oxidation occurs
– cathode = electrode at which reduction occurs
Salt bridge = completes the electrical circuit
– allows ion movement but doesn’t allow solutions to mix
– salt in glass tube with vycor frits at both ends
Since electrons flow from one electrode to the other in one
direction, there is a potential difference between the electrodes
This difference is called
– The electromotive force (EMF)
– Cell voltage
– Cell potential
Battery

Since all redox reactions occur pair wise, i.e., reduction
and oxidation always occur at the same time we cannot
measure the cell potential for just one half cell reaction
and this means we must establish a RELATIVE scale for
cell potentials
Problem: True or False


In the Daniell cell, zinc metal is reduced to zinc(II) at the
cathode and copper is oxidized to copper(II) at the anode
In the Daniell cell, zinc is the oxidant and copper is the
reductant
Reference Electrodes


Electrodes with a potential
independent of solution composition
Standard hydrogen electrode
(SHE)
– 1 M H+(aq)+ 2e- = H2(g) (1 atm)
– We define E0  0 V for this
electrode
» where 0 stands for standard
state:
 1 M all solutes
 1 atm all gases
 250C (298 K)
H2(gas)
HCl
Pt black
Reference Electrodes
Reference Electrodes
2H+(1M) + 2e-  H2(g,1atm)
Eoredn = 0.0V
Reference Electrodes
E  E o  0.0592log
a Ag aCl 
a AgCl
E  E o  0.0592logaCl 
Reference Electrodes
0.244 V v. SHE
Reference Electrodes
Reference Electrodes
Standard Reduction Potentials






Li+ + e- = Li
2H2O + 2e- = H2 + 2OHZn2+ + 2e- = Zn
2H+ + 2e- = H2
Cu2+ + 2e- = Cu
MnO4- +8H+ +5e- = Mn2+
-3.0 V
-0.83 V
-0.76 V
0 V (SHE)
0.34 V
1.51 V
Standard Reduction Potentials
 Always
write
the redox
ractions as
shown :
Standard Reduction Potentials
 Half
cell reactions are reversible, i.e.,
depending on the experimental conditions any half
reaction can be either an anode or a cathode
reaction
 Changing the stoichiometry does NOT change the
reduction potential (intensive property)
 Oxidation potentials can be obtained from
reduction potentials by changing the sign
Ecell = Eanode + Ecathode
Standard Reduction Potentials

Problem:

Calculate the cell
potential for the
Daniell cell.





Li+ + e- = Li
2H2O + 2e- = H2 + 2OHZn2+ + 2e- = Zn
2H+ + 2e- = H2
(SHE)
Cu2+ + 2e- = Cu
MnO4- +8H+ +5e- = Mn2+
-3.0 V
-0.83 V
-0.76 V
0V
0.34 V
1.51 V
Standard Reduction Potentials
Standard Reduction Potentials
Zn --> Zn2+ + 2eoxidation
Cu2+ + 2e- -->Cu
reduction
Standard Reduction Potentials





Anode reaction appears leftmost while cathode reaction
appears rightmost
All redox forms of reagents present should be listed. Phase
and concentration specified in brackets, e.g., ZnSO4(aq, 1
M)
A single vertical line (|) is used to indicate a change of
phase (s to l to g)
A double vertical line (||) indicates a salt bridge
A comma should be used to separate 2 components in the
same phase
Thermodynamic Significance of
Potentials
We usually operate electrochemical cells at
constant P and T
 Recall,

– G = H - T S (change in Gibbs free energy)
– H = E + (PV)

So, GT,P=welec = -QE = -(nF)E
– since Q = n F
– Recall, F is Faraday’s constant 96,485 C/mole
Thermodynamic Significance of
Potentials
 The
maximum electrical work done by an
electrochemical cell equals the product of the charge
flowing and the potential difference across which it
flows. The work done on the cell is:
– W = -E x Q, where E is the Electromotive Force of the
Cell (EMF), and Q is the charge flowing: Q = n x NA x e
– where n is the number of moles of electrons transferred per
mole of reaction, NA is Avogadro's Number (6.02 x 1023),
and e is the charge on an electron (-1.6 x 10-19 C).
 Note:
NA x e = F (one Faraday). Thus: W = -nFE
and: W = G = -nFE
Thermodynamic Significance of
Potentials


Recall sign of G provides information on spontaneity:
G negative  spontaneous reaction
G positive  non-spontaneous reaction
So, since G = - nFE
E positive  spontaneous reaction
E negative  non-spontaneous reaction
A a + n e = Bb
reactant
produ ct
O x + n e = Re d
Thermodynamic Significance of
Potentials



Since half-cell potentials are measured relative to SHE,
they reflect spontaneity of redox reactions relative to SHE
More positive potentials  more potent oxidants (oxidants
want to be reduced)
More negative potentials  more potent reductants
(reductants don’t want to be reduced; they spontaneously
oxidize)
Thermodynamic Significance of
Potentials

Galvanic
– Chemical energy  electrical energy
– Spontaneous
(so Ecell is positive)
EXAMPLES:
» Primary (non-rechargeable)
 Le Clanche (dry cell)
» Secondary (rechargeable)
 Lead storage battery
» Hydrogen-Oxygen Fuel Cell
Thermodynamic Significance of
Potentials

Electrolytic
– Electrical energy  chemical energy
– Non-spontaneous
(Ecell is negative)
EXAMPLE:
– Lead storage battery when recharging
– Electrolysis of water
Thermodynamic Significance of
Potentials
Thermodynamic Significance of
Potentials
Thermodynamic Significance of
Potentials
Thermodynamic Significance of
Potentials
Thermodynamic Significance of
Potentials
Thermodynamic Significance of
Potentials-Problems

