Electrodes and Potentiometry Guide the Way

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 tells us the activity of one unknown species( g y p
if the activities of the other species are known).
I Reference Electrode : It maintains a fixed potential (a known fixed composition)I. Reference Electrode : It maintains a fixed potential (a 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 ?1-15Fig.in
][Fe
][Fe
measuretoHow 3
2


][Fe

14-1. Reference Electrodes
Figure 14-2 Another view of Fig 15-1Figure 14-2. Another view of Fig. 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 EquationFrom Nernst Equation
E = Eo – 0.05916 log [Cl-]
(0.197V) (0.222V)
E ( d KCl) 25°C 0 197 VE (saturated KCl) at 25°C = + 0.197 V
(E = +0.222V when ACl = 1.0)

I. Reference Electrodes
The two half reactions :
Right electrode: Fe3+ + e- Fe2+ E+0 = 0.771V
Left electrode: AgCl(s) + e- Ag(s) + Cl- E-o = 0.222V
E (Cell Voltage) = E+ - E-
)][Cl0.05916log()
][Fe
][Fe
0.05916log( 3
2



  oo
EE
( g ) + -
][Fe
)][Cl0.05916log222.0()
][Fe
][Fe
0.05916log771.0( 3
2




][Fe
][Fe
0.05916log][Cl0.05916log549.0 3
2
-



][Fe
][
i) [Cl-] = const., because of saturated KCl solution.
ii) As the value of [Fe2+]/[Fe3+] changes, the cell voltage (E) changes.

I. Common Reference Electrodes
2) Calomel Electrode
(Saturated Calomel electrode = S.C.E)
1/2 Hg2Cl2(s) + e- Hg(l) + Cl-
Eo = +0 268V (A = 1)E +0.268V (ACl 1)
Mercury (I)Chloride (Calomel)
][Cllog05916.0 -
 o
EE
(+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 surfacei) It responds to a redox reaction at the metal surface.
ii) It does not participate in many chemical reactions (Inert).
iii) Si l i f i i i l iiii) Simply transmit e- to or from a reactive species in solution.
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) It i t b d di) It is not based on redox processes
ii) Selective migration of one type of ion across a membrane
generates an electric potential.g p

14-3. What Is a Junction Potential ?
Junction Potential : Any time two dissimilar electrolyte solution are placed
i l i l ( i i l)in contact, an electric voltage ( Junction Potential)
develops at their interface.
There is an electric potential difference at the junction of NaCl and H O phases-There is an electric potential difference at the junction of NaCl and H2O phases.

- In Table 14-2, a high concentration of KCl in one solution reduces the
magnitude of the potential.magnitude of the potential.
- This is why saturated KCl is used in salt bridges.

- There is an electric potential difference at the junction of NaCl and H2O- 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- 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)

- 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 d l ti l t iii) It responds selectively to one ion.
iii) Key feature of an ideal ion selective electrode:
- A thin membrane ideally capable of binding only the intended ion.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.

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)
hi h l ti l bi d th l t ti (C+)which selectively binds the analyte cation (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.

B ld l d iBold colored ions;
excess charge in each phase
A- : it cannot enter the membrane because it’s not soluble in the organic phase.
C+ : it diffuses from the membrane to the aqueous solution because of theq
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 solution (A0),




 lnl ti RTGG
Am
q ( 0),
the free energy change is




 lnsolvation RTGG
Ao
G due to change
G due to change
in acti itG due to change
in solvent
in activity
(concentration)
- G is always negative when a species diffuses from a region of high activity to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 of a positive charge in the water immediatelyp p g y
adjacent to membrane.
- The charge separation creates an electric potential ( Eouter) across the 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 the net change G from all processes

At equilibrium, the net change G from all processes
with diffusion of C+ across the membrane must be 0.
0)(ln outersolvation 





 nFERTG
Am
Ao
G due to transfer between G due to
phase and activity difference charge imbalance
Electric potential








lsolvation RTG
E
Am
difference across phase
boundary between
membrane and analyte (outer solution):












 lnsolvation
outer
nF
RT
nF
E
Am
Ao
membrane and analyte (outer solution):
-Eouter is proportional to the concentration of C+ in outer analyte solution,
because Am is nearly constant.
Ao

