Undergraduate Instrumental Analysis

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15
Electroanalytical Chemistry

Electrochemistry is the area of chemistry that studies the interconversion of chemical
energy and electrical energy. Electroanalytical chemistry is the use of electrochemical
techniques to characterize a sample. The original analytical applications of electrochemistry, electrogravimetry and polarography, were for the quantitative determination of
trace metals in aqueous solutions. The latter method was reliable and sensitive enough
to detect concentrations as low as 1 ppm of many metals. Since that time, many different
types of electrochemical techniques have evolved, each useful for particular applications
in organic, inorganic, and biochemical analyses.
A species that undergoes reduction or oxidation is known as an electroactive
species. Electroactive species in general may be solvated or complexed, ions or molecules,
in aqueous or nonaqueous solvents. Electrochemical methods are now used not only for
trace metal ion analyses, but also for the analysis of organic compounds, for continuous
process analysis, and for studying the chemical reactions within a single living cell. Applications have been developed that are suited for quality control of product streams in industry, in vivo monitoring, materials characterization, and pharmaceutical and biochemical
studies, to mention a few of the myriad applications. Under normal conditions, concentrations as low as 1 ppm can be determined without much difficulty. By using electrodeposition and then reversing the current, it is possible to extend the sensitivity limits for
many electroactive species by three or four orders of magnitude, thus providing a
means of analysis at the ppb level.
In practice, electrochemistry not only provides a means of elemental and molecular analysis, but also can be used to acquire information about equilibria, kinetics,
and reaction mechanisms from research using polarography, amperometry, conductometric analysis, and potentiometry. The analytical calculation is usually based on
the determination of current or voltage or on the resistance developed in a cell
under conditions such that these are dependent on the concentration of the species
under study. Electrochemical measurements are easy to automate because they are
electrical signals. The equipment is often far less expensive than spectroscopy instrumentation. Electrochemical techniques are also commonly used as detectors for LC, as
discussed in Chapter 13.

Coauthor: R.J. Gale, Department of Chemistry, Louisiana State University, Baton Rouge, LA
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15.1.

FUNDAMENTALS OF ELECTROCHEMISTRY

Electrochemistry is the study of reduction –oxidation reactions (called redox reactions)
in which electrons are transferred from one reactant to another. A chemical species that
loses electrons in a redox reaction is oxidized. A species that gains electrons is
reduced. A species that oxidizes is also called a reducing agent because it causes the
other species to be reduced; likewise, an oxidizing agent is a species that is itself
reduced in a reaction. An oxidation – reduction reaction requires that one reactant gain
electrons (be reduced) from the reactant which is oxidized. We can write the reduction
and the oxidation reactions separately, as half-reactions; the sum of the half-reactions
equals the net oxidation –reduction reaction. Examples of oxidation half-reactions
include:
Fe2ỵ ! Fe3ỵ ỵ e
Cu(s) ! Cu2ỵ ỵ 2e
AsH3 (g) ! As(s) ỵ 3Hỵ ỵ 3e
H2 C2 O4 ! 2CO2 (g) ỵ 2Hỵ ỵ 2e
Examples of reduction half-reactions include:
Co3ỵ þ eÀ À! Co2þ
1

(IO3 )À þ 6Hþ þ 5eÀ À! I2 (s) ỵ 3H2 O
2
Cl2 (g) ỵ 2e ! 2Cl
Agỵ þ eÀ À! Ag(s)
If the direction of an oxidation reaction is reversed, it becomes a reduction reaction; that is,
if Al3ỵ accepts 3 electrons, it is reduced to Al(s). All of the reduction reactions are oxidation reactions if they are written in the opposite direction. Many of these reactions
are reversible in practice, as we shall see.
A net oxidation – reduction reaction is the sum of the appropriate reduction and oxidation half-reactions. If necessary, the half-reactions must be multiplied by a factor so that
no electrons appear in the net reaction. For example, the reaction between Cu(s), Cu2ỵ,
Ag(s), and Agỵ is:
Cu(s) ỵ 2Agỵ ! Cu2ỵ ỵ 2Ag(s)
We shall see why the reaction proceeds in this direction shortly. The net reaction is
obtained from the half-reactions as follows:
Oxidation reaction: Cu(s) ! Cu2ỵ ỵ 2e
Reduction reaction: Agỵ ỵ e ! Ag(s)
Each mole of copper gives up 2 moles of electrons, while each mole of silver ion accepts
only 1 mole of electrons. Therefore the entire reduction reaction must be multiplied by 2,
so that there are no electrons in the net reaction after summing the half-reactions:
Oxidation reaction: Cu(s) ! Cu2ỵ ỵ 2e
Reduction reaction: 2(Agỵ ỵ e ! Ag(s))
Net reaction: Cu(s) ỵ 2Agỵ ! Cu2ỵ 2Ag(s)
The equal numbers of electrons on both sides of the arrow cancel out.


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Electrochemical redox reactions can be carried out in an electrochemical cell as

part of an electrical circuit so that we can measure the electrons transferred, the current,
and the voltage. Each of these parameters provides us with information about the redox
reaction, so it is important to understand the relationship between charge, voltage, and
current. The absolute value of the charge of one electron is 1.602 Â 10219 coulombs
(C); this is the fundamental unit of electric charge. Since 1.602 Â 10219 C is the charge
of one electron, the charge of one mole of electrons is:
(1:602 Â 10À19 C/eÀ )(6:022 Â 1023 eÀ =mol) ¼ 96,485 C/mol

(15:1)

This value 96,485 C/mol is called the Faraday constant (F), and provides the relationship
between the total charge, q, transferred in a redox reaction and the number of moles, n,
involved in the reaction.
q¼nÂF

(15:2)

In an electric circuit, the quantity of charge flowing per second is called the current, i. The
unit of current is the ampere, A; 1 A equals 1 C/s. The potential difference, E, between
two points in the cell is the amount of energy required to move the charged electrons
between the two points. If the electrons are attracted from the first point to the second
point, the electrons can do work. If the second point repels the electrons, work must be
done to force them to move. Work is expressed in joules, J, and the potential difference,
E, is measured in volts. The relationship between work and potential difference is:
w (in joules) ¼ E (in volts) Â q (in coulombs)

(15:3)

Since the unit of charge is the coulomb, 1 V equals 1 J/C.
The relationship between current and potential difference in a circuit is expressed by

Ohm’s Law:
i¼

E
R

(15:4)

where i is the current; E, the potential difference, and R, the resistance in the circuit. The
units of resistance are V/A or ohms, V.

