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Chapter 14
Electrodes and Potentiometry
14-1 Reference Electrodes
The two half-reactions (written as reductions) are
Right electrode:
Fe3+ + e- = Fe2+
Left electrode: AgCl(s) + e- = Ag(s) + Cl-
Eo+ = 0.771 V
Eo- = 0.222 V
E+ = 0.771 – 0.059 16 log([Fe2+]/[Fe3+])
E- = 0.222 – 0.059 16 log[Cl-]
E = {0.771 – 0.059 16 log([Fe2+]/[Fe3+]) – {0.222 – 0.059 16 log[Cl-]}
The half-cell on the left in Figure 15-1 can be thought of a s a reference electrode.
The reference electrode completes the redox reaction and provides a constant
potential to the left side of the potentiometer.
Silver-Silver Chloride Reference Electrode2
The half-cell enclosed by the dashed line in figure 15-1 is called a silver-silver
chloride electrode.
Figure 15-4 shows a double-junction electrode that minimizes contact between
analyte solution and KCl from the electrode.
Ag | AgCl electrode:
AgCl(s) + e- = Ag(s) + Cl-
Eo = +0.222 V
E(saturated KCl) = +0.197 V
Calomel Electrode
The calomel electrode in Figure 15-1 is based on the reaction
Calomel
electrode:
1/2Hg2Cl2(s)
+ e- = Hg(l) + Cl-
Mercury(I) chloride
Eo = +0.268 V
E(saturated KCl) = +0.197 V
(calomel)
A calomel electrode saturated with KCl is called a saturated calomel electrode,
abbreviated S.C.E.
Voltage Conversions Between Different Reference Scales
14-2 Indicator Electrodes
Metal electrodes described in this section develop an electric potential in
response to a redox reaction at the metal surface. Ion-selective electrodes,
described later, are not based on redox processes.
The most common metal indicator electrode is platinum, which is relatively
inertㅡit does not participate in many chemical reactions.
Ag+ + e- = Ag(s)
Eo+ = 0.799 V
Hg2Cl2(s) + 2e- = 2Hg(l) + 2Cl-
E- = 0.241 V
E = E+ - E- = {0.799 – 0.059 16 log(1/[Ag+])} – {0.241}
Potential of Ag | Ag+
indicator electrode
Potential of
S.C.E. reference electrode
E = 0.558 + 0.059 16 log [Ag+]
(15-1)
In Figure 7-9, we used a silver indicator electrode and a glass reference electrode.
We see from the example that
a silver electrode is also a
halide electrode, if solid silver
halide is present.6
E = 0.558 + 0.059 16 log(Ksp/[Cl-])
Demonstration 14-1 Potentiometry with an Oscillating Reaction7
3CH2(CO2H)2 + 2BrO3- + 2H+ 
Malonic acid
Bromate
2BrCH(CO2H)2 + 3CO2 + 4H2O
Bromomalonic acid
Trace a shows what is usually observed. The potential changes rapidly during
the abrupt colorless-to-yellow change and gradually during the gentle yellow-tocolorless change. Trace b shows two different cycles superimposed in the same
solution. This unusual event occurred in a reaction that had been oscillating
normally for about 30 min.11
14-3 What is a Junction Potential?
Whenever dissimilar electrolyte solutions are in contact, a voltage difference
called the junction potential develops at their interface.
The junction potential puts a fundamental limitation on the accuracy of direct
potentiometric measurements, because we usually do not know the contribution
of the junction to the measured voltage.
However, Cl- ion has a greater mobility than Na+.
14-4 How Ion-Selective Electrodes Work10
Ion-selective electrodes, discussed in the remainder of this chapter, respond
selectively to one ion.
Consider the liquid-based ion-selective electrode in Figure 15-8. The electrode is
said to be “liquid based” because the ion-selective membrane is a hydrophobic
organic polymer impregnated with a viscous organic solution containing an ion
exchanger and, sometimes, a ligand that selectively binds the analyte cation, C+.
The key in this example is the ligand, L (called an ionophore), that is soluble
inside the membrane and selectively binds analyte ion.
The ligand, L, is chosen to have a high affinity for analyte cation, C+, and low
affinity for other ions.
Αm
G  Gsolvation  RT ln(
)
Ao
ΔG due to change
in solvent
ΔG due to
change in activity
(concentration)
Αm
Gsolvation  RT ln(
)  (nFEouter )  0
Ao
ΔG due to transfer between phases
and activity difference
ΔG due to
charge imbalance
Electric potential
difference across phase
boundary between
membrane and analyte:
Very little C+ can diffuse out of the membrane because each C+ that enters the
aqueous phase leaves behind one R- in the membrane.
E  Eouter  Einner 
E
Gsolvation RT
A
(
) ln( m )  Einner
nF
nF
Ao
Gsolvation RT
RT
(
) ln Ao  (
) ln Am  Einner
nF
nF
nF
Constant
Constant
Constant
E  constnat  (
Electric potential
difference for ionselective electrode:
RT
) ln Ao
nF
14-5 pH Measurement with a Glass Electrode
The glass electrode used to measure pH is the most common ion-selective
electrode. A typical pH combination electrode, incorporating both glass and
reference electrodes in one body, is shown in Figure 15-9.
Glass membrane
selectively binds H+
Ag(s) | AgCl(s) | Cl-(aq) || H+(aq, outside) H+(aq, inside), Cl-(aq) | AgCl(s) | Ag(s)
Outer reference
electrode
H+ outside
glass electrode
(analyte solution)
H+ inside
glass
electrode
Inner reference
electrode
Metal ions in these hydrated gel regions of the membrane diffuse out of the glass
and into solution.
The reaction in which H+ replaces cations in the glass is an ion-exchange
equilibrium (Figure 15-13).
Equation 15-3 states that the voltage of the ideal pH electrode changes by 59.16
mV for every pH-unit change of analyte activity at 25oC.
Response of
glass electrode:
E = constant + β(0.059 16) log AH (outside)
+
E = constant – β(0.059 16) pH(outside)
(at 25oC)
(15-4)
The value of β, the electromotive efficiency, is close to 1.00 (typically > 0.98).
Calibration a Glass Electrode
E  ES1
ES2  ES1

