Announcements

Course Evaluations

Final is Wednesday Afternoon on May 9th

Homework

14-15, 14-26, 15-6, 16-3, 16-6,
Course Evaluations

Request from Thelmo


“Teaching is a complex endeavor, capable of an almost
infinite variety of successful expressions, and thus,
success as a teacher cannot be judged by any one
criterion or through one single mechanism.”
 Consider the many facets of the learning environment
over the course of whole semester
How will your feedback be used?


Read by me to evaluate which aspects of the course most
contribute to student learning
 formative
Read by PSC as part of faculty’s permanent file to
evaluate faculty for promotion and tenure
 summative
Concentration
dependency of E
Concentration Dependency of E



Eo values are based on standard conditions.
The E value will vary if any of the concentration vary
from standard conditions
Theoretically

Predicted by the Nernst Equation
The Nernst Equation
The Nernst Equation
For aA + ne-  bB

0.05916V
EE 
log Q
n
o
b
B
a
A
0.05916V
A
EE 
log
n
A
o
Example
Equilibrium constant and Eo

Find the equilibrium constant for the reaction
Cu (s) + 2Fe3+
2Fe2+ + Cu2+
Example

Find the voltage of the cell

Half reaction


The other half-reaction



Ag (s) into a solution of 0.50 M AgNO3 (aq)
Cd (s) is immersed into a 0.010 M Cd(NO3)2 (aq)
Metals are connected by wires
Solution connected with salt bridge
Find the voltage of the cell
0.010 M Cd(NO3)2
0.50 M AgNO3
Potentiometric
Methods
Potentiometric Methods

Basis of Method

The difference b/w the E (not Eo) values for two
halves of a cell give rise to Eoverall.,

If one half reaction is known and held constant,
we can measure the concentration of species on
the other side!!!
Indicating
electrode –
The part of the cell
that contains the
solutions we are
interested in
measuring
Reference
Electrodes

The previous cell would
be difficult to use for
many systems.


We would like
something that can be
placed in the solution
we wish to measure
The electrodes in the
following slides have
that goal in mind but

THEY STILL represent
a complete
electrochemical cell
when used
Reference Electrodes

Ag/AgCl
Reference Electrodes

Calomel Electrode
(SCE)



Very Common
Hg|Hg2Cl2 (sat), KCl||
Chloride is used to
maintain constant ionic
strength
Reference Electrodes

The SCE (Saturated
Calomel Electrode)

Different KCl concentrations
can (and are used)
 0.1 M – least temperature
sensitive
 Saturated – easier to make
and maintain.
Eref = 0.244 V
@STP
Reaction
Hg2Cl2 + 2e- ->2Hg(l) + 2Cl-
Eo (V)
0.244 V
Hg2Cl2 + 2e- ->2Hg(l) + 2ClAgCl (s) + e- ->Ag(s) + Cl-
0.241
0.197
Sensing electrodes

Several types




Simple Metal
Solid State Electrodes
Glass Membrane
Etc.
Let’s look at some examples.
Sensing electrodes

Several types




Simple Metal
Solid State Electrodes
Glass Membrane
Etc.
Let’s look at some examples.
Simple metal electrodes

A bare metal in contact
with a solution.

General Form:

Mn+ + ne- -> M(s)
Simple Metal Electrodes

A bare metal in contact with a
solution of its cation.