15.2. ELECTROCHEMICAL CELLS
At the heart of electrochemistry is the electrochemical cell. We will consider the creation
of an electrochemical cell from the joining of two half-cells. When an electrical conductor
such as a metal strip is immersed in a suitable ionic solution, such as a solution of its own
ions, a potential difference (voltage) is created between the conductor and the solution.
This system constitutes a half-cell or electrode (Fig. 15.1). The metal strip in the solution
is called an electrode and the ionic solution is called an electrolyte. We use the term electrode to mean both the solid electrical conductor in a half-cell (e.g., the metal strip) and the
complete half-cell in many cases, for example, the standard hydrogen electrode, the
calomel electrode. Each half-cell has its own characteristic potential difference or electrode potential. The electrode potential measures the ability of the half-cell to do work,
or the driving force for the half-cell reaction. The reaction between the metal strip and
the ionic solution can be represented as
M0 ! Mnỵ ỵ ne

(15:5)


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Figure 15.1 A half-cell composed of a metal electrode M0 in contact with its ions, Mỵ, in
solution. The salt bridge or porous membrane is shown on the lower right side.

where M0 is an uncharged metal atom, Mnỵ is a positive ion, and e2 is an electron. The
number of electrons lost by each metal atom is equal to n, where n is a whole number. This
is an oxidation reaction, because the metal has lost electrons. It has been oxidized from an
uncharged atom to a positively charged ion. In the reaction, the metal ions enter the solution (dissolve). By definition, the electrode at which oxidation occurs is called the anode.
We say that at the anode, oxidation of the metal occurs according to the reaction shown
in Eq. (15.5).
Some examples of this type of half-cell are:
Cd(s) ! Cd2ỵ ỵ 2e
Ag(s) ! Agỵ ỵ e
Cr(s) ! Cr3ỵ ỵ 3e
Note that in normal usage, the zero oxidation state of the solid metal is understood, not
shown with a zero superscript. It has been found that with some metals the spontaneous
reaction is in the opposite direction and the metal ions tend to become metal atoms,
taking up electrons in the process. This reaction can be represented as
Mnỵ ỵ ne ! M0

(15:6)

This is a reduction reaction because the positively charged metal ions have gained electrons, lost their charge, and become neutral atoms. The neutral atoms deposit on the
electrode, a process called electrodeposition. This electrode is termed a cathode. At the
cathode, reduction of an electroactive species takes place. An electroactive species is
one that is oxidized or reduced during reaction. Electrochemical cells also contain
nonelectroactive (or inert) species such as counterions to balance the charge, or electrically conductive electrodes that do not take part in the reaction. Often these inert
electrodes are made of Pt or graphite, and serve only to conduct electrons into or out of

the half-cell.
It is not possible to measure directly the potential difference of a single half-cell.
However, we can join two half-cells to form a complete cell as shown in Fig. 15.2. In
this example, one half-cell consists of a solid copper electrode immersed in an aqueous
solution of CuSO4 ; the other has a solid zinc electrode immersed in an aqueous solution


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Figure 15.2

A complete Zn/Cu galvanic cell with a salt bridge separating the half-cells.

of ZnSO4 . The two half-cell reactions and the net spontaneous reaction are shown:
Anode (oxidation) reaction: Zn(s) ! Zn2ỵ þ 2eÀ
Cathode (reduction) reaction: Cu2þ þ 2eÀ À! Cu(s)
Net reaction: Zn(s) ỵ Cu2ỵ ! Zn2ỵ ỵ Cu(s)
No reaction will take place, and no current will flow, unless the electrical circuit is complete. As shown in Fig. 15.2, a conductive wire connects the electrodes externally through
a voltmeter (potentiometer). A salt bridge, a glass tube filled with saturated KCl in agar
gel, physically separates the two electrolyte solutions. The salt bridge permits ionic
motion to complete the circuit while not permitting the electrolytes to mix. The reason
we need to prevent the mixing of the electrolytes is that we want to obtain information
about the electrochemical system by measuring the current flow through the external
wire. If we had both electrodes and both ionic solutions in the same beaker, the copper
ions would react directly at the Zn electrode, giving the same net reaction but no
current flow in the external circuit. In the electrolyte solution and the salt bridge the

current flow is ionic (ion motion), and in the external circuit the current flow is electronic
(electron motion). This cell and the one in Fig. 15.3 show the components needed for an
electrochemical cell: two electrical conductors (electrodes), suitable electrolyte solutions
and a means of allowing the movement of ions between the solutions (salt bridge in
Fig. 15.2, a semipermeable glass frit or membrane in Fig. 15.3), external connection of
the electrodes by a conductive wire and the ability for an oxidation reaction to occur at
one electrode, and a reduction reaction at the other. Of course there are counterions
present in each solution (e.g., sulfate ions) to balance the charge; these ions are not electroactive and do not take part in the redox reaction. They do flow (ionic motion) to keep
charge balanced in the cell. A cell that uses a spontaneous redox reaction to generate electricity is called a galvanic cell. Batteries are examples of galvanic cells. A cell set up to
cause a nonspontaneous reaction to occur by putting electricity into the cell is called an
electrolytic cell.
The complete cell has a potential difference, a cell potential, which can be measured
by the voltmeter. The potential difference for the cell, Ecell , can be considered to be equal


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Figure 15.3 A schematic complete cell with a porous frit separating the half-cells.

to the difference between the two electrode potentials, when both half-cell reactions are
written as reductions. That is,
Ecell ¼ Ecathode À Eanode

(15:7)

when the potentials are reduction potentials. This convention is necessary to calculate the

sign of Ecell correctly, even though the anode reaction is an oxidation. The cell potential is
also called the electromotive force or emf.
While we cannot measure a given single electrode potential directly, we can easily
measure the cell potential for two half-cells joined as described. So now we have a means
of measuring the relative electrode potential for any half-cell by joining it to a designated
reference electrode (reference half-cell). In real cells, there is another potential difference that contributes to Ecell , called a junction potential. If there is a difference in the concentration or types of ions of the two half-cells, a small potential is created at the junction
of the membrane or salt bridge and the solution. Junction potentials can be sources of error.
When a KCl salt bridge is used the junction potential is very small because the rates of
diffusion of Kỵ and Cl2ions are similar, so the error in measuring a given electrode potential is small.

15.2.1. Line Notation for Cells and Half-Cells
Writing all the equations and arrows for half-cells and cells is time consuming and takes
up space, so a shorthand or line notation is often used. For example, the half-cell composed
of a silver electrode and aqueous 0.0001 M Agỵ ion (from dissolution of silver nitrate in
water) is written in line notation as
Ag(s) j Agỵ (0:0001 M)
The vertical stroke or line between Ag and Agỵ indicates a phase boundary, that is, a
difference in phases (e.g., solid j liquid, solid 1 j solid 2, or liquid j gas) in the constituents
of the half-cells that are in contact with each other. The complete cell in Fig. 15.2 can be
represented as
Zn(s) j Zn2ỵ (0:01 M) k Cu2ỵ (0:01 M) j Cu(s)


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The double vertical stroke after Zn2ỵ indicates a membrane junction or salt bridge. The
double stroke shows the termination of one half-cell and the beginning of the second.

This cell could also be written to show the salts used, as shown:
Zn(s) j ZnSO4 (aq) k CuSO4 (aq) j Cu(s)
It is conventional to write the electrode that serves as the anode on the left in an electrochemical cell. The other components in the cell are listed as they would be encountered
moving from the anode to the cathode.

15.2.2.

