C3100 - Winter 2011
VII. ELECTROCHEMISTRY (Chapters 13-16)
FUNDAMENTALS (Chapter 13)
Basic Concepts:
¾Oxidizing agent: accepts electrons from another substance which is oxidized,
while the oxidizing agent is reduced
(examples: O2, F2, acidified MnO4-, acidified Cr2O72-, Ce4+)
¾Reducing agent: donates electrons to another substance which is reduced,
while the reducing agent is oxidized
(examples: alkali metals, SO32−, Fe2+)
¾Electric charge q is measured in Coulombs (C)
Charge of 1 electron = 1.602 x 10-19 C
Charge of 1 mole electrons = (6.022 x 1023 mol-1) x (1.602 x 10-19 C )
= 9.649 x 104 C = Faraday constant F
Charge of n mole electrons = q = nF
1
¾The quantity of charge per second is called the current I (in ampere A = Cs-1)
¾The difference in electric potential E between two points is the work needed
(or that can be done) to move an electric charge from one point to the other,
per unit charge. It is measured in Volts (V).
Work = E • q (in Joule, J)
¾The maximal possible electrical work that can be done by a chemical reaction
on its surroundings (at ct. T and p) is the free-energy change (ΔG):
-ΔG = work done on surroundings
ΔG = - E • q = - nFE
Relates the free-energy change of a reaction to
the voltage that can be generated by that reaction
¾Ohm’s law: E = R • I
(where R is the resistance, in ohm Ω)
¾Power P is work done per unit time, in units of Js-1 or watt (W)
P = work / s = E • q / s = E • I
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Dr. G. Van Biesen
C3100 - Winter 2011
Galvanic Cells
Change in ΔG
A galvanic cell (e.g. battery, fuel cell) uses a spontaneous chemical reaction to
generate electricity – one reagent is oxidized, the other is reduced. The
reagents are physically separated so that electrons have to flow through an
external circuit to go from one reactant to the other.
A potentiometer in the external circuit measures
the voltage generated by the cell.
Oxidation occurs in one half-cell (anode),
while reduction takes place in the other
(cathode).
The two half-cells are connected with a
salt bridge which contains a gel with a
high conc. of electrolyte that does not
affect the cell reaction – it allows ions to
diffuse, thereby maintaining
electroneutrality.
Cd(s)
Cd(NO3)2
Phase boundary
AgNO3
Ag(s)
Cd(s) + 2Ag+
Cd2+ + 2Ag(s)
Ecell = E+ - E-
Salt bridge
3
Standard reduction potentials (E°) for half cells are determined experimentally.
(‘Standard’ means at 25 °C and all activities 1)
Idealized exp. to determine E° for: Ag+ + e- → Ag:
LHS cell: Standard Hydrogen Electrode
(S.H.E.): Pt surface in contact with an
acidic solution (A(H+) = 1) through which
H2 gas is bubbled (A(H2) = 1)
½ H2 (g)
H+ + eBy convention: E° (S.H.E.) = 0 V
RHS cell: Ag+ + e- → Ag
By convention: the left-hand electrode is
connected to the negative (reference)
terminal of the potentiometer, the righthand electrode to the positive terminal.
e- (lost by the species undergoing oxidation) flow
from the anode to the cathode, where they are
gained by the species undergoing reduction.
The potentiometer measures the difference in reduction potentials of both half
cells, and indicates a positive voltage when electrons flow into the negative
terminal.
V or Ecell = E+ - E4
Dr. G. Van Biesen
C3100 - Winter 2011
Here, Ecell = E°Ag+ = +0.799 V, which means that e- flow into the neg.
terminal; the LH cell is the anode; the RH cell is the cathode.
With the cell: S.H.E. Cd2+ Cd(s) we find Ecell = E°Cd2+ = -0.402 V and eflow in the other direction – the LH half cell is now the cathode; the RH cell is
the anode.
Redox potentials always written as
reduction potentials. The more positive
the reduction potential, the stronger the
driving force for reduction to occur:
ΔG = - nFE
K+ is a very poor oxidizing agent –
does this imply it is a strong reducing
agent? What about K?
In a galvanic cell, reduction spontaneously occurs in the half-cell with the
more positive reduction potential (at the cathode). Oxidation spontaneously
occurs in the other half-cell (at the anode).
5
The Nernst Equation:
The sign and magnitude of Ecell can only be predicted from tabulated values if
both half cells operate under standard conditions; this will rarely be the case,
and half cell potentials under non-standard conditions have to be calculated
using the Nernst equation.
bB
aA + neE°= standard reduction potential (AA = AB = 1)
R = gas ct. = 8.314 J / (K•mol)
T = temperature in K
n = # e- in half reaction
F = Faraday ct. = 96485 C/mol
Reaction quotient Q =
ABb
; when all activities are unity, E = E°
AAa
(Note: pure solids, pure liquids, and solvents have activity = 1)
At 25 °C, we can simplify this equation to:
We also replace activities of
solutes by their concentrations;
for gases we use pressure (bar)
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Dr. G. Van Biesen
C3100 - Winter 2011
EXAMPLE: for the reduction of white phosphor to phosphine gas:
¼ P(s) + 3 H+ + 3 eE = -0.046 -
0.05916
3
PH3(g)
log
E° = -0.046 V
PPH3
[H+]3
Note that if we multiply the half-reaction by any factor, this does not
change E…
P(s) + 12 H+ + 12 eE = -0.046 -
= -0.046 -
= -0.046 -
0.05916
12
0.05916
12
0.05916
12 3
4 PH3(g)
log
P4PH3
log
PPH3
[H+]12
4 log
4
[H+]3
PPH3
[H+]3
7
…nor does it change E°: remember that work = E • q, or: E = work / q
Potential difference is work done per unit of charge carried through that
potential difference (i.e. regardless of the amount of charge; q = nF can be
any number).
