INTRODUCTION
TO ELECTROANALYTICAL CHEMISTRY
Wiliam
R.Heineman
INTRODUCTION
Electrochemistry
involves the measurement of electrical signals associated with chemical system that are incorporated
into an electrochemical cell. The cell consists of two or more electrodes that
function as transducers between the chemical system and an electrical system in
which the electrical parameters of voltage and current can be measured or
controlled. Electrochemistry plays key roles in many areas of chemistry :
analysis, thermodynamics, synthetic, kinetics, energy conversion, biological
electron transport, and nerve impulse conduction to name a few.
Electro analytical
chemistry makes use of electrochemistry for the purposes of analysis. In this
application the magnitude of a voltage or current signal originating from an
electrochemical cell is related o the activity or concentration of a particular species in the cell. A host of
electroanalytical techniques has been developed for this purpose. These
techniques have certain features that in
some situations make electroanalysis advantages
comparison with other analytical methods. Excellent detection limits
coupled with a wide dynamic range are
exhibited by many techniques. An operating of 10-8-10-3 M
is typical of some techniques. Methods are available for the rapid
determination of the relatively high concentrations found for species such as
blood electrolytes (Na+, Cl-, HCO3-)
as well as trace levels of species such as heavy metals in crop samples and
drug metabolite in blood and urine samples. Measurements can generally be made
on very small volumes of sample, for example, in the micro liter range. The
combination of low detection limits with micro liter volume samples enable
amounts of analyte at the picomole level to be measured routinely in some
instances. Measurements on nanoliter volume have been demonstrated in research
laboratories! Electroanalysis is an inexpensive technique in comparison with
many instrumental methods. Electrochemistry benefits from the feature that the
signals originating from an electrochemical cell are electrical in nature. By
comparison, many analytical techniques require conversion of the signal for
measurement. Electroanalysis lends itself to measurement made in vivo. For
example, miniature electrochemical censors are used to measure pH and pOH in
the bloodstream of patients with in-dwelling catheters.
The utility
of many electrochemical techniques extends beyond qualitative and quantitative
analysis into the fundamental characterization of chemical process. For
example, electroanalytical methods are commonly used to study the redox
properties of inorganic, organic, biological compounds.
The purposes
of this chapter is to provide a fundamental beckground for understanding the
modern electroanalytical techniques that are discussed in Chapter 28-32.
27.2
ELECTROCHEMICAL CELL : CONCEPTS, TERMS, AND, SYMBOLS.
An electrochemical
cell typically consists of two electrodes immersed in a solution of ionsin
solvent, that is, an electrolyte solution. A representative cell that serves as
a suitable illustration is shown in Fig.27.1. The cell consist of two
half-cells. An electrode of Zn immersedin an aqueous solution of ZnSO4 and an electrode of Cu in an
aqueous solution of CuSO4. The two sulfate solution are connected by a salt bridge, which consist of
a tube containing an aqueous solution of
concentrated KCl. The ends of the tube
are plugged with porousfrits that allow the passage of ions, but prevent the
contents of the tube from rapidly draining out. The purposes of the salt bridge
is two fold : to allow electrical contact based on ionic conductance to be maintained between the
electrolytes in the two containers and two prevent the two solutions from
mixing. The wires attached to the electrodes in Fig.27.1a can be connected to a
digital voltmeter (position A) or to each other (B), whereas the electrodes in
Fig.27.1b are connected to an external powersupply. The behavior of the of the
electrochemical cell can be examined by performing the three experiments
outlined below.
Cell
Potential. In the first experiment the potential of the electrochemical cell (Ecell)
is measured by connecting the wire leads to the digital voltmeter (position A).
Since this voltmeter requires neglible current, the potential measurement can
be made without perturbing the electrochemical cell (i.c. witout allowing any
electrochemical reactions to occur).
The cell
potential is a measure of the different in electron energy between the two
electrodes. The electron energy of each electrode is related to the driving
force for specific redox reactions that occur at the electrode-solution
interface. For the example in Fig.27.1a, one electrode reaction (as shown at
the bottom of the Zn electrode) is the oxidant of Zn to form Zn2+.