Standard Reduction Potentials

15.2.2.1. The Standard Hydrogen Electrode
In order to compile a table of relative electrode potentials, chemists must agree upon the
half-cell that will serve as the reference electrode. The composition and construction of
the half-cell must be carefully defined. The value of the electrode potential for this
reference half-cell could be set equal to any value, but zero is a convenient reference
point. In practice, it has been arbitrarily decided and agreed upon that the standard
hydrogen electrode (SHE) has an assigned electrode potential of exactly zero volts at
all temperatures. The SHE, shown in Fig. 15.4, consists of a platinum electrode with a
surface coating of finely divided platinum (called a platinized Pt electrode) immersed in
a solution of 1 M hydrochloric acid, which dissociates to give Hỵ. Hydrogen gas, H2 ,
is bubbled into the acid solution over the Pt electrode. The finely divided platinum on
the electrode surface provides a large surface area for the reaction
2Hỵ ỵ 2e ! H2 (g)

E0 ẳ 0:000 V

(15:8)

Figure 15.4 The standard hydrogen electrode (SHE). This design is shown with a presaturator containing the same 1 M HCl solution as in the electrode to prevent concentration changes by evaporation.
(Aikens et al., by permission, Waveland Press Inc., Long Grove, IL, 1984. All rights reserved.)

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In addition, the Pt serves as the electrical conductor to the external circuit. Under standard
state conditions, that is, when the H2 pressure equals 1 atm and the ideal concentration of
the HCl is 1 M, and the system is at 258C, the reduction potential for the reaction given in
Eq. (15.8) is exactly 0 V. (The potential actually depends on the chemical activity of the
HCl, not on its concentration. The relationship between activity and concentration is discussed subsequently. For an ideal solution, concentration and activity are equal.) The
potential is symbolized by E 0, where the superscript zero means standard state conditions.
The term standard reduction potential means that the ideal concentrations of all solutes
are 1 M and all gases are at 1 atm; other solids or liquids present are pure (e.g., pure Pt
solid). By connecting the SHE half-cell with any other standard half-cell and measuring
the voltage difference developed, we can determine the standard reduction potential developed by the second half-cell.
Consider, for example, a cell at 258C made up of the two half-cells:
Zn(s) j Zn2ỵ (aq, 1 M) k Hỵ (aq, 1 M) j H2 (g, 1 atm) j Pt(s)
This cell has a Zn half-cell as the anode and the SHE as the cathode. All solutes are present
at ideal 1 M concentrations, gases at 1 atm and the other species are pure solids, and so
both half-cells are at standard conditions. The measured cell emf is þ0.76 V and this is
the standard cell potential, E 0, because both half-cells are in their standard states. From
Eq. (15.7), we can write:
0
0
0
¼ Ecathode
À Eanode
Ecell

(15:9)

The total voltage developed under standard conditions is ỵ0.76 V. But the voltage of the
SHE is 0 by definition; therefore the standard reduction potential of the Zn half-cell is:
0
ỵ0:76 V ẳ 0:000 EZn
0
EZn
ẳ 0:76 V

Therefore we can write:
Zn2ỵ ỵ 2e ! Zn(s)

E0Zn ẳ 0:76 V

We have determined the Zn standard reduction potential even though the galvanic cell we
set up has Zn being oxidized. By substituting other half-cells, we can determine their electrode potentials (actually, their relative potentials) and build a table of standard reduction
potentials. If we set up a galvanic cell with the SHE and Cu, we have to make the SHE the
anode in order for a spontaneous reaction to occur. This cell,
Pt(s) j H2 (g, 1 atm) j Hỵ (aq, 1 M) k Cu2ỵ (aq, 1 M) j Cu(s)
has a measured cell emf ¼ þ0.34 V. Therefore the standard reduction potential for Cu is
þ0:34 V ẳ E0Cu 0:000 V
0
ẳ ỵ0:34 V
ECu

The quantity E 0 is the emf of a half-cell under standard conditions. A half-cell is said to be
under standard conditions when the following conditions exist at a temperature of 258C:
1.
2.

3.

All solids and liquids are pure (e.g., a metal electrode in the standard state)
All gases at a pressure of 1 atm (760 mmHg)
All solutes are at 1 M concentration (more accurately, at unit activity)


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The true electrode potential is related to the activity of the species in solution, not the concentration. For a pure substance, its mole fraction and its activity ¼ 1. For a pure substance
that is not present in the system, its mole fraction and its activity ¼ 0. From general chemistry, you should remember that Raoult’s Law predicts that for an ideal solution, the mole
fraction of the solute and its activity are equal. However, most solutions deviate from linearity because of interactions between the solute and solvent molecules. These deviations
can be positive or negative, because the species may attract or repel each other. The
amount of attraction or repulsion affects the activity of the solute. For dilute solutions,
the activity is proportional to concentration (Henry’s Law). Activity is equal to the concentration times the activity coefficient for the species in solution. That is
aion ¼ ½Mion Šgion

(15:10)

where aion is the activity of given ion in solution; [Mion], the molar concentration of the
ion; and gion , the activity coefficient of the ion.
Activity depends on the ionic strength of the solution. If we compare a 1 M solution
and a 0.01 M solution, the more concentrated solution may act as though it is less than
100Â more concentrated than the dilute solution. It is then said that the activity of the
1 M solution is less than unity or the activity coefficient is less than 1. For solutions
with positive deviations from Henry’s Law, the activity coefficient will be greater than
1. For very dilute solutions (low ionic strength) the activity coefficient g approaches 1,

so concentration is approximately equal to activity for very dilute solutions. We will
use concentrations in the calculations in this text instead of activities, but the approximation is only accurate for dilute solutions (,0.005 M) and for ions with single
charges. Details on activity corrections can be found in most analytical chemistry texts,
such as the ones by Harris or Enke listed in the bibliography.
Looking back at our cell in Fig. 15.2, with the Zn half-cell as the anode and the Cu
half-cell as the cathode, we can calculate the standard cell potential for this galvanic cell.
In the spontaneous reaction, Zn is oxidized and Cu2ỵ is reduced, therefore Zn is the anode
and Cu is the cathode.
Zn2ỵ ỵ 2e ! Zn0

E0 ẳ 0:76 V

Cu2ỵ ỵ 2e ! Cu0

E0 ẳ ỵ0:34 V

The standard cell potential developed is calculated from Eq. (15.9):
ỵ 0:34 (0:76 V) ẳ ỵ1:10 V
In tables of standard potentials, all of the half-cell reactions are expressed as reductions.
The sign is reversed if the reaction is reversed to become an oxidation. In a spontaneous
reaction, when both half-cells are written as reductions, the half-cell with the more negative potential will be the one that oxidizes. The negative sign in Eq. (15.9) reverses one of
the reduction processes to an oxidation. Some standard reduction potentials for common
half-cells are given in Appendix 15.1. These can be used to calculate E 0 for other electrochemical cell combinations as we have done for the Zn/Cu cell. More complete lists of
half-cell potentials can be found in references such as Bard et al., listed in the
bibliography.
In the reaction of our example, zinc metal dissolves, forming zinc ions and liberating
electrons. Meanwhile, an equal number of electrons are consumed by copper ions, which
plate out as copper metal. The net reaction is summarized as
Zn0 ỵ Cu2ỵ ! Cu0 ỵ Zn2ỵ

ỵ1:10 V


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Zinc metal is oxidized to zinc ions, and copper ions are reduced to copper metal. The
copper cathode becomes depleted of electrons because these are taken up by the copper
ions in solution. At the same time the zinc anode has an excess of electrons because the
neutral zinc atoms are becoming ionic and liberating electrons in the process. The
excess electrons from the anode flow to the cathode. The flow of electrons is the source
of external current; the buildup of electrons at the anode and the depletion at the
cathode constitute a potential difference that persists until the reaction ceases. The reaction
comes to an end when either all the copper ions are exhausted from the system or all the
zinc metal is dissolved, or an equilibrium situation is reached when both half-cell potentials are equal. If the process is used as a battery, such as a flashlight battery, the battery
becomes dead when the reaction ceases.
When a cell spontaneously generates a voltage, the electrode that is negatively
charged is the anode and the positively charged electrode is the cathode.