Stepwise procedure for finding the potential of a galvanic cell:
¾Identify in each half-cell the element that occurs in two oxidation states
¾Write reduction half-reactions for each half-cell – find E° for each in a table
(e.g. Appendix H in Harris 7th Ed.). Multiply half-reactions so that they
contain the same # of e- (do not multiply E°!).
¾Write Nernst equations for E+ (RH cell; pos. terminal) and E- (LH cell; neg.
terminal).
¾Find: Ecell = E+ - E- If Ecell > 0, then net cell reaction is spontaneous, if
Ecell < 0 then net cell reaction is spontaneous in the reverse direction.
¾For a balanced net cell reaction, subtract left half-reaction from right halfreaction (i.e. reverse left half-reaction and add it to the right half-reaction).
8
Dr. G. Van Biesen
C3100 - Winter 2011
A more intuitive way of looking at cell potentials:
Electrons always flow towards
the more pos. potential
Half-cell with higher E ‘wants to
be reduced’, the one with the
lower E ‘wants to be oxidized’
Half-cell reactions can sometimes be written in
different ways, but the half-cell potential should be
the same:
Ag(s) + Cl-
e.g.: AgCl(s) + e-
E°+ = 0.222 V
E+ = 0.222 – 0.05916 log[Cl-]
= 0.222 – 0.05916 log(0.0334)
= 0.309 V
9
We could also have written the RH half-cell reaction as:
Ag+ + e-
Ag(s)
is reduced to Ag)
1
E+ = 0.799 – 0.05916 log
[Ag+]
= 0.310 V
(In both reactions,
E°+ = 0.799 V
Ag+
[Ag+] =
Ksp
[Cl-]
1.8 x 10-10
=
0.0334
= 5.4 x 10-9 M
E° and the Equilibrium Constant:
A galvanic cell produces electricity because
the cell reaction is not at equilibrium.
Replacing the potentiometer with a wire,
there would be an appreciable current flowing
through it, and the concentrations of the
reactants would change until equilibrium is
reached (Ecell = 0)
The potentiometer that measures the
voltage of the cell has a very high
resistance (1013 Ω), and thus allows
only a very small current (e.g. if Ecell =
1 V, then I = 10-13 A). This does not
noticeably change the concentrations
of the reactants in the cell.
10
Dr. G. Van Biesen
C3100 - Winter 2011
aA + nedD + ne-
cC
bB
E°+
E°-
Special case: cell is at equilibrium: Ecell = 0; Q = K
True at any time
11
EXAMPLE: Find K for the reaction:
2Fe2+ + Cu2+
Cu(s) + 2Fe3+
The two half-reactions are:
2Fe3+ + 2e- (Cu2+ + 2e-
2Fe2+
2Cu(s))
E° = E°+ - E°- = 0.432 V
E°+ = 0.771 V
E°- = 0.339 V
K = 10(2)(0.432)/(0.05916) = 4 x 1014
Note: the procedure can also be used to find K for reactions that are not redox
Fe2+ + CO32- K = Ksp).
reactions! (e.g. FeCO3(s)
It is just a matter of finding half-reactions with known E° values that, when
combined, add up to that particular reaction. A redox potential is simply another
way of expressing the free-energy change of a reaction. See Box 13-3 on
Latimer diagrams in Harris 8th Ed.
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Dr. G. Van Biesen
C3100 - Winter 2011
Biochemists use E°':
Standard reduction potentials are defined with all participating species at
activity = 1. Often, H+ is involved in reactions, and this means that all E°
values are for pH = 0. This is not very appropriate for biological systems,
where pH ≈ 7.
E°’ is the formal potential at pH 7
(‘formal’ means that it applies under a specific set of conditions e.g. at certain
ionic strength, conc. of complexing agents, or at a certain pH)
aA + neE = E° -
bB + mH+
0.05916
log
n
E°
A and B could be acids/bases
[B]b[H+]m
[A]a
Conversion from [A] to FA : see
fractional composition equations.
IV. Acid/Base Chemistry, slides
35-39
13
ELECTRODES AND POTENTIOMETRY (Chapter 14)
Potentiometry = use of electrodes to measure voltages that provide chemical
information
A solution containing an electroactive analyte (analyte that can donate or accept
electrons at an electrode) is turned into a half-cell by inserting an indicator
electrode (e.g. Pt wire), and is connected via a salt bridge to another half-cell
with a fixed composition (fixed potential), the reference electrode. The cell
voltage is then measured, and depends on the concentration of the analyte.
Reference Electrodes:
Consider a galvanic cell with Fe2+/Fe3+ and a Pt wire as one half-cell, and a
constant potential half-cell:
Fe2+
E°+ = 0.771 V
RH cell: Fe3+ + eAg(s) + ClE°- = 0.222 V
LH cell: AgCl(s) + eE = 0.771 – 0.05916 log
Cell voltage only depends
on [Fe2+] / [Fe3+] !
