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Announcements
Course Evaluations
Final is Wednesday Afternoon on May 9th
Homework 14-15, 14-26, 15-6, 16-3, 16-6,
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Course Evaluations
Request from ThelmoRequest 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?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
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Concentration Concentration dependency of Edependency of E
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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
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The Nernst Equation
The Nernst Equation
For aA + ne- bB
Qn
VEE o log
05916.0
aA
bBo
n
VEE
AA
log05916.0
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Example Equilibrium constant and Eo
Find the equilibrium constant for the reaction
Cu (s) + 2Fe3+ 2Fe2+ + Cu2+
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Example
Find the voltage of the cell Half reaction
Ag (s) into a solution of 0.50 M AgNO3 (aq)
The other half-reactionCd (s) is immersed into a 0.010 M Cd(NO3)2 (aq)
Metals are connected by wires Solution connected with salt bridge
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0.50 M AgNO0.50 M AgNO330.010 M Cd(NO0.010 M Cd(NO33))22
Find the voltage of the cell
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Potentiometric Methods
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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!!!
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ReferenceReference
Indicating Indicating electrode – electrode – The part of the cell The part of the cell that contains the that contains the solutions we are solutions we are interested in interested in measuringmeasuring
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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
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Reference Electrodes
Ag/AgCl
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Reference Electrodes
Calomel Electrode (SCE) Very Common Hg|Hg2Cl2 (sat), KCl|| Chloride is used to
maintain constant ionic strength
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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 Eo (V)Hg2Cl2 + 2e- ->2Hg(l) + 2Cl- 0.244 V
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HgHg22ClCl22 + 2e + 2e-- ->2Hg(l) + 2Cl ->2Hg(l) + 2Cl-- 0.241 0.241AgClAgCl (s) (s) + e + e-- ->Ag(s) + Cl ->Ag(s) + Cl-- 0.197 0.197
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Sensing electrodes
Several types Simple Metal Solid State Electrodes Glass Membrane Etc.
Let’s look at some examples.
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Sensing electrodes
Several types Simple Metal Solid State Electrodes Glass Membrane Etc.
Let’s look at some examples.
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Simple metal electrodes
A bare metal in contact with a solution.
General Form: Mn+ + ne- -> M(s)
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Simple Metal Electrodes A bare metal in contact with a
solution of its cation.
Ag+ + 1e- -> Ag(s) 0.799 V
General formMn+ + ne- -> M(s)
][
1log
0592.0
AgnEE o
ind
][
1log
0592.0n
oind Mn
EE
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Example
A potential of 0.5000V was measured vs. SCE. What is the concentration of Ag+?
Hg2Cl2 + 2e- 2Hg(l) + 2 Cl- Eo = 0.241V
Ag+ + e- Ag(s) Eo = 0.799VUsing 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!!no calibration plot required!!
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Simple Metal Electrodes
Example Silver sensing
electrode
][
1log
1
0592.0799.0
AgVEE indred
])log[(0592.0799.0 AgVEind pAgVEind 0592.0799.0
redoxcell EEE redEVV 244.05000.0 pAgVVV 0592.0799.0241.05000.0
pAg0592.0058.0 pAg
0592.0
0580.0
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Example (cont’d)
pAg
0592.0
0580.0
pAg9797.0
][101 9797.0 Agx
][104.0 7 AgM
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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!No quantitation but suitable for titrations!
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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)
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Simple Metal Electrodes
Eoverall = Eox + Ered
Calomel(Hg2Cl2)
][
][log
1
0592.03
2
Fe
FeEE o
red
Constant = -0.241 V
Reduction at Platinum Electrode:Reduction at Platinum Electrode:
Reaction Eo
Fe3+ + 1e- -> Fe2+ 0.771 V
][
][log0592.0771.0
3
2
Fe
FeVEred
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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)
CeCe4+4+
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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
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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.
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Equivalence Point
][
][log
05916.0
ox
red
A
oAA A
A
n
VEE
][
][log
05916.0
ox
red
B
oBB B
B
n
VEE
Since at equilibrium, [Ared] = [Box] and [Bred] = [Aox] we massage the two general equations to yield:
BA
oBB
oAA
eq nn
EnEnE
Nernst Equation for ANernst Equation for A
Nernst Equation for BNernst Equation for B
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Equivalence Point
BA
oBB
oAA
eq nn
EnEnE
Note: This expression only works for simple REDOX TITRATIONS:
Simple redox titrations:Only Aox, Box, Ared, Bred are involved in the reaction …
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Two examples
Determine Eeq for the following reactions: Fe2+ + Ce4+ -> Fe3+ + Ce3+
Sn2+ + 2Ce4+ -> Sn4+ + 2Ce3+
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Titration curves
What does a titration curve look like for an acid/base titration?
Typical pH titration
0
2
4
6
8
10
12
14
0 5 10 15 20
mL of HBr
pH
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REDOX Titrations
Ecell
OverTitration
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Just like Acid/Base Titrations
There are four significant regions, The StartThe Start The Buffer RegionThe Buffer Region The equivalence PointThe equivalence Point OvertitrationOvertitration
Let’s Use our simple example:Let’s Use our simple example: FeFe2+2+ + Ce + Ce4+4+ Fe Fe3+3+ + Ce + Ce3+3+
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Our simple example
Let’s Use our simple example:Let’s Use our simple example: FeFe2+2+ + Ce + Ce4+4+ Fe Fe3+3+ + Ce + Ce3+3+
Titrate 50 mL of 0.05 M Fe2+ with 0.10 M Ce4+
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0% Titration0% 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
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0% Titration0% Titration
][
][log
05916.03
2
Fe
Fe
n
VEE
A
oFeFe
0
05.0log
1
05916.0771.0
VVEFe
FeENO … 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.