The electrons released. By this process contribute to an excess negative charge
on the Zn electrodes as indicated by the (-) sign at the top of the electrode.
The other electrode reaction (as shown at the bottom of the Cu electrode) is
the reduction of Cu2+ to form Cu. The electrons consumed by this
process contribute to a positive charge on the Cu electrode, as indicated at
the top of electrode. Thus, the potential of an electrode depends on an excess
or deficit of charge on the electrode. The energy required to add or substract
an e electron from the electrodes can be expressed in terms of this potential.
With an excess of negative. An excess in positive charge corresponds to low
electron energy an a positive potential. The digital voltmeter responds to the
magnitude of the electron energy difference between the two electrodes, which
is Ecell.
The
difference of potential between two points is measured by the work necessary to
carry a unit positive charge from one point to the other. The unit in which potential is generally expressed is the volt
(V) or milivolt (mV). Typical values for electrochemical cells range from a few
tenths of a milivolt to a few volts. A volt is that potential difference
against which one joule of work is done in the transfer of one coulomb of
charge. Ohm’s Law states that the volt is the electrical potential which when applied
to a resistor of one ohm causes a current of one ampere. These and other terms,
units, constants, symbols, and conversions in electrochemistry are listed in
Table 27.1
Electrolysis
in a Galvanic Cell : Current , Charge, and Faraday’s Law. In the second
experiment the two wire leads are connected (position B). This completion of
the electrical circuit for the electrochemical cell is accompanied by the onset
of several phenomena : electrolysis at the two electrodes, electrons flowing
through the wire leads, and ions flowing through the salt bridge. The cell is
now functioning as a galvanic cell, which means that it is producing energy spontaneously. The
electrolysis reactions at the two electrodes consists of reduction-oxidation
(redox) reactions that can be described as shown at the bottom of Fig.27.1a.
The electrode at which oxidation occurs
is termed the anode, which in this cell is the Zn electrode. The
electrode at which reduction occurs is termed the cathode, which is the Cu
electrode. The electrochemical cell can be thought of in terms of the two half-cells,
namely the anode compartment and the cathode compartment. The overall chemical
reaction is simply the sum of the two half-cell reactions. In this cell the
overall chemical reaction is the reduction of copper ion to copper metal by
zinc metal. Since Zn reduces Cu2+
to Cu, Zn is termed the reduction in the redox reaction. Conversely , Cu2+
is termed the oxidant, since it oxidizes Zn to Zn2+.
Table 27.1
Examination
of the wire leads shows electrons to be flowing from the Zn anode to the Cu
cathode as a result of the two half-cell reaction and in response to the
difference in electron energies of the two electrodes. The flow of electrons is termed current, which is the rate of
transfer of electricity. Current is an expression of the rate at which the two
electrode processes are occurring. Since the conversion of each Zn atom to a Zn2+
ion releases 2e, the current is a direct measure of the rate at which the
oxidation process is occurring. The same argument applies to the rate of
reduction of Cu2+ at the Cu electrode.
The
practical unit for current is the ampere (A), which is the transfer of one
coulomb per second. This corresponds to the passage of 1.05 x 105 moles of
electrons per second. Since the current involved in most electroanalytical
techniques is very small, miliamperes (mA), microamperes (µA), and nanoamperes (nA) are commonly used units.
Charge is a
quantity of electricity. The charge passed during a period of time can be to
obtained by integration of the current during that period :
RUMUS
The unit for
charge is the coulomb ©, which corresponds to 1.05 x 10-5 moles of electrons.
In
electroanalytical chemistry, it is important to relate the amount of electrical
charge passed through an electrochemical cell to the quantity of material that
has undergone electrolysis. Faraday’s law gives the relationship.
Q= Nfn
Where F is
the Faraday constant (96,486 C/mol), N is the number of moles
electrolyzed, and n is the number of
electrons involved in the electrode or redox reaction (n can be taken as a
dimensionless parameter that defines the electron stoichiometry of the
reaction). Differentiation of Eqs.