[Fe2+]
[Fe3+]
- 0.222 - 0.05916 log[Cl-]
= ct
Dr. G. Van Biesen
14
C3100 - Winter 2011
Reference electrode
connected to reference
terminal (-) of potentiomenter
The type of reference electrode in the RH figure is a silver-silver chloride
reference electrode:
AgCl(s) + e-
Ag(s) + Cl-
E°- = 0.222 V
Its standard reduction potential is 0.222 V, but this is with A(Cl-) = 1.
The activity of Cl- in a saturated solution ≠ 1, and Esat. KCl = 0.197 V
15
Problem with these type of electrodes: can
get clogged, not compatible with some types
of solutions (e.g. solutions containing Ag and
Ag-complexing compounds such as Tris).
Double-junction may be necessary
Another commonly used reference electrode is
the saturated calomel electrode (S.C.E.):
½ Hg2Cl2(s) + e-
Hg(l) + Cl-
E° = 0.268 V
Esat. KCl= 0.241 V
16
Dr. G. Van Biesen
C3100 - Winter 2011
The S.H.E. (slide 4) is not commonly used as a reference electrode because
it is not practical to work with.
The following diagram allows conversion from voltages obtained using one
reference electrode, to another:
Point A: –0.220 V from the S.H.E.
-0.461 V from the S.C.E.
-0.417 V from the Ag/AgCl electrode
Point B: +0.230 V from the S.H.E.
-0.011 V from the S.C.E.
+0.033 V from the Ag/AgCl electrode
17
Note: four types of electrodes used in electrochemistry:
M(s)
M(s), MX
Mn+(aq)
X-(aq)
Metal / metal ion
e.g. Cd/Cd2+
n (s)
Pt(s)
Pt(s)
Mn+(aq),
Mm+(aq)
Metal / 'insoluble' salt
e.g. Ag/AgCl/Cl-
Redox electrode
e.g. Pt/Sn2+/Sn4+
Gas electrode
e.g. S.H.E
Limitations to the Use of Electrode Potentials:
Voltages measured in lab are not always the same as calculated ones, mainly
because of two reasons:
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Dr. G. Van Biesen
C3100 - Winter 2011
Liquid junction potentials:
Most galvanic cells have a salt bridge → electrolyte solutions of different
composition in contact with each other (with a porous glass disk: allows ions to
go through, but minimizes mixing) = liquid junction
Liquid junctions always develop a potential at their interface, usually a few mV.
This potentials contributes to the cell voltage (because the voltage of a galvanic
cell is due to the potential difference developed at each of the electrode-solution
and liquid-liquid interfaces), but is generally not known and puts a fundamental
limitation on the accuracy of potentiometric measurements
Development of a liquid junction potential:
Na+ and Cl- diffuse into the water (from high to low conc.)
Cl- has a higher mobility than Na+ → a region rich in Cl(with excess neg. charge) develops at the front;
immediately behind it is a pos. charged region,
with more Na+ than Cl-. This creates a potential difference at the junction of the NaCl and H2O phases.
The steady-state potential opposes the movement of Cl-,and accelerates the movement of Na+.
Since K+ and Cl- have similar mobilities, KCl is often used in salt bridges
because this minimizes the junction potential. Where Cl- cannot be used (e.g.
with half-cells containing Ag+), NO3- is a good substitute.
19
Reversibility of the electrode reaction:
For the potential of an electrode to be properly described by the Nernst
equation, the electrode reaction must be reversible, and rapid, but that is not
always the case!
H2C2O4
e.g.: 2 CO2(g) + 2 H+ + 2 eE = E° -
0.05916
2
log
[H2C2O4]
(pCO2)2 [H+]2
The rate at which CO2 reacts to produce oxalic acid is extremely
slow. Changes in partial pressure of CO2 therefore have little effect
on E; the Nernst equation does not apply.
Indicator Electrodes:
Metal electrodes: electric potential develops in response to a redox reaction at
the metal surface
Ion-selective electrodes: selective binding of analyte generates electric potential
no oxidation-reduction takes place!
20
Dr. G. Van Biesen
C3100 - Winter 2011
Metal electrodes can be made from the same metal as the cation to be
analyzed (Ag/Ag+, Cu/Cu2+,…) or from an inert metal (Pt, Au), or from C.
Ag+ + e½ Hg2Cl2(s) + e-
Ag(s)
E°+ = 0.799 V
Hg(l) + Cl- Esat. KCl= 0.241 V
E = 0.799 – 0.05916 log
1
[Ag+]
- 0.241 V = (0.558 + 0.05916 log [Ag+]) V
Ideally, E changes by 59.16 mV for every
factor of 10 change in [Ag+]
This type of cell can also be used to
measure halide concentrations (e.g. Cl-)
if AgX is present at the surface of the
Ag electrode, since [Ag+] [X-] = Ksp
21
Ion-selective electrodes respond selectively to one ion (ideally) – they do not
involve redox processes. There are various types, but most have a thin
membrane which binds only a specific analyte ion (solid-state ion-selective
electrodes are based upon doped inorganic crystals). Analyte ions equilibrate
with ion-exchange sites at the outer surface of the membrane. This creates a
charge imbalance (=potential) across the phase boundary between the solution
and the membrane. This potential difference can be related to concentration
using calibration curves.