15.2.3. Sign Conventions
The sign of half-cell potentials has been defined in a number of different ways, and this
variety of definitions has led to considerable confusion. The convention used here is in
accord with the recommendations of the IUPAC meeting in Stockholm in 1953. In this
convention the standard half-cell reactions are written as reductions. Elements that are
more powerful reducing agents than hydrogen show negative potentials, and elements
that are less powerful reducing agents show positive potentials. For example, the
Zn j Zn2ỵ half-cell is negative and the Cu j Cu2ỵ half-cell is positive.

15.2.4. The Nernst Equation
We have seen how to use standard reduction potentials to calculate E 0 for cells. Real cells
are usually not constructed at standard state conditions. In fact, it is almost impossible to
make measurements at standard conditions because it is not reasonable to adjust concentrations and ionic strengths to give unit activity for solutes. We need to relate standard
potentials to those measured for real cells. It has been found experimentally that certain
variables affect the measured cell potential. These variables include the temperature, concentrations of the species in solution, and the number of electrons transferred. The
relationship between these variables and the measured cell emf can be derived from
simple thermodynamics (see any introductory general chemistry text). The relationship
between the potential of an electrochemical cell and the concentration of reactants and
products in a general redox reaction
aA ỵ bB ! cC ỵ dD
is given by the Nernst equation:
E ẳ E0

RT ẵCc ẵDd
ln
nF ẵAa ẵBb

(15:11)

where E is the measured potential (emf) of the cell; E 0, the emf of the cell under standard
conditions; R, the gas constant (8.314 J/K mol ¼ 8.314 V C/K mol); T, the temperature
(K); n, the number of moles of electrons transferred during reaction (from the balanced
half-reactions); F, the Faraday constant (96,485 C/mol e2); and ln ¼ natural logarithm
to base e.


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The logarithmic term has the same form as the equilibrium constant for the reaction.
The term is called Q, the reaction quotient, when the concentrations (rigorously, the activities) are not the equilibrium values for the reaction. As in any equilibrium constant
expression, pure liquids and pure solids have activities equal to 1, so they are omitted
from the expression. If the values of R, T (258C ¼ 298 K), and F are inserted into the
equation and the natural logarithm is converted to log to the base 10, the Nernst equation
reduces to
E ẳ E0

0:05916
ẵCc ½DŠd
log a b
½AŠ ½BŠ
n

(15:12)

It should be noted that the square brackets literally mean the molar concentration of. For
example, [Fe2ỵ] means “the molar concentration of ferrous ion” or moles of ferrous ion
per liter of solution.
Concentrations in molarity should really be the activities of the species, but we often
0
do not know the activities. For that reason, we define the formal potential, E 0 , as the
measured potential of the cell when the species being oxidized and reduced are present
at concentrations such that the ratio of the concentrations of oxidized to reduced
species is unity and other components of the cell are present at designated concentrations.
The use of the formal potential allows us to avoid activity coefficients, which are often
unknown. This gives us:
0

E ¼ E0 À

0:05916
½CŠc ½DŠd
log a b
½AŠ ½BŠ
n

(15:13)

The Nernst equation is also used to calculate the electrode potential for a given half-cell at
nonstandard conditions. For example, for the half-cell Fe3ỵ ỵ e2 ! Fe2ỵ which has an
E 0 ẳ 0.77 V and n ¼ 1, the Nernst equation would be:
E ¼ 0:77

0:05916
ẵFe2ỵ
log 3ỵ
1
ẵFe

To calculate the electrode potential, the molar concentrations of ferrous and ferric ion used
to construct the half-cell would be inserted. The general form of the Nernst equation for an
electrode written as a reduction is:


0:0591
ẵred
log

EẳE
n
ẵox
0

(15:14)

where [red] means the molarity of the reduced form of the electroactive species and [ox]
means the molarity of the oxidized form of the electroactive species. In cells where the
reduced form is the metal (e.g., in the Cu/Cu2ỵ half-cell) [red] ẳ 1 because pure
metals such as Cu have unit activity. There is the equivalent definition of formal potential
for each half-cell.
The Nernst equation gives us the very important relationship between E, the emf of
the half-cell, and the concentration of the oxidized and reduced forms of the components
of the solution. Measurements using pH electrodes and ion-selective electrodes are based
on this relationship. If the two electrode reactions are written as reductions, the potentials
can be calculated for the cathode and anode (or the electrode inserted into the positive
terminal of the potentiometer, Eỵ and the electrode inserted into the negative terminal


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of the potentiometer, E2) The cell voltage is the difference
Ecell ¼ Eỵ E

(15:15)

15.2.5. Activity Series
The tendency for a species to become oxidized or reduced determines the sign and potential of the half-cell. The tendency is strongly related to the chemical reactivity of the
species concerned in aqueous systems. Based on the potential developed in a half-cell
under controlled conditions, the elements may be arranged in an order known as the
activity series or electromotive series (Table 15.1). In general, the metals at the top of
the activity series are most chemically reactive and tend to give up electrons easily, following the reaction of M0 ! Mnỵ ỵ ne2. The metals at the bottom of the series are
more “noble” and therefore less active. They do not give up electrons easily; in fact,
their cations will accept electrons from metals above them in the activity series. In the
process, the cations become neutral metal atoms and plate out of solution, while the
more active metals become ionic and dissolve. This is illustrated as follows:
metal A (active) À! metal ion Aỵ ỵ e
metal ion Bỵ (noble) ỵ e ! metal B
net result: A ỵ Bỵ ! Aỵ ỵ B
Table 15.1 The Activity Series of Metals
Metal

E0 (V)

Chemical reactivity

Li

23.05

These metals displace hydrogen from acids and dissolve in all acids, including
water

K
Ba
Sr

Ca
Na
Mg
Al
Mn
Zn
Cr
Fe
Cd
Co
Ni
Sn
Pb
H2
Bi
Cu
Ag
Hg
Pd
Pt
Au

22.93
22.91
22.89
22.87
22.71
22.37
21.66
21.18

20.76
20.74
20.44
20.40
20.28
20.26
20.14
20.13
0.00
ỵ0.32
ỵ0.34
ỵ0.80
ỵ0.85
ỵ0.92
ỵ1.12
ỵ1.50

These metals react with acids or steam

These metals react slowly with all acids

These metals react with oxidizing acids (e.g., HNO3)

These metals react with aqua regia (3:1 v/v HCl/HNO3)


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In short, the more active metals displace the less active metals from solution. As an
example, if an iron strip is immersed in a solution of copper sulfate, some of the iron dissolves, forming iron ions, while the copper ions become metallic and copper metal plates
out on the remaining iron strip. The activity series can be used to predict displacement
reactions between atoms and ions in compounds of the type A ỵ BC ! AC ỵ B, where
A and B are atoms. Using the activity series, any atom A will displace from a compound
any element B listed below it, but will not displace any element listed above it.
This reaction is particularly important when Bỵ in BC refers to a hydrogen ion solution (acid). Based on this principle, all elements above hydrogen in the activity series are
capable of displacing hydrogen from solution; that is, it is possible for them to be dissolved
in an acid solution by reducing the Hỵ ion. The metal ionizes (oxidizes) and enters the
solution while the Hỵ (acid) reduces to H2 and usually bubbles off. We would predict
that Al and Zn would dissolve in HCl, but that Cu will not. In contrast, a simple
mineral acid such as HCl cannot dissolve noble metals, such as platinum and gold,
because the metals will not displace hydrogen ion. These metals require an oxidizing
acid such as nitric acid plus a complexing ion such as the chloride ion from HCl, as is
found in aqua regia, a mixture of HCl and HNO3 , to force them into solution.
15.2.6.

