CHAPTER 14:
ELECTRODES AND POTENTIOMETRY
Chapter 14 Electrodes and Potentiometry
Potentiometry : The use of electrodes to measure voltages that provide chemical
information.
((The cell voltage
g tells us the activity
y of one unknown species
p
if the activities of the other species are known).
I Reference Electrode : It maintains a fixed potential (a known
I.
known, fixed composition)
II. Indicator Electrode : It responds to analyte, an electroactive species
that can donate or accept electron at the electrode)
How to use potentiometry :
1) We connect two half-cells (indicator & reference electrodes) by a salt bridge.
2) We measure the cell voltage which is the difference between the potential of
the indicator electrode and the constant potential of the reference electrode.
3) We make an equation of first degree to get the unknown concentration of analyte.
14-1. Reference Electrodes
[Fe 2 ]
How to measure
in Fig.15 - 1 ?
3
[Fe ]
14-1. Reference Electrodes
Figure 14-2.
14-2 Another view of Fig.
Fig 15-1.
15-1
The dashed box = reference electrode.
I. Common Reference Electrodes
1) Silver-Silver chloride Electrode
AgCl(s) + e- ֖ Ag(s) + Cl-
Eo = +0.222
From Nernst Equation
E = Eo – 0.05916 log [Cl-]
(0.197V) (0.222V)
E (saturated
(
d KCl) at 25°C = + 00.197
197 V
(E = +0.222V when ACl = 1.0)
I. Reference Electrodes
The two half reactions :
Fe3+ + e- ֖ Fe2+
Right electrode:
Left electrode:
AgCl(s) + e- ֖ Ag(s) + Cl-
E+0 = 0.771V
E-o = 0.222V
E ((Cell Voltage)
g ) = E+ - E-
[Fe 2 ]
o

 ( E  0.05916log
)

(
E

0.05916log
[Cl
])

3
[Fe ]
o

[Fe 2 ]

 (0.771  0.05916log
)