A glass electrode for pH measurements is the most common ion-selective
electrode. It is usually a combination electrode, which incorporates a Ag/AgCl
reference electrode.
Other ion-selective electrodes: K+, Ca2+, Mg2+, F-, Cl-, S2Extensively used in clinical diagnosis
Respond to activity of uncomplexed analyte ion only!
Often used with standard addition
22
Dr. G. Van Biesen
C3100 - Winter 2011
pH Measurement with a Glass Electrode
Glass electrode = ion-selective electrode
Sensitive to H+, to some extent also to Na+ (especially at pH > 12)
Usually as a combination electrode = both glass and reference in one unit
Ag(s) AgCl(s) Cl-(aq)
H+(aq, outside)
glass membrane
H+(aq, inside), Cl-(aq) AgCl(s) Ag(s)
Int. ref. electrode
Ext. ref. electrode
Eref1 Ej
Eb
Glass electrode
Easy Eref2
Ecell = Eref2 + Eb + Easy – Eref1 + Ej
The two reference electrodes measure the electric potential difference across
the glass membrane. Except for Eb, which depends on [H+] on either side of
the membrane, all other potentials are constant. Since [H+]intside is fixed, Eb in
fact only depends on [H+]outside (i.e. pH of analyte solution).
23
24
Dr. G. Van Biesen
C3100 - Winter 2011
The glass membrane consists for ~70% SiO2,
with the remainder oxides of Ca, Ba, Li, and Na.
In the silicate lattice of the glass membrane, those
oxygen atoms that are not shared by two Si
O
atoms have a neg. charge and are coordinated to
Si
cations. Singly charged cations (Na+, Li+) are
cation
mobile in this lattice and are responsible for
electrical conduction within the membrane.
(H+ cannot cross the membrane)
The surfaces of the glass membrane in
contact with water become hydrated (they
swell), and act as cation-exchangers. Metal
cations in these regions become mobile,
diffuse out of the membrane, and can be
replaced by H+ from the solution– H+ is the
only ion that binds significantly to the
hydrated gel layer.
25
H+ + Na+Glsoln
glass
Na+ + HGl
soln
glass
K is large, so ordinarily surface of
hydrated glass membrane is entirely
HGl (except at high pH)
The glass in the hydrated layer can be
considered as a weak acid:
HGl
H+ + Gl-
glass
soln
glass
Each side of the membrane acquires a negative charge, the magnitude of
which depends on the [H+] of the solution with which it is in contact. The
potential that develops across the membrane is the result of an unequal
charge buildup at opposing surfaces of the membrane
The response of the glass electrode is given by:
(Ao is the activity of H+ in the outer solution)
E = k + 0.05916 log Ao
Or: E = k - 0.05916 pH
In practice: E = k - β (0.05916) pH
26
Dr. G. Van Biesen
C3100 - Winter 2011
Calibration of a glass electrode, and pH measurement
Use two (or more) buffer solutions:
First buffer (known pHS1) gives a voltage ES1
Second buffer (known pHS2) gives a voltage ES2
With the second buffer β is determined; should be
close to 1
Equation of the line
through both points:
For a solution of unknown
pH, we measure Eunknown
and pHunknown is
automatically calculated
and displayed via the
previously determined
relationship
27
Using glass electrodes:
•Electrode has to be stored (ideally) in same solution as that in the reference
compartment. If the membrane dehydrates, it has to be rehydrated for several
hours before use.
•Remove cap at upper end of electrode which covers the air inlet (prevents
evaporation of filling solution when not in use) – see slide 24
•Calibrate the electrode with appropriate buffers – equilibrate with stirring for at
least a minute – let reading stabilize.
•Rinse the electrode with deionized water when transferring to another solution –
the membrane can be gently blotted, but do not wipe it, because this may
produce a static charge on the glass.
•Most pH meters have a dial to compensate for temperature – see slide 6.
•Accuracy of pH measurements with glass electrodes are ± 0.02 pH units (this
corresponds to a uncertainty of ± 5% in AH+), although measurements of pH
differences between solutions can be 10x more accurate. Main sources of
errors are standards and liquid junction potentials.
28
Dr. G. Van Biesen
C3100 - Winter 2011
REDOX TITRATIONS (Chapter 15)
Ce4+ + Fe2+
Ce3+ + Fe3+
Reactions at the Pt electrode:
Fe3+ + eCe4+ + e-
Fe2+
Ce3+
E° = 0.767 V
E° = 1.70 V
E° for titration reaction = 1.70 – 0.767
= 0.933 V; K = 10(0.933/0.05916) ≈ 1016
(i.e. quantitative)
The Pt indicator electrode responds to
relative conc. (activities) of Ce4+ and
Ce3+, or Fe2+ and Fe3+
Before EP:
With the addition of each aliquot of Ce4+, Fe2+ is consumed and converted
into Fe3+. We can easily calculate [Fe2+], [Fe3+] and [Ce3+]; [Ce4+] is more
difficult to calculate. Therefore, we use:
29
E = E+ - E- = 0.767 – 0.05916 log
E = 0.526 – 0.05916 log
[Fe2+]
[Fe3+]
- 0.241
ES.C.E.