Reference Electrodes

In order to measure the emf of a given half-cell, it is necessary to connect it with a second
half-cell and measure the voltage produced by the complete cell. In general, the second halfcell serves as a reference cell and should be one with a known, stable electrode potential.
Although the standard hydrogen electrode serves to define the standard reduction potential, in practice it is not always convenient to use an SHE as a reference electrode. It is
difficult to set up and control. Other, more convenient reference electrodes have been
developed. In principle, any metal-ion half-cell could be used under controlled conditions
as a reference electrode, but in practice, many metals are unsatisfactory materials. Active
metals, such as sodium and potassium, are subject to chemical attack by the electrolyte.
Other metals, such as iron, are difficult to obtain in the pure form. With some metals,
the ionic forms are unstable to heat or to exposure to the air. Also, it is frequently difficult
to control the concentration of the electrolytes accurately. As a result, only a few systems

provide satisfactory stable potentials.
The characteristics of an ideal reference electrode are that it should have a fixed
potential over time and temperature, long term stability, the ability to return to the
initial potential after exposure to small currents (i.e., it should be reversible), and it
should follow the Nernst equation. Two common reference electrodes that come close
to behaving ideally are the saturated calomel electrode and the silver/silver chloride
electrode.
15.2.6.1. The Saturated Calomel Electrode
The saturated calomel electrode (SCE) is composed of metallic mercury in contact with
a saturated solution of mercurous chloride, or calomel (Hg2Cl2). A Pt wire in contact
with the metallic Hg conducts electrons to the external circuit. The mercurous ion concentration of the solution is controlled through the solubility product by placing the calomel in
contact with a saturated potassium chloride solution. It is the saturated KCl solution
that gives this electrode the “saturated” name; there are other calomel reference electrodes
used that differ in the concentration of KCl solution, but all contain saturated mercurous
chloride solution. A typical calomel electrode is shown in Fig. 15.5. The half-cell


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Figure 15.5 The saturated calomel electrode (SCE). (Aikens et al., by permission, Waveland
Press Inc., Long Grove, IL, 1984. All rights reserved.)

reaction is
Hg2 Cl2 (s) ỵ 2e

! 2Hg(l) ỵ 2Cl

E0 ẳ ỵ0:268 V

Applying Eq. (15.12), we obtain
0:05916
½CŠc ½DŠd
log a b
½AŠ ½BŠ
n
 0 2 2
0:0591
ẵHg ẵCl
log
E ẳ E0
ẵHg2 Cl2 Š
2
E ¼ E0 À

But Hg2Cl2(s) and Hg(l) are in standard states at unit activity; therefore
E ¼ E0 À
¼ E0 À



0:0591
1  ½ClÀ Š2
log
1
2
0:0591

log (½ClÀ Š2 )
2

When the KCl solution is saturated and its temperature is 258C, the concentration of
chloride ion, [Cl2], is known and
E ẳ ỵ 0:244 V for the SCE
For a 1 N solution of KCl, the electrode is called a normal calomel electrode (NCE) and
E(NCE) ẳ ỵ0.280 V. The advantage of the SCE is that the potential does not change if
some of the liquid evaporates from the electrode, because the Cl2 concentration does
not change. Remember that “saturated” for the SCE refers to the KCl concentration, not
to the mercurous chloride (calomel).


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15.2.6.2. The Silver/Silver Chloride Electrode
Another common reference cell found in the chemical-processing industry and useful in
organic electrochemistry is the silver/silver chloride half-cell. The cell consists of
silver metal coated with a paste of silver chloride immersed in an aqueous solution saturated with KCl and AgCl. The half-cell reaction is
AgCl(s) ỵ e

! Ag(s) þ ClÀ

E0 ¼ þ0:222 V

The same principle applies as in the SCE, but in this case the silver ion activity depends on
the solubility product of AgC1, which is in contact with a solution of known chloride ion

activity. The measured E for an Ag/AgCl electrode saturated in KCl is ỵ0.199 V at 258C.
A saturated KCl solution is about 4.5 M KCl. This reference electrode can also be filled
with 3.5 M KCl (saturated with AgCl); the potential in this case is ỵ0.205 V at 258C.
The silver/silver chloride electrode provides a reproducible and reliable reference
electrode free from mercury salts.
Both reference electrode designs can permit KCl to leak through the porous plug
junction and contaminate the analyte solution. In addition, analytes that react with Ag
or Hg ions, such as sulfides, can precipitate insoluble salts that clog the junction and
impair the performance of the electrode. Electrode manufacturers have designed
double-junction electrodes with an outer chamber that can be filled with an electrolyte
that does not interfere with a given measurement and electrodes with large, flushable
sleeve junctions that can be cleaned easily and are not prone to clogging.
15.2.7.

The Electrical Double Layer

While it is easy to say that we can measure the potential difference in an electrochemical cell,
the reality of what we are measuring is not obvious. The potential difference between a single
electrode and the solution cannot be measured. A second electrode immersed in the solution
is required. The second electrode has its own potential difference between itself and the solution; this difference cannot be measured either. All we can measure are relative potential
differences. The potential difference between an electrode and the solution actually exists
only in a very small region immediately adjacent to the electrode surface. This region of
potential difference is often called the “electrical double layer” and is only nanometers
wide. A very simplistic view of this interface is presented. A negatively charged electrode
surface will have a “layer” of excess positive ions in solution adjacent to (or adsorbed to)
the surface of the electrode; hence the term “double layer”. Immediately adjacent to the positive ion layer there is a complex region of ions in solution whose distribution is determined by
several factors. Outside of that, and only nanometers away from the electrode surface, there is
the bulk solution. A positively charged electrode surface will have a similar interfacial region
with the charges reversed. The exact nature of the charged interface and the ion distribution is
very complex and is not yet completely understood. Outside of this very narrow region of

high potential gradient next to each electrode, there is no potential gradient in the bulk of
the solution. As a consequence of the placement of electrodes in solution and the creation
of charged interfaces between the electrode surface and the solution, electrochemical
measurements are made in a very nonhomogeneous environment.
Any reactions that occur must occur at the electrode –solution interface and the
reacting species must be brought to the electrode surface by diffusion or mass transport
through stirring of the solution (convection). The ions in the bulk of the solution are
not attracted to the electrodes by potential difference; there is no potential gradient in
the bulk of the solution. Even when we are interested in the bulk properties of the solution,
we are only analyzing an extremely small amount of the solution that is no longer


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homogeneous because of the formation of the complex layers of charged species at the
electrode interface.

15.3.