Why does is constant during the process?Am
Th h i lAmThe reason why is very nearly constant :
i) C+ + L  LC+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 the net change G from all processes

At equilibrium, the net change G from all processes
with diffusion of C+ across the membrane must be 0.
0)(ln innersolvation 





 nFERTG
Am
Ai
G due to transfer between G due to
phase and activity difference charge imbalance
Electric potential
difference across phase
boundary between 













 lnsolvation
inner
nF
RT
nF
G
E
Am
Aiy
membrane and inner filling solution
 Ai
- Einner is constant because and are constant.Ai Am

- The potential difference between the outer and inner solution :
inner
solvation
innerouter ln E
F
RT
F
G
EEE 














Am
A
- The potential difference between the outer and inner solution :
inner
solvation
ln-ln E
RTRTG
E 













 Ao
Am
innerinnerouter
nFnF 


 Ao
inner
nFnFnF








o m
C Constant Constant
Constant Constant Constant
- Combing the constant terms,
lnconstant 






nF
RT
E Ao
Electric potential
)C25at(voltslog
05916.0
constant 
n
E  Ao
lect ic potential
difference for ion-
selective electrode:

lnconstant 




RT
E Alnconstant 




nF
E Ao
)C25at(voltslog
05916.0
constant 
E  Ao
Electric potential
difference for ion-
selective electrode: )(g
nselective electrode:
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 pH units would lead to a potential difference of) p p
4.00 x 59.16 = 237 mV.
iv) For every factor - of - 10 change in activity of Ca+2 would lead toiv) For every factor of 10 change in activity of Ca would lead to
a potential difference of 59.16/2 = 29.58 mV.

Ion Selective Electrodes
Nitrate Chloride

14-6. Ion-Selective Electrodes
*Doctor needs blood chemistry information
quickly to help a critically ill patientquickly to help a critically ill patient
make a diagnosis and begin treatment.
Ion-selective electrodes are the method ofIon-selective electrodes are the method of
choice for Na+, K +, Cl- , pH, and Pco2
.

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: (14-9)
A: analyte ion, X: interfering iony g
Pot: potentiometric

Response of ion-selective electrode:
(14-10)
th ti it f i i th ti it f i t f i iA A: the activity of primary ion, : the activity of interfering species,
: the selectivity coefficient, + : A is a cation, - : A is an anion
AA AX
XA,k
Z : the magnitude of charge A
Changes in in the solution change the potential difference E across theA
Reminder : How Ion-Selective Electrode Work
ZA : the magnitude of charge A
- Changes in in the solution change the potential difference, E across the
outer boundery of the ion selective electrode.
- By using the calibration curve, E is related to
AA
AA
- An ion-selective electrode responds to the activity of free analyte, not complexed
analyte.

Classification of Ion-selective electrodes :
1) Gl b f H+ d t i l t ti1) Glass membranes for H+ and certain monovalent cations.
2) Solid-state electrodes2) Solid state electrodes
3) Liquid-based electrodes
4) Compound electrodes

2) Solid – State Electrodes
Sit t it t t ti f F i id th t lSite to site transportation of F – inside the crystal.
Filling solution ; 0.1 M NaF and 0.1 M NaCl

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 Fe 3+ and Al 3+, which would otherwise bind F-p ,
and interfere with the analyte, F -.