Ag+ + 1e- -> Ag(s)
0.799 V

General form
Mn+ + ne- -> M(s)
Eind  E o 
Eind
0.0592
1
log
n
[ Ag  ]
0.0592
1
E 
log
n
[M n ]
o
Example

A potential of 0.5000V was measured vs.
SCE. What is the concentration of Ag+?
Hg2Cl2 + 2e-  2Hg(l) + 2 ClAg+ + e-  Ag(s)
Eo = 0.241V
Eo = 0.799V
Using a simple metal electrode (Ag) and a reference
electrode (Calomel), the voltage determined from this
potentiometric set-up provides us with a direct measure
of concentration
no calibration plot required!!
Simple Metal Electrodes


Example
Silver sensing electrode
Ered  Eind
0.0592
1
 0.799V 
log
1
[ Ag  ]
 
E

0
.
799
V

0
.
0592
pAg
Eind

0
.
799
V

0
.
0592
(

log[
Ag
])
ind
00
.5000
VVE0
.0241
V V 0.799
V

0
.
0592
pAg
.5000
.
244
E
E
E
red
cell
ox
red
 0.058  0.0592 pAg
 0.0580
 pAg
 0.0592
Example (cont’d)
 0.0580
 pAg
 0.0592
0.9797  pAg
1x10
0.9797

 [ Ag ]

0.1047 M  [ Ag ]
Simple Metal Electrodes

For some metals, a good electrode can’t be made or no metals
are involved – just ions or gas! An inert indicating electrode is
used (graphite or Pt).

This type only measures the ratios of ions.

No quantitation but suitable for titrations!
Simple Metal Electrodes

For some metals, a good
electrode can’t be made or
no metals are involved –
just ions or gas! An inert
indicating electrode is used
(graphite or Pt).

This type only measures the
ratios of ions.

No quantitation but suitable
for titrations!
Calomel
(Hg2Cl2)
Simple Metal Electrodes

Eoverall = Eox + Ered
Constant = -0.241 V
Reduction at Platinum Electrode:
Reaction
Fe3+ + 1e- -> Fe2+
Ered
Ered
Eo
0.771 V
2
0
.
0592
[
Fe
]
o
E 
log
1
[ Fe3 ]
[ Fe2 ]
 0.771V  0.0592 log
[ Fe3 ]
Calomel
(Hg2Cl2)
Simple Metal Electrodes

For some metals, a good
electrode can’t be made or
no metals are involved –
just ions or gas!

This type only measures the
ratios of ions.

No direct quantitation but
suitable for titrations!
Calomel
(Hg2Cl2)
Ce4+
REDOX titrations

“Your titrant is commonly an oxidizing agent
although reducing titrants can be used.”
Consider:
Ce4+ + Fe2+  Ce3+ + Fe3+
General form:
Aox + Bred  Ared + Box
Determination of the
Equivalence Point

The equivalence point is based on the concentration
of the oxidized and reduced form of all species
involved

Use Nernst Equation to find Eeq.
Equivalence Point
EA  EA
EB  EB
o
o
[ Ared ]
0.05916V

log
nA
[ Aox ]
[ Bred ]
0.05916V

log
nB
[ Box ]
Nernst Equation for A
Nernst Equation for B
Since at equilibrium, [Ared] = [Box] and [Bred] = [Aox] we massage the two
general equations to yield:
n A E Ao  nB EBo
Eeq 
n A  nB
Equivalence Point
n A E  nB E
Eeq 
n A  nB
o
A
o
B
Note: This expression only works for simple REDOX TITRATIONS:
Simple redox titrations:
Only Aox, Box, Ared, Bred are involved in the reaction …
Two examples

Determine Eeq for the following reactions:


Fe2+ + Ce4+ -> Fe3+ + Ce3+
Sn2+ + 2Ce4+ -> Sn4+ + 2Ce3+
Titration curves

What does a titration
curve look like for an
acid/base titration?
Typical pH titration
14
12
pH
10
8
6
4
2
0
0
5
10
mL of HBr
15
20
OverTitration
REDOX
Titrations
Ecell
Just like Acid/Base Titrations
There are four significant regions,




The Start
The Buffer Region
The equivalence Point
Overtitration
Let’s Use our simple example:

Fe2+ + Ce4+  Fe3+ + Ce3+
Our simple example
Let’s Use our simple example:

Fe2+ + Ce4+  Fe3+ + Ce3+
Titrate 50 mL of 0.05 M Fe2+ with 0.10 M Ce4+
0% Titration
Unlike acid/base titrations, we can’t find this point
exactly.