(
0
.
222

0.05916log
[Cl
])
3
[Fe ]
[Fe 2 ]
 0.549  0.05916log[Cl ]  0.05916log
[[Fe3 ]
[Cl-] = const., because of saturated KCl solution.
As the value of [Fe2+]/[Fe3+] changes, the cell voltage (E) changes.
-
i)
ii)
I. Common Reference Electrodes
2) Calomel Electrode
(Saturated Calomel electrode = S.C.E)
1/2 Hg2Cl2(s) + e- ֖ Hg(l) + ClEo = +0.268V
+0 268V (ACl = 1)
Mercury (I)Chloride (Calomel)
E  E o  0.05916 log [Cl- ]
(+0.241V at 25oC) (0.268V)
*Saturated KCl solution make the conc. of Cl- does
not change if some of liquid evaporates.
Voltage conversions between different reference scales
14-2. Indicator Electrodes
Indicator Electrodes
1) Metal Electrode
i) It responds to a redox reaction at the metal surface.
surface
ii) It does not participate in many chemical reactions (Inert).
iii) Simply
Si l transmit
i e- to or from
f
a reactive
i species
i in
i solution.
l i
iv) It works best when its surface is large and clean
(A brief dip in conc. HNO3,followed by rinsing with distilled water
is effective for cleaning).
v) Au, Pt, Ag, Cu, Zn, Cd and Hg can be used as indicator electrode (The
reaction of M ֖ Mn+ + ne- should be fast)
14-2. Indicator Electrodes
2) Ion Selective Electrode
i)
ii)
It is
i nott based
b
d on redox
d processes
Selective migration of one type of ion across a membrane
generates an electric p
g
potential.
14-3. What Is a Junction Potential ?
Junction Potential : Any time two dissimilar electrolyte solution are placed
i contact, an electric
in
l
i voltage
l
( Junction
i Potential)
i l)
develops at their interface.
-There
There is an electric potential difference at the junction of NaCl and H2O phases
phases.
- In Table 14-2, a high concentration of KCl in one solution reduces the
magnitude of the potential.
- This is why saturated KCl is used in salt bridges.
14-3. What Is a Junction Potential ?
-
There is an electric potential difference at the junction of NaCl and H2O
phases.
-
Steady-state junction potential : A balance between the unequal mobilities
that create a charge imbalance and the tendency of the resulting charge
imbalance to retard the movement of Cl-.
-
Junction Potential puts a fundamental limitation on the accuracy of direct
potentiometric measurements, because we don’t know the contribution
of the junction to the measured voltage:
E(measured) = E(cell) + E(junction)
14-3. What Is a Junction Potential ?
- Junction Potential exists at the interface between the salt bridge and each
half-cell.
- The junction potentials at each end of a salt bridge often partially cancel
each other.
- Although a salt bridge necessarily contributes some unknown net potential
to a galvanic cell, the contribution is fairly small (a few mV).
14-4. How Ion-Selective Electrode Work ?
Ion Selective Electrode
i) It is not based on redox processes
ii) It responds
d selectively
l ti l tto one iion.
iii) Key feature of an ideal ion selective electrode:
- A thin membrane ideally capable of binding only the intended ion.
- Selective migration of one type of ion across a membrane generate
an electric potential.
14-4. How Ion-Selective Electrode Work ?
For example, Liquid-based ion-selective electrode
- ion-selective electrode : a hydrophobic organic polymer impregnated with a
viscous organic solution containing an ionophore (L, ligand)
which
hi h selectively
l ti l binds
bi d the
th analyte
l t cation
ti (C+).
)
- Inside of the electrode : filling solution with C+ (aq) and B-(aq)
- Outside of the electrode : it is immersed in analyte solution with C+ (aq) and A-(aq).
-Two reference electrodes: to measure the electric potential difference (voltage)
across the membrane depending on [C+ ] in analyte.
Inside the membrane:
Membrane : polymer (polyvinyl chloride) impregnated with a nonpolar liquid that
dissolves L, LC+, and R- (hydrophobic anion)
L : Ionophore. it has high affinity for C+. It binds only C+(ideal electrode).Howeve
it has some affinity for other cations (Real). L is soluble in the organic phase.
R- : hydrophobic anion for charge neutrality. R- cannot leave membrane
because it is soluble in membrane, but poorly soluble in water.
Bold
B
ld colored
l d iions;
excess charge in each phase
A- : it cannot enter the membrane because it’s not soluble in the organic phase.
q
solution because of the
C+ : it diffuses from the membrane to the aqueous
favorable solvation of the ion by water.
In the membrane, LC+ is in equilibrium with L + C+ (small amount).
- As soon as a few C+ ions diffuse from the membrane into the aqueous solution,
there is excess positive charge in the aqueous phase.
-This imbalance creates an electric potential difference that opposes diffusion of
more C+ into the aqueous phase.
First, Let’s see what happens when C+ diffuses
from membrane to outer solution
-When C+ diffuses from membrane (activity in membrane, Am)
to the outer aqueous
q
solution (A
( 0),
the free energy change is
 Am


 G   G solvation

RT
ln
l ti
 Ao
G due to change
in solvent
G due to change
in acti
activity
it
(concentration)
- G is always negative when a species diffuses from a region of high activity to
one of lower activity.
- When C+ diffuses from membrane to the outer aqueous solution,
there is a buildup
p of a positive
p
charge
g in the water immediately
y
adjacent to membrane.
- The charge separation creates an electric potential ( Eouter) across the membrane.
- The free energy difference for C+ in the two phases is G = -nFEouter.
First, Let’s see what happens when C+ diffuses
from membrane to outer solution
- At equilibrium
equilibrium, the net change G from all processes
with diffusion of C+ across the membrane must be 0.
 G solvation
 Am
  (  nFE outer )  0
 RT ln 
 Ao 
G due to transfer between
phase and activity difference
G due to
charge imbalance
Electric potential
 G solvation
 RT   Am