[Fe2+]
[Fe3+]
Note: 1. When V = ½ VEP, E+ = E°+ for the Fe3+/Fe2+ couple
2. The voltage at V = 0 cannot be calculated (E = -∞?)
At EP:
All Fe2+ and Ce4+ are converted to Fe3+ and Ce3+; which exist in equilibrium
with Fe2+ and Ce4+ as:
Fe3+ + Ce3+
Ce4+ + Fe2+
Since [Fe3+] = [Ce3+], [Fe2+] = [Ce4+]
Both half-reactions are in equilibrium at the Pt electrode at any time:
E+ = 0.767 – 0.05916 log
[Fe2+]
[Fe3+]
E+ = 1.70 – 0.05916 log
[Ce3+]
[Ce4+]
30
Dr. G. Van Biesen
C3100 - Winter 2011
2 E+ = 0.767 – 0.05916 log
2 E+= 2.467 – log
2 E+ = 2.467 V
[Fe2+]
[Fe3+]
+ 1.70 – 0.05916 log
[Ce3+]
[Ce4+]
[Fe2+] [Ce3+]
[Fe3+] [Ce4+]
[Fe3+] = [Ce3+] and [Fe2+] = [Ce4+] at EP
⇒ E+ = 1.23 V
The cell voltage E = E+ - Ecalomel = 1.23 – 0.241 = 0.99 V
Independent of
conc., for this
particular titration
After EP:
The # moles of Ce3+ = the # moles of Fe3+, and there is a known excess of
(unreacted) Ce4+. We now use:
E = E+ - Ecalomel = 1.70 – 0.05916 log
[Ce3+]
[Ce4+]
- 0.241
When V = 2 VEP, [Ce3+] = [Ce4+], and E+ = E°+ = 1.70 V
E = E+ - Ecalomel = 1.70 – 0.241 = 1.46 V
31
EXAMPLE: 100.0 mL 0.0500 M Fe2+ titrated with 0.100 M Ce4+
What are the cell potentials at 36.0, 50.0 (= VEP) and 63.0 mL?
Ce4+ + Fe2+
Ce3+ + Fe3+
•At 36.0 mL: A fraction of Fe of 36.0/50.0 is now in the form of Fe3+; a
fraction of 14.0/50.0 is still in the form of Fe2+
E = 0.526 – 0.05916 log
E = 0.550 V
14/50
36/50
The actual concentrations of Fe2+
and Fe3+ are 0.0103 and 0.0265
M, respectively
•At 50.0 mL (=VEP), the cell voltage here is
independent of concentration, and V = 0.99 V
•At 63.0 mL: with the first 50.0 mL of Ce4+
converted into Ce3+, there is now a 13.0 mL
excess of Ce4+:
E = E+ - Ecalomel = 1.70 – 0.05916 log
50
13
- 0.241
E = 1.424 V
The actual concentrations of
Ce3+ and Ce4+ are 0.0307 and
0.00798 M, respectively
32
Dr. G. Van Biesen
C3100 - Winter 2011
The titration curve is symmetrical around the EP only because the reaction
stoichiometry is 1:1. For a 2:1 ratio, the curve is not symmetrical. However,
with a steep rise in E near the EP, the error in VEP is minimal.
IO3- + 2Tl+ + 2Cl- + 6H+
ICl2- + 2Tl3+ + 3H2O
The more the E° values of the halfreactions differ, the bigger the
voltage change at the EP – best
results are obtained with strong
oxidizing/reducing agents.
A difference in formal potentials of
> 0.200 V usually gives satisfactory
results.
Since half-cell potentials depend on the ratio of concentrations, they are
independent of the concentration! In practice, the lower limit is ~ 1 mM, since at
lower concentrations impurities will be present at much larger relative amounts,
and may consume a significant proportion of titrant.
33
EXAMPLE: potentiometric titration of Fe2+ (400.0 mL; 3.75 mM) with MnO4(20.0 mM); calomel electrode as reference (Ecalomel = 0.241 V) in 1.00 M H2SO4
Fe3+ + eFe2+
+
MnO4 + 8H + 5eMnO4 +
-
VEP?
8H+
+
5Fe2+
Mn2+
E° = 0. 68 V (in 1 M H2SO4)
E° = 1.507 V
+ 4H2O
Mn2+
+ + 5Fe3+ + 4H2O
# moles MnO4- = # moles Fe2+
1 mol MnO45 mol Fe2+
VEP x 20 mM = 1/5 x 400 mL x 3.75 mM
⇒ VEP = 15.0 mL
•Before EP, e.g. 12.0 mL MnO4- added:
E = E+ - E- = 0.68 – 0.05916 log
E = 0.439 – 0.05916 log
E = 0.475 V
[Fe2+]
[Fe3+]
- 0.241
3.0/15.0
12.0/15.0
34
Dr. G. Van Biesen
C3100 - Winter 2011
•At EP: we again add both half-reactions:
[Fe2+]
E+ = 0.68 – 0.05916 log
5 E+ = 1.507 –
[Fe3+]
0.05916
5
log
6 E+ = 8.215 – 0.05916 log
6 E+ = 8.215 – 0.05916 log
We multiply by 5 so we can sum
these equations more easily – this is
a purely algebraic operation and
now we have to multiply E+ as well!