5105
05.0log
1
05916.0771.0
x
VVEFe
SHE vs.594.0177.0771.0 VVV
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“Buffer Region”
FeFe2+2+ + Ce + Ce4+4+ Fe Fe3+3+ + Ce + Ce3+3+
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.
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“Buffer Region”
][
][log
05916.03
2
Fe
Fe
n
VEE
A
oFeFe
2
2
107.1
105.2log
1
05916.0771.0
V
VEFe
VVEFe 761.0010.0771.0
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Closer look at the “buffer” region
Fe2+/Fe3+ E
9 0.715
4 0.735
1.5 0.761
1 0.771
.25 0.807
.11 0.829
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Equivalence PointEquivalence Point
From Before Eeq = 1.24 V
What volume?
25 ml
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Excess Ce4+ (post titration) FeFe2+2+ + Ce + Ce4+4+ Fe Fe3+3+ + Ce + Ce3+3+
The predominate change is that CeThe predominate change is that Ce4+4+ is being added and is being added and diluteddiluted into a solution of Ceinto a solution of Ce3+3+..
All FeAll Fe2+2+ has been converted to Fe has been converted to Fe3+3+ and no longer figures into the and no longer figures into the calculationscalculations
We just need to keep track of the amounts of CeWe just need to keep track of the amounts of Ce3+3+ and Ce and Ce4+4+ as as well as the well as the VOLUME of the system.VOLUME of the system.
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Excess Ce4+ (post titration)
At 30.0 mL Ce4+ Vt = 30.0 mL+ 50.0 mL
][
][log
05916.04
3
Ce
Ce
n
VEE oCeCe
][
][log
1
05916.070.1
4
3
Ce
CeVECe
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Excess Ce4+ (post titration)
FeFe2+2+ + Ce + Ce4+4+ Fe Fe3+3+ + Ce + Ce3+3+
Ce3+/Ce4+
?][ 3 Ce
?][ 4 Ce
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Excess Ce4+ (post titration)
][
][log
1
05916.070.1
4
3
Ce
CeVECe
3
2
102.6
101.3log
1
05916.070.1
x
xVECe
SHE vs.66.1041.070.1 VECe
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Redox IndicatorsRedox Indicators
General
Specific
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General Redox Indicators
Varies as a function of Ecell
Rely on a color change with Indox and Indred being different colors.
Indox + ne- Indred
][
][log
05916.0
ox
redoind Ind
Ind
n
VEE
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General Redox Indicators
In order to see a color change, you typically need approximately a 10% conversion from one form to another.
1
10
10
1
][
][ or
Ind
Ind
ox
red
n
VEE oind
05916.0
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General Redox Indicators
Examples Consider 1,10 phenanthrolene-Fe
C
C
N N
Fe(III)
C
C
N N
Fe(II)
+ e-
BLUEBLUE REDRED
Eo = 1.06 V
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General Redox Indicators
NH
S
O
O
OH
Examples Consider Diphenylamine sulphonic acid
Used with the iron in the dichromate method
Eo = 0.80V
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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.
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Common Titrants
Usually oxidizing agents. Cr2O7
2- - 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
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Common titrants
Reducing Titrants Fe2+
Usually Fe(NH4)2(SO4)2.6H2O in 1M H2SO4
Solution must be standardized each day I-
Indirect methodYour lab was an excellent example
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Sensing electrodes
Several types Simple Metal Glass Membrane Solid State Electrodes Etc.
Let’s look at some examples.
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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
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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!
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pH membrane
Special Glass (72% SiO2) Doped with Na2O (22%)
and CaO (6%)
SiOCation
Key
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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
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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?
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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:
)(log)0592.0(constant outsideAE H B is the electromotive efficiency (ideally =1, usually > 0.98)
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Sensing electrodes
Several types Simple Metal Glass Membrane Solid State Electrodes Etc.
Let’s look at some examples.
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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
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F- Inorganic CrystalThe solid state electrode is a very popular type of ISE. As easy to maintain as a pH electrode (sometimes easier).
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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.
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Solid State Electrodes
Our TISAB the pH was 5-6 and the ionic strength was held constant. Why?
)(log)0592.0(constant outsideAE F
)]([log)0592.0(constant outsideFE F
)](log[)0592.0(log)0592.0(constant outsideFE F
Constant
)](log[)0592.0('constant outsideFE
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Conclusions Several types
Simple Metal – Using Metal associated with Ion
Direct Quantitation Using Inert Electrode
Yields Information on Ratio of concentrations Glass Membrane
pH Electrode Two reference electrodes (Constant Potential) Measuring the ‘junction’ potential Alkali Error
Solid State Electrodes Flouride ISE Measuring junction potential Acid and Base Error
Interferences are based on similar size and charge for Membrane electrodes and SS Electrodes
Detection limits are between 10-6 M and 10-8 M