ELECTROANALYTICAL METHODS

Diverse analytical techniques, some highly sensitive, have been developed based on
measurements of current, voltage, charge, and resistance in electrochemical systems.
One variable is measured while the others are controlled. Electroanalytical methods can
be classified according to the variable being measured. Table 15.2 provides a summary
of the more important methods. The methods are briefly defined below and then discussed
at length in subsequent sections.

The Nernst equation indicates the relationship between the activity of species in solution and the emf produced by a cell involving those species. The electrochemical technique
called potentiometry measures the potential developed by a cell consisting of an indicator
electrode and a reference electrode. In theory, the indicator electrode response is a measure
of the activity of a single component of the solution, the analyte. In practice, the indicator
electrode is calibrated to respond to concentration rather than activity and is usually not
specific for a single analyte. The potential, Ecell , is measured under negligible current flow
to avoid significant changes in the concentration of the component being measured.
Modern potentiometers permit measurement of potential with currents ,1 pA, so potentiometry can be considered to be a nondestructive technique. Potentiometry is the basis for
measurement of pH, ion-selective electrode measurements, and potentiometric titration.
Coulometry is the term used for a group of methods based on electrolytic oxidation
or reduction of an analyte. The electrolysis is performed either by controlling the potential
or the current, and is carried out to quantitatively convert the analyte to a new oxidation
state. One form of coulometry is electrogravimetry, in which metallic elements are
reduced, plated out onto an electrode, and weighed. The weight of the metal deposited
is a measure of the concentration of the metal originally in solution. Coulometry is
based on Faraday’s Law, which states that the extent of reaction at an electrode is proportional to the current. It is known that 1 F (96,485 C) of electricity is required to
reduce (or oxidize) 1 gram-equivalent weight of an electroactive analyte. By measuring
the quantity of electricity required to reduce (or oxidize) a given sample exhaustively,
the quantity of analyte can be determined, provided the reaction is 100% efficient (or of
known efficiency). Mass, or charge q ¼ i (A) Â t (s), can be used as a measure of the
extent of the electrochemical reaction.
Table 15.2 Electroanalytical Techniques
Technique
Conductometry
Conductometric titration
Potentiometry
Potentiometric titration
Cyclic voltammetry
Polarography
Anodic stripping voltammetry

Coulometry
Electrogravimetry
Coulometric titration

Controlled parameter

Parameter measured

Voltage, V (AC)
Voltage, V (AC)
Current, i ¼ 0
Current, i ¼ 0
Potential, E
Potential, E
Potential, E
E or i
E or i
i

Conductance G ¼ 1/R
Titrant volume vs. conductance
Potential, E
Titrant volume vs. E
i vs. E
i vs. E
i vs. E
Charge, q (integrated current)
Weight deposited
Time, t

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In voltammetry a controlled potential is applied to one electrode and the current
flowing through the cell is monitored over time. A powerful family of techniques is available using voltammetry. Polarography is a technique that requires three electrodes. Polarography uses as the working electrode a dropping mercury electrode or a static (hanging)
mercury drop. The auxiliary electrode (or counterelectrode) is normally a Pt wire or foil. A
third (reference) electrode is used as a basis for control of the potential at the working electrode. The current of analytical interest flows between the working and auxiliary electrodes, and the reference acts only as a high-impedance probe. As the voltage is progressively
increased or decreased with time (sweep voltammetry), resultant changes in the anodic or
cathodic currents occur whenever an electroactive species is oxidized or reduced, respectively. Polarography is a special case of linear sweep voltammetry because the electrode
area increases with time as each drop grows and falls every 4 s or so; that is, the
voltage is changing as the electrode area increases. Polarography is especially useful
for analyzing and studying metal ion and metal complex reductions and solution equilibria. Another technique for studying electrochemical reaction rates and mechanisms
involves reversing the potential sweep direction to reveal the electroactive products
formed in the forward sweep. In this way it is possible to see if the products undergo reaction with other species present or with the solvent. This technique is called cyclic voltammetry and is usually carried out at a solid electrode. In a special case of voltammetry called
anodic stripping voltammetry the electrolyzed product is preconcentrated at an electrode
by deposition for a reasonable period at a fixed potential. The product is then stripped off
with a rapid reverse potential sweep in the positive direction. Peak currents on the reverse
sweep are used to determine the analyte concentration from a standard additions calibration. In principle, this method is applicable to both anodic and cathodic stripping.
Amperometry is the measurement of current at a fixed potential. An analyte undergoes oxidation or reduction at an electrode with a known, applied potential. The amount of
analyte is calculated from Faraday’s law. Amperometry is used to detect titration endpoints, as a detector for liquid chromatography and forms the basis of many new
sensors for biomonitoring and environmental monitoring applications.
In conductometry an alternating (AC) voltage is applied across two electrodes
immersed in the same solution. The applied voltage causes a current to flow. The magnitude of the current depends on the electrolytic conductivity of the solution. This method
makes it possible to detect changes of composition in a sample during chemical reactions
(e.g., during a titration) although the measurement itself cannot identify the species carrying the current. Conductivity or conductance measurements are used routinely to monitor
water quality and process streams. Conductivity detectors are used for measuring ion
concentrations in commercial ion chromatography instruments.

A variety of electroanalytical methods are used as detectors for liquid chromatography. Detectors based on conductometry, amperometry, coulometry, and polarography
are commercially available.
15.3.1.

Potentiometry

Potentiometry involves measurement of the potential, or voltage, of an electrochemical
cell. Accurate determination of the potential developed by a cell requires a negligible
current flow during measurement. A flow of current would mean that a faradaic reaction
is taking place, which would change the potential from that existing when no current is
flowing.
Measurement of the potential of a cell can be useful in itself, but it is particularly
valuable if it can be used to measure the potential of a half-cell or indicator electrode


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(also called a sensing electrode), which responds to the concentration of the species to be
determined. This can be accomplished by connecting the indicator electrode to a reference
half-cell to form a complete cell as shown in Fig. 15.6. When the total voltage of the cell is
measured, the difference between this value and the voltage of the reference electrode is
the voltage of the indicator electrode. This can be expressed as
E(total) ¼ E(indicator) À E(reference)
Compare this equation with Eqs. (15.7) and (15.15). By convention, the reference electrode
is connected to the negative terminal of the potentiometer (the readout device). The
common reference electrodes used in potentiometry are the SCE and the silver/silver
chloride electrode, which have been described. Their potentials are fixed and known

over a wide temperature range. Some values for these electrode potentials are given in
Table 15.3. The total cell potential is measured experimentally, the reference potential is
known, and therefore the variable indicator electrode potential can be calculated and
related to the concentration of the analyte through the Nernst equation. In practice, the concentration of the unknown analyte is determined after calibration of the potentiometer with
suitable standard solutions. The choice of reference electrode depends on the application.
For example, the Ag/AgCl electrode cannot be used in solutions containing species such as
halides or sulfides that will precipitate or otherwise react with silver.
15.3.1.1.

Indicator Electrodes

The indicator electrode is the electrode that responds to the change in analyte activity. An
ideal indicator electrode should be specific for the analyte of interest, respond rapidly to

Figure 15.6 An electrochemical measuring system for potentiometry. The indicator (sensing,
working) electrode responds to the activity of the analyte of interest. The potential difference developed between the reference electrode and the indicator electrode is “read out” on the potentiometer
(voltmeter). [Courtesy of Thermo Orion, Beverly, MA (www.thermoorion.com).]