(27.1) and (27.1) gives the expression:
RUMUS
Which
clearly delineats the direct
relationship between the rate at which electricity is moved across the
electrode-solution interface (dQ/dt) and how fast the chemistry is accomplished
at the interface (dN/dt).
In an
electrochemical cell, the current at the anode must equal the current at the
cathode or huge potential differences would result from the loss of
electroneutrality . Thus, the electrons removed from the anode compartment
replaced in the cathode compartment. In order of maintain electroneutrality in
each half-cell. The flow of charge by the movement of electrons in the
electrode and wire leads of the cell must be accompanied by the flow of ions in the solution components of
the cell, that is, the electron current must equal the ionic current. The salt
bridge provides the path for ion flow to maintain electrical neutrality in each
half-cell compartment. The movement of ions in this particular cell is shown
diagrammatically at the two ends of the salt – bridge tube (Fig.21.1a). In the
Zn2+ compartment, the development of a positive electrostatic charge from the
electrolytic production of Zn2+ is prevented by the movement of Zn2+
into the salt bridge and of Cl- out of the bridge. At the other end
of the bridge, K+ moves out an SO2-4 moves into the bridge to prevent the
buildup of a negative electrostatic charge in the Cu2+ half-cell compartment
due to the loss of Cu2+ by reduction to Cu. An overall movement of
positive ionic charge from the anode half-cell to the cathode half-cell and of
negative charge in the reverse direction occurs to maintain electrical
neutrality in both half-cell compartments and the salt bridge. The proportion
of ionic charge carried by each type of ion (K+, Zn2 ,Cl ,
and SO24) depends on the charge, mobility, and
concentration of each ion. From a practical, point of view, removing the salt
bridge halts electrolysis in the electrochemical cell just as effectively as
disconnecting the two wire leads. In one case the path for ions is disrupted,
in the other the path for electrons is disrupted. Both are essential for
completion of the circuit for the cell.
As the
electrolysis in the electrochemical cell proceeds, the overall chemical
reaction is approaching a position of equilibrium. The attainment of
equilibrium is signated by the measurement of zero voltage and current in what
is now a “dead” battery.
Electrolysis
in an electrolyte cell.
The last
experiment involves the application of a potential to the electrochemical cell
from an external power supply, as shown in Fig.27ib. If an external voltage of
the appropriate polarity is impressed on the electrochemical cell the overall
chemical reaction can be forced in the opposite direction of that observed for
the galvanic cell, as sown at the bottom of Fig.27ib. In so doing, we find that
the Cu electrode is now the anode and the Zn electrode is cathode. The
electrochemical cell is now functioning as an electrolytic cell in that it is
consuming electrical power, which is driving the chemical reaction. The
external power supply is forcing the electron energy of the Zn electrode to a
sufficiently high level to cause reduction of Zn2+ at the electrode,
correspondingly, the electron energy of the Cu electrode is diminished to the
point that electrons can be removed to form Cu2+.
Schematic
Representation of Cell.
The
portrayal of an electrochemical cell can be simplified by a schematic
representation based on symbols. The commonly used symbols are as follows :
(,) two species in the same phase or of the same phase type but where no potential is developed : (/) phase boundary at which a potential may developed; and (//) salt bridge, which has two phase boundary at which potentials may developed. The chemical components of the cell are identified by the usual symbols with appropriate activities or concentrations indicated in parentheses. By convention, the anode half-cell is written left of the salt-bridge symbol. Also by convention the anode is considered the negative (-) electrode in a galvanic cell, but it is the positive (+) electrode in an electrolyte cell.
(,) two species in the same phase or of the same phase type but where no potential is developed : (/) phase boundary at which a potential may developed; and (//) salt bridge, which has two phase boundary at which potentials may developed. The chemical components of the cell are identified by the usual symbols with appropriate activities or concentrations indicated in parentheses. By convention, the anode half-cell is written left of the salt-bridge symbol. Also by convention the anode is considered the negative (-) electrode in a galvanic cell, but it is the positive (+) electrode in an electrolyte cell.