E outer 

l 
 ln
difference across phase
nF
nF   Ao

boundary between
membrane and analyte (outer solution):
-Eouter is proportional to the concentration of C+ in outer analyte solution, Ao
because Am is nearly constant.
Why does Am is constant during the process?
Th reason why
The
h Am is
i very nearly
l constant :
i)
C+ + L 
LC+
In this equilibrium in the membrane, C+ is very small, but LC+ is high concentration.
ii) R- ( hydrophobic) is poorly soluble in water and thus cannot leave the membrane.
Very little C+ can diffuse out of the membrane because each C+ that enters
the aqueous phase leaves behind one R- .
iii) As soon as a tiny fraction of C+ diffuse from the membrane into solution,
further diffusion is prevented by excess positive charge in the solution
near the membrane.
Second, Let’s see what happens when C+ diffuses
from membrane to inner filling solution
- At equilibrium
equilibrium, the net change G from all processes
with diffusion of C+ across the membrane must be 0.
 G solvation
 Am
  (  nFE inner )  0
 RT ln 
 Ai 
G due to transfer between
phase and activity difference
G due to
charge imbalance
Electric potential
 G solvation
 RT  Am 
difference across phase

E inner 

 ln 
nF
boundaryy between
 nF   Ai 
membrane and inner filling solution
- Einner is constant because Ai
andAm
are constant.
14-4. How Ion-Selective Electrode Work ?
- The potential difference between the outer and inner solution :
 G solvation
 RT   Am 
  E inner
E  E outer  E inner 