While some Fe3+ must be present, we can only
guess what the concentration is.

No Ce4+ or Ce3+ present, so we don’t have a
complete reaction
0% Titration
EFe  EFe
2
o
0.05916V
[ Fe ]

log
nA
[ Fe3 ]
0.05916V
0.05
EFe  0.771V 
log
1
0
EFe  
NO … some of the iron is oxidized by air to give some
Fe3+ … how much ? We generally estimate that less
Than one in 1000 are oxidized.
0.05916V
0.05
EFe  0.771V 
log
1
5 x10 5
 0.771V  0.177V  0.594V vs. SHE
“Buffer Region”
Fe2+ + Ce4+  Fe3+ + Ce3+
10 ml of Ce4+ is added
Goes to completion … Excess Fe2+ pushes
equilibrium to the right.
Thus E is not dependent on Ce3+/Ce4+, but only
on Iron.
“Buffer Region”
EFe  EFe
2
o
0.05916V
[ Fe ]

log
3
nA
[ Fe ]
2
0.05916V
2.5 10
EFe  0.771V 
log
2
1
1.7 10
EFe  0.771V  0.010  0.761V
Closer look at the “buffer”
region
Fe2+/Fe3+
9
4
1.5
1
.25
.11
E
0.715
0.735
0.761
0.771
0.807
0.829
Equivalence Point


From Before
Eeq = 1.24 V
What volume?
25 ml
Excess Ce4+ (post titration)

Fe2+ + Ce4+  Fe3+ + Ce3+

The predominate change is that Ce4+ is being added and diluted
into a solution of Ce3+.

All Fe2+ has been converted to Fe3+ and no longer figures into the
calculations

We just need to keep track of the amounts of Ce3+ and Ce4+ as
well as the VOLUME of the system.
Excess Ce4+ (post titration)

At 30.0 mL Ce4+
Vt = 30.0 mL+ 50.0 mL
3
0
.
05916
V
[
Ce
]
o
ECe  ECe 
log
4
n
[Ce ]
3
0.05916V
[Ce ]
ECe  1.70 
log
1
[Ce 4 ]
Excess Ce4+ (post titration)

Fe2+ + Ce4+  Fe3+ + Ce3+
Ce3+/Ce4+
3
[Ce ]  ?
4
[Ce ]  ?
Excess Ce4+ (post titration)
3
0.05916V
[Ce ]
ECe  1.70 
log
4
1
[Ce ]
2
0.05916V
3.1x10
ECe  1.70 
log
3
1
6.2 x10
ECe  1.70  0.041  1.66V vs. SHE
Redox Indicators
General
Specific
General Redox Indicators

Varies as a function of Ecell

Rely on a color change with Indox and Indred
being different colors.
Indox + ne-  Indred
EE
o
ind
[ Ind red ]
0.05916V

log
n
[ Ind ox ]
General Redox Indicators

In order to see a color change, you typically
need approximately a 10% conversion from
one form to another.
[ Ind red ] 1
10

or 
[ Ind ox ] 10
1
0.05916V
o
E  Eind 
n
General Redox Indicators

Examples

Consider 1,10 phenanthrolene-Fe
C
C
N
BLUE
C
+ e-
C
N
RED
Fe(III)
N
N
Fe(II)
Eo = 1.06 V
General Redox Indicators

Examples
Consider Diphenylamine sulphonic acid

OH
O
S

Used with the iron in the dichromate method

Eo = 0.80V
O
H
N
SPECIFIC INDICATORS


Example from lab

Starch

Starch + I3-  blue complex
It is easy to detect and color change is rapid!!
This interaction explains why we use iodine
as a titrant even though it is a very weak
oxidant.
Common Titrants

Usually oxidizing agents.