E = constant - (0.05916) log AF (outside) (14-12)
Response of F- electrode:
E constant (0.05916) log AF- (outside) (14 12)
A routine procedure is to dilute the unknown in a high ionic strength buffer containing- 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.
Th b ff k ll t d d d k t t t i i t th th- The buffer keeps all standards and unknowns at a constant ionic strength, so the
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 is constant becausep
F- is constant at constant ionic strength

3) Liquid–Based Ion–Selective Electrodes
-A liquid-based ion-selective electrode is similar to the solid-state electrode
(Fig 14 19) except that the liquid based electrode has a hydrophobic membrane(Fig. 14-19), except that the 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. 14-23)
(Fig. 14-19)

L; Ionophore (neutral)
i fR- ; anion for charge
neutralization

- A liquid-based ion-selective electrode is similar to the solid-state electrode
(14-13)
Response of Ca2+ electrode:
(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 a metal ion buffer.2 y
 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 f th i i (Pb+2) f th i t l filli l ti th h th ileakage of the primary ion (Pb+2) from the internal filling solution through the ion
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 concentration is far below 10- 6 M.y

4) Compound Electrodes
- Compounds electrodes contain- Compounds electrodes contain
a conventional electrode surrounded
by a membrane that isolates (or generates)
th l t t hi h th l t d dthe analyte to which the electrode responds.
-CO2 diffuses through the semi-permeable
bb brubber membrane,
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.2

14-7. Using Ion – Selective Electrodesg
Advantages of ion-selective electrodes:
1) Linear response to log over a wide range (4 to 6 orders of magnitude).A
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)5) Unaffected by color or turbidity (unlike spectrophotometry and titrations).

14-7. Using Ion – Selective Electrodes
Di d t f i l ti l t dDisadvantages of ion-selective electrodes:
1) They respond to the activity of analytes .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 ?)2) They respond to the activity of uncomplexed ions (advantage or disadvantage ?)
3) Precision is rarely better than 1%.
* I V  4% i l t i ti it* I mV error  4% error in monovalent ion activity.
 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 electrodes:Disadvantages of ion selective electrodes:
1) They respond to the activity of analytes .
* ll i i i i*we usually want concentrations, not activities.
 How to solve this problem:
An inert salt is added to all the standards and samples to bring them
to constant and high ionic strength. If the activity coefficients remain constant,g g y ,
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 exists.y
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 standardThe 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.
X]log[
10ln
β 






nF
RT
kE (15-9)
 n
E : meter reading in volts
0.05916 V at 25 0C
g
[X] : concentration of analyte
: constants depending on particular ion-selective electrodeβ,k

15-7. Standard Addition with Ion - Selective Electrodes
X]log[
10ln
β 




RT
kE (14-14)X]log[β 




nF
kE (14 14)
Let V0 : the initial volume of unknown
C : the initial concentration of analyteCx : 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 C + V C ) / (V0 + V )(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 (14-15)
y b m
x
Where S = 





nF
RT 10ln
β

(V0 + VS)10E/S = 10k/SV0cX + 10k/ScSVS
(14 15)
y b m
x
(14-15)
S
X0
S
/
X0
/
10
10
intercept
c
cV
c
cV
m
b
x Sk
Sk
 (14-16)
From equation (15-12), Cx is obtained from x-intercept, Cs and V0.

Metal Ion Buffers
It i i tl t dil t C Cl t 10 6 M f t d di i i l ti l t d- It is pointless to dilute CaCl2 to 10-6 M for standardizing an ion-selective electrode.
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 cationson 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 ligandAn alternative is to prepare a metal ion buffer from the metal and a suitable ligand.
Metal Ion Buffers is used to keep metal ion concentration so low !

Metal Ion Buffers
M t l I B ff i d t k t l i t ti lMetal Ion Buffers is used to keep metal ion concentration so low.
- How to keep Ca+2 concentration less than 10-6 ?
Ca2+ + NTA3- CaNTA- ( at high pH)
p C
(15-14)3
46.6
32f KNOM0.1in10
]][NTA[Ca
][CaNTA
 

K
]][NTA[Ca
If you add NTA at high pH into the high concentration of Ca+2 solution
3 2+
][CaNTA 
and make [CaNTA-] = [NTA3-] , then you obtain so low Ca2+ concentration
which does not vary substantially due to the metal buffer action.
M10
][NTA
][CaNTA
]Ca[ 46.6
3
f
2 



K

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