[Mn2+]
[MnO4-] [H+]8
From the net reaction, we
see that at the EP [Fe2+] = 5
[MnO4-], and 5 [Mn2+] = [Fe3+]
[Fe2+] [Mn2+]
[Fe3+] [MnO4-] [H+]8
1
[H+]8
With [H+] =
400
415
1.00 M = 0.964 M
E+ = 1.368 V; the cell voltage E = 1.368 – 0.241 = 1.127 V
•After EP: e.g. 17.0 mL MnO4- added: excess of 17.0 – 15.0 = 2.0 mL MnO4We now use the other half-reaction:
35
MnO4- + 8H+ + 5e-
Mn2+ + 4H2O
E° = 1.507 V
[Mn2+]? All the Mn2+comes from oxidation of Fe2+ by MnO4-, and only as much
Mn2+ can be formed as the amount of MnO4- added at VEP:
[Mn2+] = 15.0 mL x 20.0 mM
= 0.719 mM
(400.0 mL + 17.0 mL)
Or using [Fe2+]:
[MnO4-]? All MnO4- that is added after the
EP is in excess:
(17.0 mL – 15.0 mL) x 20.0 mM
[MnO4-] =
(400.0 mL + 17.0 mL)
[Mn2+] =
400.0 mL x 3.75 mM x 1/5
400.0 mL + 17.0 mL
= 0.719 mM
= 0.0959 mM
[H+]? The original [H+] is simply diluted by the addition of the titrant:
[H+] = 1.00 M
E+ = 1.507 –
400.0 mL
400.0 mL + 17.0 mL
= 0.959 M
The small amount of H+
consumed during the
reaction can be ignored.
0.05916
[Mn2+]
log
5
[MnO4-] [H+]8
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Dr. G. Van Biesen
C3100 - Winter 2011
0.05916
0.719 x 10-3
log
= 1.495 V
5
(0.0959 x 10-3) x (0.959)8
E+ = 1.507 –
The cell voltage E = 1.495 – 0.241 = 1.254 V
Finding the End Point of a Redox Titration:
Can use 2nd derivative method from a plot of V vs. volume, analogous to
acid-base titrations (Section V, slide 57), or can use a redox indicator.
Sometimes, the color of the titrant itself indicates the end point (e.g. the
previously described titration of Fe2+ with MnO4-).
A redox indicator changes color going from the oxidized to the reduced state.
Prediction of the potential range over which an indicator changes:
In(red)
In(ox) + neE = E° – 0.05916
n
log
In(red)
In(ox)
37
As with acid-base indicators, the color
of In(red) will be observed when:
10
In(red)
≥
1
In(ox)
The color of In(ox) will be observed when:
In(red)
In(ox)
≤
1
10
The color change thus occurs over the range: E = E° ±
0.05916
n
V
Ferroin (E° = 1.147 V) will change color in the range of 1.088 – 1.206 V with
respect to the S.H.E.; this is the range of 0.847 – 0.965 V vs. S.C.E. This
would be a good indicator for the titration on slide 29.
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Dr. G. Van Biesen
C3100 - Winter 2011
Adjustment of Analyte Oxidation State:
Sometimes an analyte has to be oxidized or reduced before it can be titrated.
This adjustment of the analyte oxidation state has to be quantitative, and the
reagent used has to be eliminated/removed completely before analysis.
Preoxidation:
¾Peroxydisulfate (or persulfate): S2O82- (requires Ag+ as a catalyst)
S2O82- + Ag+
SO42- + SO4- + Ag2+
2 powerful oxidants (E°(Ag2+) ≈ 2.0 V)
Excess reagent is destroyed by boiling after oxidation is complete:
2 S2O82- + 2 H2O
4 SO42- + O2 + 4 H+
¾Silver(II)oxide: AgO
Dissolves in mineral acids to give Ag2+; similar oxidizing power as persulfate
Excess AgO is removed by boiling: 4 Ag2+ + 2 H2O
4 Ag+ + O2 + 4 H+
¾Solid sodium bismuthate: NaBiO3
Similar oxidizing strength as above oxidants, excess reagent removed by
39
filtration.
Analytes that can be pre-oxidized by the reagents listed above:
Mn2+ to MnO4-; Ce3+ to Ce4+; Cr3+ to Cr2O72The oxidized analytes can then be titrated with e.g. a standardized Fe2+ solution
¾Hydrogen peroxide: H2O2 (in basic solution); medium oxidizing power
H2O2 + 2e-
2 OH-
Can be used for oxidation of
Co2+
E° = 0.88 V
→ Co3+; Fe2+ → Fe3+; Mn2+ → MnO2
Excess removed by boiling: 2 H2O2
2 H2O + O2 (disproportionation)
In acidic solution, it can reduce Cr2O72- to Cr3+, and MnO4- to Mn2+
Prereduction:
¾Stannous chloride (SnCl2): reduces Fe3+ to Fe2+ in hot HCl
Excess SnCl2 is destroyed by adding HgCl2:
Sn4+ + Hg2Cl2 + 4 ClSnCl2 + 2 HgCl2
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Dr. G. Van Biesen
C3100 - Winter 2011
¾Jones reductor: uses a column filled with Zn / Zn(Hg):
Zn(s) + HgCl2
Zn(Hg)(s) + ZnCl2
Zn(Hg) is preferred over Zn because it reduces H+ much more
slowly than Zn, and thus can be used for acidic solutions
Ox + Zn(Hg)(s)
H+
Red + Zn2+ + Hg(l)
(analyte)
(analyte)
Zn(Hg)(s)
Non-selective (E0 = -0.80 V); reduces many ions e.g. Fe3+, Cr3+, UO22+
Most reduced analytes are oxidized again by air, so the eluent has to be
titrated immediately.