 ln 
nF
F
F   Ao 
 nF
 G solvation
 RT 
 RT  A
E 

ln
A

 ln m  E inner
o 
nF
 nF 
 nF 
C
Constant
Constant
Constant
- Combing the constant terms,
Electric
lect ic potential
difference for ionselective electrode:
 RT  A
E  constant  
 ln o
 nF 
0 . 05916
E  constant 
log Ao
n
(volts at 25  C )
14-4. How Ion-Selective Electrode Work ?
Electric potential
difference for ionselective electrode:
 RT  A
E  constant  
 ln o
 nF 
0 . 05916
E  constant 
log
g Ao
n
((volts at 25  C )
Remarks:
i) This equation applies to any ion-selective electrode (including a glass pH electrode).
ii) If the analyte is anion, the sign n (charge of analyte ) is negative.
iii)) A difference of 4.00 ppH units would lead to a ppotential difference of
4.00 x 59.16 = 237 mV.
iv) For every factor - of - 10 change in activity of Ca+2 would lead to
a potential difference of 59.16/2 = 29.58 mV.
Ion Selective Electrodes
Nitrate
Chloride
Ion Selective Electrodes
Ion Selective Electrodes
14-6. Ion-Selective Electrodes
*Doctor needs blood chemistry information
quickly to help a critically ill patient
make a diagnosis and begin treatment.
Ion-selective electrodes are the method of
choice for Na+, K +, Cl- , pH, and Pco2.
14-6. Ion-Selective Electrodes
Selectivity Coefficient : the relative response of the electrodes
to different species with same charge.
* No electrode responds exclusively to one kind of ion.
Selectivity coefficient:
A: analyte
y ion, X: interfering
g ion
Pot: potentiometric
(14-9)
14-6. Ion-Selective Electrodes
Response of ion-selective electrode:
(14-10)
AA : the
th activity
ti it off primary
i
ion,
i
k A, X : the selectivity coefficient,
AX : the
th activity
ti it off interfering
i t f i species,
i
+ : A is a cation, - : A is an anion
ZA : the magnitude of charge A
Reminder : How Ion-Selective Electrode Work
- Changes in AA in the solution change the potential difference,
difference E across the
outer boundery of the ion selective electrode.
- By using the calibration curve, E is related to AA
- An ion-selective electrode responds to the activity of free analyte, not complexed
analyte.
14-6. Ion-Selective Electrodes
Classification of Ion-selective electrodes :
1) Glass
Gl
membranes
b
for
f H+ andd certain
t i monovalent
l t cations.
ti
2) Solid
Solid-state
state electrodes
3) Liquid-based electrodes
4) Compound electrodes
2) Solid – State Electrodes
2) Solid – State Electrodes
Sit to
Site
t site
it ttransportation
t ti
off F – inside
i id the
th crystal.
t l
Filling solution ; 0.1 M NaF and 0.1 M NaCl
2) Solid – State Electrodes
Response of F- electrode:
(14-12)
- The electrode is more responsive to F- than to most other ions by > 1,000.
- OH- is the only interfering species ( kF-, OH- = 0.1 )
- At low pH, F- is converted to HF (pKa = 3.17), to which the electrode is insensitive.
-At pH is 5.5, no interference by OH- and little conversion of F- to HF.
- Citrate complexes
p
Fe 3+ and Al 3+, which would otherwise bind Fand interfere with the analyte, F -.
2) Solid – State Electrodes
Response of F- electrode:
E = constant - (0.05916) log AFF (outside)
(14-12)
(14
12)
- A routine procedure is to dilute the unknown in a high ionic strength buffer containing
acetic acid, sodium citrate, NaCl, and NaOH to adjust the pH to 5.5.
- The
Th buffer
b ff keeps
k
all
ll standards
t d d andd unknowns
k
att a constant
t t ionic
i i strength,
t
th so the
th
fluoride activity coefficient is constant in all solutions (and can therefore be ignored).
E = constant - (0.05916) log [F-]F= constant - (0.05916) logF- - (0.05916) log [F-]
This expression
p
is constant because
F- is constant at constant ionic strength
2) Solid – State Electrodes
2) Solid – State Electrodes
3) Liquid–Based Ion–Selective Electrodes
-A liquid-based ion-selective electrode is similar to the solid-state electrode
(Fig 14-19),
(Fig.
14 19) except that the liquid-based
liquid based electrode has a hydrophobic membrane
impregnated with a hydrophobic ion exchanger (ionophore) that is selective
for analyte ion (Fig. 14-23),
(Fig 14-19)
(Fig.
14 19)
(Fig. 14-23)
3) Liquid–Based Ion–Selective Electrodes
L; Ionophore (neutral)
R- ; anion
i for
f charge
neutralization
3) Liquid–Based Ion–Selective Electrodes
- A liquid-based ion-selective electrode is similar to the solid-state electrode
Response of Ca2+ electrode:
(14-13)
(14
13)
β is close to 1.00
Breakthrough in Ion-Selective Electrode Detection Limits
Black curve: the electrode detects changes in the Pb+2 concentration above 10-6 M,
but not below 10 -6 M when PbCl2 = 0.5 mM in the internal solution.
Blue Curve: the elctrode responds to change in Pb+2 concentration down to ~10-11M.
when PbCl2 =10 -12 M in the internal solution by
y a metal ion buffer.
 go to 14-7 metal ion buffers
Breakthrough in Ion-Selective Electrode Detection Limits
- The sensitivity of liquid-based ion selective electrodes has been limited by the
l k
leakage
off the
th primary
i
ion
i (Pb+2) from
f
the
th internal
i t
l filling
filli solution
l ti through
th
h the
th ion
i
selective membrane.
- Leakage provides a substantial concentration of primary ion at the external of the
membrane (10- 6 M) and thus the electrode always responds to 10- 6 M although
the real analyte
y concentration is far below 10- 6 M.
4) Compound Electrodes
- Compounds electrodes contain
a conventional electrode surrounded
by a membrane that isolates (or generates)
th analyte
the
l t to
t which
hi h the
th electrode
l t d responds.
d
-CO2 diffuses through the semi-permeable
rubber
bb membrane,
b
it lowers the pH in the electrolyte.
-The response of the glass pH electrode
to the change in pH is a measure of
the CO2 concentration outside the electrode.
14-7. Using
g Ion – Selective Electrodes
Advantages of ion-selective electrodes:
1) Linear response to log A over a wide range (4 to 6 orders of magnitude).
2) Nondestructive ( they don’t consume unknown ).
3) Noncontaminating (they introduce negligible contamination.)
* They can be used inside living cells.
4) Short response time (seconds or minutes)
5) Unaffected by color or turbidity (unlike spectrophotometry and titrations)
titrations).
14-7. Using Ion – Selective Electrodes
Di d
Disadvantages
t
off ion-selective
i
l ti electrodes:
l t d
1) They respond to the activity of analytes .
*we usually want concentrations, not activities
2) They respond to the activity of uncomplexed ions (advantage or disadvantage ?)
3)
Precision is rarely better than 1%.
* I mV
V error  4% error iin monovalent
l t iion activity.
ti it
 It doubles for divalent ions and tripled for trivalent ions.
4) They can be fouled by organic solutes like proteins which leads to sluggish,
drifting response.
5) They are fragile and have limited shelf-life.
2) They respond to the activity of uncomplexed ions (advantage or disadvantage ?)
14-7. Using Ion – Selective Electrodes
Disadvantages of ion-selective
ion selective electrodes:
1) They respond to the activity of analytes .
* usually
*we
ll want concentrations,
i
not activities.
i ii
 How to solve this problem:
An inert salt is added to all the standards and samples to bring them
to constant and high
g ionic strength.
g
If the activity
y coefficients remain constant,,
the electrode potential gives concentrations directly because we know
the concentrations of standards.
Standard Addition with Ion - Selective Electrodes
Matrix: the medium in which the analyte
y exists.
Standard Addition Method:
- It is used when the matrix of unknown sample is different from that of standard.
- The electrode immersed in the unknown and then a small volume of standard
solution is added intermittently until the concentration of the analyte increases
to 1.5 to 3 times its original concentration.
- The graphical procedure based on the equation for the response of the ion-selective
electrode.
 RT ln 10
E  k  β
 nnF