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Table 15.3 Potentials of Reference Electrodes at
Various Temperatures
Potential (V) vs. SHE
Temperature
(8C)
15

20
25
30
35

Saturated
calomel (SCE)

Saturated
Ag/AgCl

0.251
0.248
0.244
0.241
0.238

0.209
0.204
0.199
0.194
0.189

changes in activity, and follow the Nernst equation. There are no specific indicator electrodes, but there are some that show a high degree of selectivity for certain analytes. Indicator electrodes fall into two classes, metallic electrodes and membrane electrodes.
Metallic Electrodes. A metal electrode of the first kind is just a metal wire, mesh,
or solid strip that responds to its own cation in solution. Cu/Cu2ỵ, Ag/Agỵ, Hg/Hgỵ, and
Pb/Pb2ỵ are examples of this type of electrode. There are significant problems encountered with these electrodes. They have poor selectivity, responding not only to their
own cation but also to any other more easily reduced cation. Some metal surfaces are
easily oxidized, giving erratic or inaccurate response unless the solution has been
purged of air. Some metals can only be used in limited pH ranges because they will dissolve in acids or bases. Silver and mercury are the most commonly used electrodes of the

first kind.
A metal electrode of the second kind consists of a metal coated with one of its sparingly soluble salts (or immersed in a saturated solution of its sparingly soluble salt). This
electrode responds to the anion of the salt. For example, a silver wire coated with AgCl
will respond to changes in chloride activity because the silver ion activity is controlled
by the solubility of AgCl. The electrode reaction is AgCl(s) ỵ e2 ! Ag(s) ỵ Cl2,
with a potential E 0 ¼ 0.222 V. The Nernst equation expression for the electrode potential
at 258C is E ¼ 0.222 2 0.05916 log[Cl2].
A metal electrode of the third kind uses two equilibrium reactions to respond to a
cation other than that of the metal electrode. EDTA complexes many metal cations, with
different stabilities for the complexes but a common anion (the EDTA anion) involved in
the equilibria. A mercury electrode in a solution containing EDTA and Ca will respond to
the Ca ion activity, for example. The complexity of the equilibria make this type of electrode unsuitable for complex sample matrices.
The last type of metallic electrode is the redox indicator electrode. This electrode
is made of Pt, Pd, Au, or other inert metals, and serves to measure redox reactions for
species in solution (e.g., Fe2ỵ/Fe3ỵ, Ce3ỵ/Ce4ỵ). These electrodes are often used to
detect the endpoint in potentiometric titrations. Electron transfer at inert electrodes is
often not reversible, leading to nonreproducible potentials. Although not a metal electrode,
it should be remembered that carbon electrodes are also used as redox indicator electrodes,
because carbon is also not electroactive at low applied potentials.
Membrane Electrodes. Membrane electrodes are a class of electrodes that
respond selectively to ions by the development of a potential difference (a type of junction
potential) across a membrane that separates the analyte solution from a reference solution.
The potential difference is related to the concentration difference in the specific ion
measured on either side of the membrane. Remember that electrodes really respond to


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activity differences, but we will think in terms of concentration because we are interested
(usually) in the concentration of the analyte in our sample. These electrodes do not involve
a redox reaction at the surface of the electrode as do metallic electrodes. Because these
electrodes respond to ions, they are often referred to as ion-selective electrodes (ISEs).
The ideal membrane allows the transport of only one kind of ion across it; that is, it
would be specific for the measurement of one ionic species only. As of this writing,
there are no specific ISEs, but there are some highly selective ones. Each electrode is
more or less selective for one ion; therefore a separate electrode is needed for each
species to be measured. In recent years, a large number of different types of membrane
electrodes has been developed for a wide variety of measurements.
ISEs are relatively sensitive, as we will see. They are capable of detecting concentrations as low as 10212 M for some electrodes. To avoid writing small concentrations in
exponential form, the term pIon has been defined, where pIon equals the negative logarithm (base 10) of the molar concentration of the ion. That is,
pIon ẳ logẵIon

(15:16)

For example, pH is the term used for the negative logarithm of the hydrogen ion concentration, where Hỵ is expressed as (moles of Hỵ)/L of solution. Concentrations of other
ions can be expressed similarly: pCa for calcium ion concentration, pF for fluoride ion
concentration, pOH for hydroxide ion concentration, and pCl for chloride ion
concentration. If the concentration of Hỵ ion in solution equals 3.00 1025 M, the
pH ¼ 2log(3.00 Â 1025) ¼ 4.522, for example. If the concentration is 1.00 Â 1027 M,
the pH ¼ 2log(1.0 Â 1027) ¼ 7.00.
Glass Membrane Electrodes. The first membrane electrode to be developed was
the glass electrode for measurement of pH, the concentration of hydrogen ion, Hỵ, in solution. The pH electrode consists of a thin hydrogen ion-sensitive glass membrane, often
shaped like a bulb, sealed onto a glass or polymer tube. The solution inside the electrode
contains a known concentration of Hỵ ion, either as dilute HCl or a buffer solution. The
solution is saturated in AgCl. The activity of Hỵ inside the electrode is constant and keeps
the internal potential fixed. An internal reference electrode is sealed inside the tube and is
attached to one terminal of the potentiometer. The glass pH electrode is shown schematically in Fig. 15.7(a). The glass pH electrode is used in combination with a reference electrode, either a separate Ag/AgCl electrode or an SCE, as shown in Fig. 15.7(b). Both

electrodes are immersed in a solution of unknown pH and the cell potential developed
is a measure of the hydrogen ion concentration in the solution on the outside of the
glass membrane of the pH electrode, since all other potentials are fixed.
In a standard pH electrode, the glass membrane is composed of SiO2 , Na2O, and
CaO. The response of this glass to changes in hydrogen ion activity outside the membrane
is complex. The glass electrode surfaces must be hydrated in order for the glass to function
as a pH sensor. It is thought that a hydrated gel layer containing adsorbed Hỵ ions exists on
the inner and outer glass surfaces. It is necessary for charge to move across the membrane
in order for a potential difference to be measured, but studies have proved that Hỵ ion does
not move through the glass membrane. The singly charged Naỵ cation is mobile within the
3D silicate lattice. It is the movement of sodium ions in the lattice that is responsible for
electrical conduction within the membrane. The inner and outer glass membrane surfaces
contain negatively charged oxygen atoms. Hydrogen ions from the solution inside the
electrode equilibrate with the inner glass surface, neutralizing some of the negative
charge. Hydrogen ions from the solution outside the electrode (our sample) equilibrate
with the oxygen anions on the outer glass surface and neutralize some of the charge.


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Figure 15.7 (a) A schematic glass electrode for pH measurement. (b) A complete pH measurement cell, with the glass indicator electrode and an external saturated calomel reference electrode.
(c) A commercial combination pH electrode, with built-in internal Ag/AgCl reference electrode.

The side of the glass exposed to the higher Hỵ concentration has the more positive charge.
Naỵ ions in the glass then migrate across the membrane from the positive side to the
negative side, which results in a change in the potential difference across the membrane.