The eluent can also be collected in an acidic Fe3+ solution (except when Fe
is analyzed), which is reduced by the analyte(s) to Fe2+ (stable) and can then
be titrated with an oxidant such as MnO4- (indirect determination)
¾Walden reductor: column is filled with Ag and 1 M HCl: more selective
(higher E°: 0.222 V), Cr3+ and TiO2+ are not reduced and thus do not
interfere with the analysis of e.g. Fe3+
41
Oxidizing Agents for Redox Titrations:
Potassium Permanganate: KMnO4
MnO4- + 8H+ + 5eMnO4 +
-
4H+
MnO4- + e-
+
3e-
Mn2+ + 4H2O
E° = 1.507 V
acid
MnO2 + 2H2O
E° = 1.692 V
neutral
E° = 0.56 V
basic
MnO42-
In strongly acidic solutions, MnO4- is its own indicator (Mn2+ is colorless)
KMnO4 is not a primary standard (contains traces of MnO2), and dissolved
KMnO4 reacts with organic impurities to produce some MnO2. Freshly
prepared KMnO4 solutions are boiled for an hour (speeds up the reaction)
and MnO2 is filtered (not with filter paper!). In addition, it oxidizes H2O:
4 MnO4- + 2 H2O
4 MnO2(s) + 4 OH- + 3 O2
Frequent standardization is necessary – can use Na2C2O4 or pure iron wire:
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Dr. G. Van Biesen
C3100 - Winter 2011
[MnO4− + 8 H+ + 5 e−
[H2C2O4
Mn2+ + 4 H2O] x 2
2 CO2 + 2 H+ + 2 e−] x 5
2 MnO4− + 5 H2C2O4 + 6 H+
2 Mn2+ + 10 CO2 + 8 H2O
This reaction is slow at room temperature; when most of the titrant (90-95%)
is added, the reaction mixture is heated up to ~60 °C to drive off CO2 and
shift the equilibrium to the right. A blank is performed to account for the
amount of titrant necessary to impart a pink color to the solution.
A pure iron wire can be dissolved in warm 1.5 M H2SO4 (under N2); the cooled
solution can be titrated directly – 5 mL of H3PO4 / 100 mL solution can be
added to mask the yellow color of Fe3+ to make the endpoint more distinct.
If great accuracy is not needed, Fe(NH4)2(SO4)2.6H2O can also be used
(sufficiently pure for most purposes).
An indirect application of KMnO4 as a titrant is in the analysis of non-oxidizable
or difficult to oxidize cations such as Ca2+, Mg2+, Ce3+, Cu2+. They can be
precipitated with Na2C2O4, filtered, redissolved in acid and the H2C2O4 can then
be titrated as above.
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Ammonium hexanitratocerate: (NH4)2Ce(NO3)6
Primary standard – usually dissolved in 1 M H2SO4 (slow decomposition in
other mineral acids such as HClO4and HNO3)
Ce(IV) binds anions such as ClO4-, NO3-, Cl- etc. strongly, as indicated by
variation of the E° in HClO4 (E° = 1.70 V), HCl (E° = 1.47 V) etc.
Need an indicator (Ce4+ is yellow, Ce3+ is colorless, but no sharp change),
e.g. ferroin.
Can be used instead of KMnO4 in most procedures.
Potassium dichromate: K2Cr2O7
Cr2O72- + 14 H+ + 6 e-
2 Cr3+ + 7 H2O
E° = 1.36 V
Primary standard, cheap, its solutions (orange) are stable. Cr3+ complexes
can be green to violet, so indicator necessary (or potentiometric).
Not as strong an oxidant as MnO4- and Ce4+; mainly used for determination
of Fe2+ and for indirect determination of species that can oxidize Fe2+ to
Fe3+ (e.g. NO3-, MnO4-): a measured excess of Fe2+ is added to the
unknown, and excess Fe2+ is titrated with K2Cr2O7.
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Dr. G. Van Biesen
C3100 - Winter 2011
Methods Involving Iodine:
Iodimetry: titration using I2 (I3-); I- is formed during the titration
Iodometry: titration of I2 (produced by a chemical reaction) with Na2S2O3
¾Molecular I2 is poorly soluble in water (1.3 x 10-3 M at 20 °C), but its solubility
increases by complexation with I- to form triiodide, and I2 solutions for titration
are prepared by dissolving I2 in water and adding excess I-:
I2 + I-
I3-
K = 700
I3- + 2e-
3 I-
E° = 0.535 V
¾Sublimed I2 is a primary standard, but because of its high vapour pressure, it
is not practical to weigh it accurately. Instead, an approximate amount is
weighed, and dissolved with excess KI, and the solution is standardized with
Na2S2O3 or As4O6:
S4O62- + 3 II3- + 2 S2O32As4O6 + 6 H2O
4 H3AsO3
H3AsO3 + I3 + H2O
H3AsO4 + 3 I⎯ + 2 H+
⎯
Titration performed in
bicarbonate buffer to
keep [H+] low
45
Prepared solutions are stable at neutral pH (in the absence of heat, light…),
2 I3- + 2 H2O - slow) and basic pH
but not at acidic (6 I- + O2 + 4 H+
(disproportionation of I3- to HOI, IO3-, I-).