pH  pH S1 pH S2  pH S1
Eunknown  ES1
ES2  ES1

pH unknown  pH S1 pH S2  pH S1
(15 - 5)
(15 - 6)
Wash the electrode with distilled water and gently blot it dry with a tissue. Do
not wipe it, because this action might produce a static charge on the glass.
Box 14-1 Systematic Error in rainwater pH Measurement:
The Effect of Junction Potential
oxidation
SO2 + H2O

H2SO3
Sulfurous acid

H2SO4
Sulfuric acid
Errors in pH Measurement
1.
Standards. A pH measurement cannot be more accurate than our standards,
which are typically ±0.01 pH unit.
2.
Junciton potential. A junction potential exists at the porous plug near the
bottom of the electrode in figure 15-9. If the ionic composition of the analyte
solution is different from that of the standard buffer, the junction potential
will change even if the pH of the two solutions is the same (Box 15-1). This
effect gives an uncertainty of at least ~0.01 pH unit.
3.
Junction potential drift. Most combination electrodes have a Ag | AgCl
reference electrode containing saturated KCl solution. More than 350 mg
Ag/L dissolve in the KCl, mainly as AgCl43- and AgCl32-. In the porous plug,
KCl is diluted and AgCl can precipitate. If analyte solution contains a
reducting agent, Ag(s) also can precipitate in the plug. Both effects change
the junction potential, causing a slow drift of the pH reading (solid colored
circles in Figure 15-14). You can compensate for this error by recalibrating
the electrode every 2 h.
4.
Sodium error. When [H+] is very low and [Na+] is high, the electrode
responds to Na+ and the apparent pH is lower than the true pH. This is
called the sodium error or alkaline error (Figure 15-15).
5.
Acid error. In strong acid, the measured pH is higher than the actual pH,
perhaps because the glass is saturated with H+ and cannot be further
protonated (Figure 15-15).
6.
Equilibration time. It takes time for an electrode to equilibrate with a
solution. A well-buffered solution requires ~30 s with adequate stirring. A
poorly buffered solution (such as one near the equivalence point of a
titration) needs many minutes.
7.
Hydration of glass. A dry electrode requires several hours of soaking before
it responds to H+ correctly.
8.
Temperature. A pH meter should be calibrated at the same temperature at
which the measurement will be made.
9.
Cleaning. If an electrode has been exposed to a hydrophobic liquid, such as
oil, it should be cleaned with a solvent that will dissolve the liquid and then
conditioned well in aqueous solution. The reading of an improperly cleaned
electrode can drift for hours while the electrode re-equilibrates with
aqueous solution.
Measurement of pH differences between solutions can be accurate to about
±0.002 pH unit, but knowledge of the true pH will still be at least an order of
magnitude more uncertain.
14-6 Ion-Selective Electrodes22, 23
1.
Glass membranes for H+ and certain monovalent cations
2.
Solid-state electrodes based on inorganic salt crystals
3.
Liquid-based electrodes using a hydrophobic polymer membrane saturated
with a hydrophobic liquid ion exchanger
4.
Compound electrodes with a species-selective electrode enclosed by a
membrane that is able to separate that species from others or that generates
the species in a chemical reaction.
Selectivity Coefficient
The selectivity coefficient gives the relative response of the electrode to different
species with the same charge:
Selectivity coefficient:
Response of ionselective electrode:
kA,X = (response to X)/(response to A)
(15-7)
(15-8)
BOX 14-2 Measuring Selectivity Coefficients for an
Ion-Selective Electrode
Reminder: How Ion-Selective Electrodes Work
An ion-selective electrode responds to the activity of free analyte, not
complexed analyte.
The discrepancy arose because the inductively coupled plasma measures all