 log[ X]

(15-9)
0.05916 V at 25 0C
E : meter reading
g in volts
[X] : concentration of analyte
k , β : constants depending on particular ion-selective electrode
15-7. Standard Addition with Ion - Selective Electrodes
 RT ln 10 
E  k  β
 log[ X]
 nF

(14-14)
(14
14)
Let V0 : the initial volume of unknown
Cx : the initial concentration of analyte
Vs : the volume of added standard
Cs : the concentration of standard
Then the concentration of analyte after standard is added:
(V0 Cx + Vs Cs ) / (V0 + Vs )
Substituting this expression for [X] in equation 15-9 gives 15-10
(V0 + VS)10E/S = 10k/SV0cX + 10k/ScSVS
y
Where S =
b
 RT ln 10 
β

 nF 
m
x
(14-15)
(V0 + VS)10E/S = 10k/SV0cX + 10k/ScSVS
y
b
m
(14 15)
(14-15)
x
V0cX
10 k / S V 0 c X
b
x  intercept  


k/S
m
cS
10
cS
(14-16)
From equation (15-12), Cx is obtained from x-intercept, Cs and V0.
Metal Ion Buffers
- It is
i pointless
i tl to
t dilute
dil t CaCl
C Cl2 to
t 10-66 M ffor standardizing
t d di i an ion-selective
i
l ti electrode.
l t d
At this low concentration, Ca +2 will be lost by adsorption on glass or reaction with
impurities.
* Glass vessels are not used for very dilute solutions, because ions are adsorbed
on the glass. Plastic bottles are better than glass for dilute solutions.
* Adding strong acid (0.1 – 1M) to any solution helps minimize adsorption of cations
on the wall of container. It is because H+ competes with other cations
for ion-exchange sites.
* An alternative is to prepare a metal ion buffer from the metal and a suitable ligand.
ligand
Metal Ion Buffers is used to keep metal ion concentration so low !
Metal Ion Buffers
M t l Ion
Metal
I Buffers
B ff
is
i used
d to
t keep
k
metal
t l ion
i concentration
t ti so low.
l
- How to keep
p Ca
C +2 concentration less than 10-6 ?
Ca2+ + NTA3- ֖ CaNTA- ( at high pH)
Kf 
[CaNTA
[Ca
2

][NTA
]
3
]
 10 6 . 46 in 0.1 M KNO
3
(15-14)
If you add NTA at high pH into the high concentration of Ca+2 solution
3 ] , then you obtain so low Ca2+ concentration
and make [CaNTA-] = [NTA3which does not vary substantially due to the metal buffer action.
[ Ca
2
[CaNTA
]
K f [NTA

]
 6 . 46

10
M
3
]