¾Alternatively, KIO3 can be added to a small excess of KI, then strong acid is
added to bring the solution to pH ≈ 1, and I3- is produced by quantitative
reverse disproportionation:
IO3- + 8 I- + 6 H+
3 I3- + 3 H2O
¾Na2S2O3 is an almost universal titrant for triiodide. Titrations are carried
out in neutral or acidic solution (pH < 9) to prevent disproportionation of I3-.
Na2S2O3 is not a primary standard, but is standardized with I3- prepared
from KIO3, or from a I3- solution standardized with As4O6.
¾The universal indicator for iodi- and iodometry is starch. The amylose
portion of starch (which is helical) binds iodine (as I6 chains) to form a dark
blue complex. Best at low temperature.
Has to be fresh, or preservative (HgCl2) has to be added – hydrolysis
product is glucose, which is a reducing agent (!).
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Dr. G. Van Biesen
C3100 - Winter 2011
Iodimetry:
reducing agent + I33 ICan add starch at the beginning – first drop of excess I3- turns solution blue
oxidizing agent + 3 II3 Iodometry:
Here, an excess of I- is added to the solution containing the analyte; the I3formed is then titrated with Na2S2O3. Starch is added immediately before EP
(as indicated by fading I3- color), otherwise some I2 will remain bound to
47
starch after EP.
Applications of iodimetry: analysis of SO2, As3+, Sn2+, formaldehyde, glucose,
vitamin C…
Some of these analyses are back-titrations, whereby a known excess of I3- is
added to the analyte solution, and the remaining I3- is titrated with Na2S2O3
Applications of iodometry: analysis of Cl2, Br2, MnO4-, Cr2O72-…
In all these applications, excess I- is initially added to the analyte solution to
reduce the analyte and generate a stoichiometric amount of I3- which is
titrated with Na2S2O3
ELECTROANALYTICAL TECHNIQUES (Chapter 16)
(a brief, qualitative overview of Chapter 16)
Previous chapters dealt with potentiometry: measuring voltage in the absence
of any significant current. Following techniques all involve a significant current
to force chemical reactions at an electrode surface (i.e. electrolysis).
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Dr. G. Van Biesen
C3100 - Winter 2011
Electrogravimetric Analysis:
Analyte is quantitatively deposited on an electrode
(cathode) by electrolysis. The electrode is weighed
before and after deposition.
e.g.: Cu2+ + 2e-
Cu(s)
Check for completion of the reaction by
disappearance of color, or by exposing fresh
surface of the cathode to the solution and
checking if deposit forms with continuing
electrolysis.
Coulometric Titration:
Controlled delivery of electrons to form a reagent (titrant) in situ.
Br
e.g.: Br2 +
Br
+ 2 Br-
Fig. 16-5,
Harris 8th Ed.
Analysis of cyclohexene
by titration with Br2
Br2 is generated by oxidation of Br- (in large excess in solution) at a Pt anode
49
When just enough Br2 has been formed to
react with all the cyclohexene, the moles of eliberated = 2 x moles of cyclohexene.
A constant current is applied (controlled via
hand-operated switch) between the two
generator electrodes
#moles of e- = I • t / F
End point: excess Br2 detected by measuring
current between two detector electrodes:
Br2 + 2 eanode: 2 Brcathode: Br2 + 2 e2 Br(no current before any Br2 remains in solution)
Other types of titrations:
2 OH- + H2(g)
acids - via OH- generated from: 2 H2O + 2 e+
precipitation – via Ag generated at a Ag anode
End point detection can be via color change of an indicator, or potentiometry.
50
Dr. G. Van Biesen
C3100 - Winter 2011
Amperometry:
Electric current I between pair of electrodes that drive an electrolysis reaction
is measured – analyte is one of the reactants and I ~ [analyte].
There are numerous variations on this technique.
Example: blood glucose monitor:
Working electrode 1 is coated with the enzyme glucose oxidase
(and a mediator):
51
Early glucose monitors measured
[H2O2] by oxidation at a single
working electrode held at +0.6 V vs.
Ag / AgCl:
H2O2
O2(g) + 2 H+ + 2e-
I ~ [H2O2] ~ [glucose]
Problem: depends on pO2 in enzyme layer, which is not well controlled.
Mediator substitutes for O2 (shuttles e- between glucose and electrode, is
regenerated).
Another problem: Vitamin C, acetaminophen (Tylenol), uric acid are also
oxidized at the applied potential. This is corrected for by having a 2nd working
electrode coated with mediator, but not with glucose oxidase. These species
are thus oxidized at this electrode as well, but not glucose. The current due
to glucose is Ielectrode1 – Ielectrode2.
Voltammetry:
Number of techniques where the relationship between current and voltage is
observed during electrochemical processes. These techniques include:
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Dr. G. Van Biesen
C3100 - Winter 2011
¾Polarography
Uses a dropping-Hg electrode
(fresh Hg surface = reproducible I – V behaviour)
Qualitative (identify analyte by half-wave potential) and quantitative
(diffusion current ~ [analyte])
¾Stripping Analysis
Analytes are first reduced from a solution onto an electrode (Hg)
Analytes are then oxidized by applying a positive potential – I ~ [analyte]
Most sensitive voltammetric technique.
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Dr. G. Van Biesen