Cr2O72-  need an indicator
 Very stable
 E=1.44 V
MnO4 Solutions must be standardized
 Reagent slowly degrades
 No indicator needed excess reagent is pink  E=1.51 V
Ce4+ - Example in Class
Common titrants

Reducing Titrants

Fe2+
Usually Fe(NH4)2(SO4)2.6H2O in 1M H2SO4
 Solution must be standardized each day

 I-
Indirect method
 Your lab was an excellent example

Sensing electrodes

Several types




Simple Metal
Glass Membrane
Solid State Electrodes
Etc.
Let’s look at some examples.
Membrane Electrodes

A potential difference is
created across a
membrane that can be
measured.



THERE IS NO
CHANGE IN THE
SOLUTIONS
“These electrodes are
fundamentally different
from metal electrodes in
that they DO NOT
involve redox reactions!!
These Electrodes
‘selectively bind’ the ion
of interest
Membrane electrodes

pH Electrode


First Discovered in early 1900’s! Refined through
the 1950’s
Probably the most important




Relies on a Glass Membrane
H3O+ selectively binds to glass membrane
Na+ sluggishly transported across
Potential is measured across the membrane!
pH membrane

Special Glass (72%
SiO2)

Doped with Na2O (22%)
and CaO (6%)
Key
Si
O
Cation
Membrane Electrodes

In order to work the Glass
must be hydrated



To allow for diffusion of H+
and Na+
H3O+ populates BOTH side
of the electrode BUT DOES
NOT cross the membrane
To perform an electrical
measurement - Must be a
complete circuit!



But Na+ ‘sluggishly’ crosses
the membrane.
Na+ transport ~ salt bridge
Membranes resistance ~
1x108-9 W
Membrane Electrodes

While H3O+ causes a response, other ions also
‘interfere’.





Alkali Error
Many alkali metals (Li+, Na+, K+)
Severe interference result when Alkali ion is in greater
concentration than H3O+
This false response is called Alkaline Error b/c of error
associated when measuring solutions of sodium hydroxide.
(NaOH)
Note – the electrode shows little interference with OH-.
Why?
Membrane Electrodes

Acid Error

Too many of the Si-O- sites are saturated with
H3O+ and no more sites are available for
protonation.
The response of real glass electrodes is described by the following
equation:
E  constant   (0.0592) log AH  (outside)
B is the electromotive efficiency (ideally =1, usually > 0.98)
Sensing electrodes

Several types




Simple Metal
Glass Membrane
Solid State Electrodes
Etc.
Let’s look at some examples.
Solid State Electrodes

The F- ISE



The original solid state
electrode
Works due to defects in a
LaF3 crystal.
Other Solid state
electrodes work based
on the presence of
primary absorbed ion.
LaF3/Eu
F- Inorganic Crystal
The solid state electrode is a very popular type of ISE. As easy to
maintain as a pH electrode (sometimes easier).
Solid State Electrodes

Our TISAB the pH was 5-6 and the ionic strength
was held constant. Why?



F- and OH- are about the same size AND same CHARGE!!
LaF3/Eu2+ doped crystal selects for size and charge
Thus, OH- will cause a response.
Solid State Electrodes

Our TISAB the pH was 5-6 and the ionic
strength was held constant. Why?
E  constant   (0.0592) log AF  (outside)
E  constant   (0.0592) log  F  [ F  ](outside)
E  constant   (0.0592) log  F    (0.0592) log[ F  ](outside)
Constant
E  constant ' (0.0592) log[ F  ](outside)
Conclusions

Several types

Simple Metal –

Using Metal associated with Ion


Using Inert Electrode





pH Electrode
Two reference electrodes (Constant Potential)
Measuring the ‘junction’ potential
Alkali Error
Solid State Electrodes




Yields Information on Ratio of concentrations
Glass Membrane


Direct Quantitation
Flouride ISE
Measuring junction potential
Acid and Base Error
Detection limits are
between 10-6 M and
10-8 M
Interferences are based on similar size and charge for Membrane
electrodes and SS Electrodes