lead and the ion-selective electrode measures free Pb2+.
Solid-State Electrodes
A solid-state ion-selective electrode based on an inorganic crystal is shown in
Figure 15-16.
Doping means adding a small amount of Eu2+ in place of La3+.
Response of F- electrode:
E = constant – β(0.059 16) log AF (outside)
-
(15-9)
E = constant – β(0.059 16) log[F-]γF
-
= constant – β(0.059 16) log γF - (0.059 16) log[F-]
-
This expression is constant because
γF is constant at constant ionic strength
-
Liquid-Based Ion-Selective Electrodes
A liquid-based ion-selective electrode is similar to the solid-state electrode in
Figure 15-16, except that the liquid-based electrode has a hydrophobic
membrane impregnated with a hydrophobic ion exchanger (called an
ionophore) that is selective for analyte ion (Figure 15-20).
Response of Ca2+
electrode:
E  constnat  β(
0.059 16
) log ACa 2 (outside)
2
(15 - 10)
Breakthrough in Ion-Selective Electrode Detection Limits24
The colored curve in Figure 15-21 was obtained with the same electrode
components, but the internal filling solution was replaced by a metal ion buffer
(Section 15-7) that fixes [Pb2+] at 10-12 M.
Compound Electrodes
Compound electrodes contain a conventional electrode surrounded by a
membrane that isolates (or generates) the analyte to which the electrode
responds.
These electrodes can be used to measure gases in solution or in the gas phase.
Numerous ingenious compound electrodes using enzymes have been built.29
14-7 Using Ion-Selective Electrodes
Electrodes respond to the activity of uncomplexed analyte ion.
Standard Addition with Ion-Selective Electrodes
The medium in which the analyte exists is called the matrix. For complex or
unknown matrixes, the standard addition method (Section 5-3) can be used.
E  k  β(
RT ln 10
) log[ X]
nF
(15 - 11)
Standard addition plot for
E/S
k/S
k/S
(
V

V
)
10

10
V
c

10
cSVS
o
s
o
X
ion-seletive electrode:
y
b
10k / S Vo cX
Vo cX
b
x  intercept    


m
10k / S cS
cS
m
(15 - 12)
x
(15 - 13)
Metal Ion Buffers
An alternative is to prepare a metal ion buffer from the metal and a suitable ligand.
Ca 2  NTA 3  CaNTA 
[CaNTA  ]
Kf 
 106.46 in 0.1 M KNO3
2
3
[Ca ][ NTA ]
[CaNTA  ]
[Ca ] 
 106.46 M
3
K f [ NTA ]
2
(15 - 14)
14-8 Solid-State Chemical Sensors36
Semiconductors and Diodes
Semiconductors such as Si (Figure 15-25), Ge, and GaAs are materials whose
electrical resistivity30 lies between those of conductors and insulators.
A phosphorus impurity, with five valence electrons, provides one extra conduction
electron that is free to move through the crystal (Figure 15-26b). An aluminum
impurity has one less bonding electron than necessary, creating a vacancy called a
hole, which behaves as a positive charge carrier.
A semiconductor with excess conduction electrons is called n-type, and one with
excess holes is called p-type.
A diode is a pn junction (Figure 15-27a).
The diode is said to be forward biased.
If the polarity is reversed (Figure 15-27b), electrons are drawn out of n-Si and
holes are drawn out of p-Si, leaving a thin depletion region devoid of charge
carriers near the pn junction. The diode is reverse biased and does not conduct
current in the reverse direction.
Chemical-Sensing Field Effect Transistor
The base of the field effect transistor in Figure 15-28 is constructed of p-Si
with two n-type regions called source and drain. An insulating surface layer of
SiO2 is overcoated by a conductive metal gate between source and drain.
The potential of the gate therefore regulates the current flow between source and
drain.
The essential feature of the chemical-sensing field effect transistor in Figure 1529 is the chemically sensitive layer over the gate.
The voltage that must be applied by an external circuit to bring the current back
to its initial value is the response to Ag+.