The only variable is the hydrogen ion concentration in the analyte solution. Because the


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electrode behavior obeys the Nernst equation, the potential changes by 0.05916 V for
every 10-fold change in [Hỵ] or for every unit change in pH. The glass pH electrode
is highly selective for hydrogen ions. The major interfering ion is Naỵ. When Naỵ concentration is high and Hỵ is very low, as occurs in very basic solutions of sodium hydroxide, the electrode responds to sodium ion as if it were hydrogen ion. This results in a
negative error; the measured pH is lower than the true pH. This is called the alkaline
error. The use of pH electrodes to measure pH is discussed below under applications
of potentiometry.
Commercial glass pH electrodes come in all sorts of shapes and sizes to fit into every
imaginable container, including into NMR tubes and to measure pH in volumes of solution
as small as a few microliters. Some electrodes come as complete cells, with a second reference electrode built into the body of the pH electrode. These are called combination electrodes, and eliminate the need for a second external reference electrode. Combination
electrodes are required if you want to measure small volumes in small containers and
have no room for two separate electrodes. A combination electrode is shown schematically
in Fig. 15.7(c). Many glass pH electrodes have polymer bodies and polymer shields around
the fragile glass bulb to help prevent breakage. A microelectrode for measuring microliter
volumes in well plates is shown in Fig. 15.8.
Other glass compositions incorporating aluminum and boron oxides have been used
in membrane electrodes to make the membrane selective for other ions instead of hydrogen ion. For example, a glass whose composition is 11% Na2O, 18% Al2O3 , 71% SiO2 is
highly selective toward sodium, even in the presence of other alkali metals. For example,
at pH 11 this electrode is approximately 3000Â more sensitive to Naỵ than to Kỵ. The
ratio of the response of the electrode to a solution of potassium to its response to a solution
of sodium, the analyte, for solutions of equal concentration, is called the selectivity coefficient. The selectivity coefficient should be a very small number ((1) for high selectivity
for the analyte. An ISE has different selectivity coefficients for each ion that responds.
Commercial glass ISEs are available for all of the alkali metal ions (Li, Na, K, Rb, and

ỵ
3ỵ
2ỵ
2ỵ
Cs), and for ammonium ion (NHỵ
4 ), Ag , Fe , Pb , and Cu .
Crystalline Solid-State Electrodes. Crystalline solid-state electrodes have membranes that are single crystal ionic solids or pellets pressed from ionic salts under high
pressure. The ionic solid must contain the target analyte ion and must not be soluble in
the solution to be measured (usually aqueous solution). These membranes are generally
about 1– 2 mm thick and 10 mm in diameter. Sealing the solid into the end of a
polymer tube forms the electrode. Like the pH electrode, the interior of the polymer
tube contains an internal electrode to permit connection to the potentiometer and a
filling solution containing a fixed concentration of the analyte ion. A concentration difference in the analyte ion on the outside of the crystalline membrane causes the migration of
charged species across the membrane. These electrodes generally respond to concentrations as low as 1026 M of the analyte ion.
The fluoride ion selective electrode is the most commonly used single crystal ISE. It
is shown schematically in Fig. 15.9. The membrane is a single crystal of LaF3 doped with
EuF2 . The term “doped” means that a small amount of another substance (in this case,
EuF2) has been added intentionally into the LaF3 crystal. (If the addition were not intentional, we would call the europium an impurity or contaminant!) Note that the two salts do
not have the same stoichiometry. Addition of the europium fluoride creates fluoride ion
vacancies in the lanthanum fluoride lattice. When exposed to a variable concentration
of F2 ion outside the membrane, the fluoride ions in the crystal can migrate. Unlike the
pH electrode, it is the F2 ions that actually move across the membrane and result in the
electrode response. The F2 ISE is extremely selective for fluoride ion. The only ion


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Figure 15.8 A commercial microelectrode for pH measurements in volumes as small as 10 mL.
The electrode has a solid-state pH sensor and a flexible polypropylene stem, making it extremely
rugged and suitable for use in the field. This electrode can be used to determine pH in single droplets
of water on leaves of plants or blades of grass to study acid rain deposition. [Courtesy of Lazar
Research Laboratories, Inc., Los Angeles, CA (www.lazarlab.com).]

that interferes is OH2, but the response of the electrode to fluoride ion is more than 100Â
greater than the response of the electrode to hydroxide. The hydroxide interference is only
significant when the OH2 concentration is 0.1 M or higher. The electrode only responds
to fluoride ion, so the pH of the solution must be kept high enough so that HF does not
form.
Other crystalline solid-state electrodes are commercially available to measure chloride, bromide, iodide, cyanide, and sulfide anions. Most of these electrode membranes are
made from the corresponding silver salt mixed with silver sulfide, due to the low solubility
of most silver salts in water. In addition, mixtures of silver sulfide and the sulfides of
copper, lead, and cadmium make solid-state electrodes for Cu2ỵ, Pb2ỵ, and Cd2ỵ available. An advantage of the silver sulfide-based electrodes is that a direct connection can
be made to the membrane by a silver wire, eliminating the need for electrolyte filling


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Figure 15.9 A commercial solid-state fluoride ISE. The ion-sensitive area is a solid crystal of LaF3
doped with EuF2 . The filling solution contains NaF and NaCl. The electrical connection is made by
an Ag/AgCl electrode. [Courtesy of Thermo Orion, Beverly, MA (www.thermoorion.com).]

solutions. These electrodes will also respond to both silver ion and sulfide ion as well as

the intended analyte.
Liquid Membrane ISEs. Liquid membrane electrodes are based on the principle
of ion exchange. Older electrodes, such as the one diagrammed in Fig. 15.10(a), consisted
of a hydrophilic, porous membrane fixed at the base of two concentric tubes. The inner
tube contains an aqueous solution of the analyte ion and the internal reference electrode.
The outer tube contains an ion-exchanger in organic solvent. The ion-exchanger may be a
cation exchanger, an anion exchanger, or a neutral complexing agent. Some of the organic
phase is absorbed into the hydrophilic membrane, forming an organic ion-exchange phase
separating the aqueous sample solution and the aqueous internal solution with a known
concentration of analyte ion. An ion-exchange equilibrium is established at both surfaces
of the membrane and the concentration difference results in a potential difference. Modern
liquid membrane electrodes have the liquid ion-exchanger immobilized in or covalently
bound to a polymer film, shown schematically in Fig. 15.10(b). The selectivity of these
electrodes is determined by the degree of selectivity of the ion-exchanger for the
analyte ion. Selective lipophilic complexing agents have been developed and this area
is still an important area of research.
Commercial liquid membrane electrodes are available for calcium, calcium plus
magnesium to measure water hardness, potassium, the divalent cations of Zn, Cu, Fe,
2
Ni, Ba, and Sr, and anions BF2
4 and nitrate, NO3 , among others. In general, these electrodes can be used only in aqueous solution, to avoid attack on the membrane. Lifetimes are
limited by leaching of the ion-exchanger from the membrane, although newer technology
(such as covalent attachment of the ion-exchanger) is improving this.
The polymer film membrane is being used to coat metal wire electrodes to make
miniature ISEs for in vivo analysis. These coated wire ISEs require no internal reference solution and have been made with electrode tip diameters of about 0.1 mm. Electrodes have been made small enough to measure ions inside a single cell, as seen in
Fig. 15.11.
Gas-Sensing Electrodes. Gas-sensing electrodes are really entire electrochemical
cells that respond to dissolved gas analytes or to analytes whose conjugate acid or base is a