Arrange the following in order of increasing oxidizing
strength:
– MnO4- in acidic media
– Sn2+
– Co3+

Co3+ + e- = Co2+
MnO4- + 4H+ + 3e- = MnO2 + 2H2O
MnO4- + 8H+ + 5e- = Mn2+ + 4H2O
Sn2+ + 2e- = Sn

So, Co3+ > MnO4- > Sn2+



1.82 V
1.70 V
1.51 V
-0.14 V
Thermodynamic Significance of
Potentials-Problems


A galvanic cell consists of a Mg electrode in a 1.0 M
Mg(NO3)2 solution and a Ag electrode in a 1.0 M AgNO3
solution. Calculate the standard state cell potential and
diagram the cell.
Consider the following cell:
Ag(s)/AgNO3(aq, 1 M)//CuSO4(aq, 1 M)/Cu(s)
a) what is the anode reaction?
b) what is the cathode reaction?
c) what is the net number of electrons involved?
d) what is the net reaction?
e) what is the cell potential at standard state?
f) is the cell galvanic or electrolytic?
Thermodynamic Significance of
Potentials -Problems

Is the following redox reaction spontaneous?
Mg2+ + 2Ag = Mg + 2Ag+
given:
Ag+ + e- = Ag
+0.80 V
Mg2+ + 2e- = Mg
-2.37 V
Thermodynamic Significance of
Potentials

Using a table of standard reduction potentials, any species on the
left of a given half reaction will react spontaneously with any
species appearing on the right of any half reaction that appears
below it when reduction potentials are listed from highest and
most positive to lowest and most negative.
Thermodynamic Significance of
Potentials -Problems


What would the cell potential be for the following cell?
Ag(s)/AgNO3(aq, 1 M)//CuSO4(aq, 0.5 M)/Cu(s)
This represents a set of non-standard state conditions so we
need derive an equation relating the standard state to the
non-standard state or the Nernst Equation

Standard state:
–
–
–
–
–
Temperature 250C (K = 273.15 + 0C)
Pressure 1 atm
Concentrations of all solutes 1 M
0 (not) is used to indicate at standard state
Example: E0 = cell potential at standard state
How do Cell Potentials Change if
We are Not at Standard State?
 For
the reaction:
aA + bB = cC + dD
 G = G0 + 2.303 RT log Q
where Q is the reaction quotient:
Q   a b
c

 Where
d
c is the activity for product C
How do Cell Potentials Change if
We are Not at Standard State?
G = - nFE then
E = E0 - 2.303 (RT/nF) log Q
 At standard state,
E = E0 - (0.0591 /n) log Q
This is called the Nernst equation
 Apply the Nernst Equation to a pH sensor: pH=log[H+]
 What is the cell potential for the following
electrochemical cell? What type of cell is it?
Ni(s) | Ni2+ (aq, 0.1 M) || Co2+ (aq, 2.5 M) | Co(s)
 Since
Nernst Equation
G  Go  RT ln Q
Nernst Equation


The Nernst equation underlies the operating principle of
potentiometric sensing electrodes and reference
electrodes
Electrolysis vs. battery is determined by Eo sign
Two-electrode and three-eletrode cells,
potentiostat, galvanostat



Electrolytic cell (example):
– Au cathode (inert surface for e.g.
Ni deposition)
– Graphite anode (not attacked by
Cl2)
Two electrode cells (anode, cathode,
working and reference or counter
electrode) e.g. for potentiometric
measurements (voltage measurements)
(A)
Three electrode cells (working,
reference and counter electrode) e.g.
for amperometric measurements
(current measurements)(B)
Cyclic voltammetry: activation control

At equilibrium the exchange
current density is given by:


ie  i  k c zF

kT
e
h
(1  )Fe
RT


 i  k a zF
kT
e
h
Fe
RT
The reaction polarization is then
given by:
e
 
i i  i

The measurable current density is
then given by:
i  ie (e
(1 )F 
RT
 e
 F 
RT
)
(Butler-Volmer)

For large enough overpotential:
  a  blog(i)
(Tafel law)
Cyclic voltammetry: diffusion control

From activation control to diffusion
control:dC C 0  C
dX


C
RT
ln x=0
nF
C 0
C  Cx 0

At a certain potential C x=0=0 and
then: I  nFAD C  0
l
0

Since
x0
Using Faraday’s law we may write
also:
0
i  nFAD 0

x
Concentration difference leads to
another overpotential i.e.
concentration polarization:
c 



i  il (1
C x=0 i l - i
0 
C
i l we get :
nFc
 e RT
)
Cyclic voltammetry and potentiometric and
amperometric sensors



Scan the voltage at a given
speed (e.g. from + 1 V vs SCE
to -0.1 V vs SCE and back at
100 mV/s) and register the
current
Potentiometric: the voltage
between the sensing electrode
and a reference electrode is
registered
Amperometric: the current at a
fixed voltage in the diffusion
plateau is registered
Ferricyanide
Cyclic voltammetry (also polarography) and
potentiometric and amperometric sensors
Homework
1.
2.
3.
4.
Calculate the potential of a battery with a Zn bar in a 0.5 M Zn 2+
solution and Cu bar in a 2 M Cu 2+ solution.
Show in a cyclic voltammogram the transition from kinetic control to
diffusion control and why does it really happen ?
Derive how the capacitive charging of a metal electrode depends on
potential sweep rate.
What do you expect will be the influence of miniaturization on a
potentiometric sensor and on an amperometric sensor?