CELL
POTENTIALS AND THE NERNST EQUATION
Free Energy
and cell potential.
The
free-energy change (∆G) for a
chemical reaction is a measure of the thermodynamic driving force for the
reaction to occur. The free-energy change for the chemical reaction of an
electrochemical cell is related to the equilibrium cell potential by the
equation :
RUMUS
By the thermodynamic convention, the cell
reaction is spontaneous when Ecell is positive and Gcell
is negative. If Ecell is negative an Gcell is positive,
the reaction is not spontaneous as written and will proceed in the reserved
direction. The cell is at equilibrium when Ecell and Gcell
are zero.
The free-energy change of a reaction and the
potential of an electrochemical cell are said to be the standard free-energy
change ∆Gcell and the standard cell potential Ecell
respectively, when all of the reactants and products are in the standard state,
which is defined as unit activity . The standard free-energy change is related
to the standard cell potential by the equation.
RUMUS
Since analytical measurements are rarely, if
ever, made under the conditions of standard state, an expression that relates
cell potential to activity is of utmost
importance.
Nernst Equation
Consider a general chemical reaction that is
comprised of two-half-cell redox reactions as shown below.
RUMUS
The free energy change for the overall
reaction, Eq (27.8), can be related to the standard free energy change by:
RUMUS
Where a is the activity of the constituent of
the cell reaction, R is the gas constant, and T is temperature. Substitution
for ∆G From Eqs (27.4) and (27.5) and division by the term-nF gives the
Nersnt equation.
RUMUS
Which is one of the most important equation
in electroanalytical chemistry. This general expression can be converted into a
commonly used from of the Nersnt equation at room temperature (25oC)
by conversion to a base ten
logarithm and substation for the
constant terms (R=8,314 J mol-1K-1, T=298 k, F= 96,485 C mol-1) to
give a constant in front of the log of 0,0591/n with units of JC-1 or V.
RUMUS
The Nersnt equation enables to standard
potential of cell to be used to calculate the cell potential for reactant and
product activities that are different
from those of standard state. The activities of soluble ionic or molecular
species should be expressed in terms of moles per liter. The activity for
solvent and a pure solid are taken as unity; the activity of a gas is taken a
the partial pressure in atmosphere.
Figure 27.2 (left ordinate) shows how the
potential of an electrochemical cell at 25oC is influenced by the ratio of
activities in the logarithmic term. When the activities are such that the
logarithmic term is zero, the cell potential is the standard potential Ecell.
As the logarithmic term increase, the
cell potential increases. The slope of the plot, -0,0591/n, is determined by
the electron stoichiometry of the redox reaction.
FORMAT CELL POTENTIAL
Since analytical chemists are generally more
interested in measuring concentration than activity, it is useful to express
activity in terms of concentration C and
activity coefficient ∞ where :
RUMUS
Which the substituted into Eq (27.10) gives:
RUMUS
This general expression can be converted into
a commonly used form of the Nerst equation by combining the activity coefficient
terms and Ecell to give the formal cell potential Ecell :
RUMUS
The appropriate substitutions for C are
concentration (ml L-1) for soluble ionic and molecular species, parcial
pressure (atm) for gases, and unity for solvent and pure solids.
EQUILIBRIUM CONSTANT
As mentioned above, electrolysis in a cell
with the two electrodes connected will proceed until the position of
equilibrium for the overall chemical reaction has been reached. At equilibrium,
the free energy of the cell has been expended so that ∆Gcell =0 (and Ecell=0), and the logarithmic
term of activities becomes the equilibrium constant K for the reaction.
Equation (27.9) can then the written ;
RUMUS
Substitution of Eq (27.5) gives
RUMUS
The equilibrium constant for a chemical
reaction can be calculated from Ecell of the appropriate electrochemical cell.
CALCULATION OF CELL POTENTIAL FROM HALF-CELL
POTENTIAL
An electrochemical cell based on the redox
reactioning Eq (27.8) consists of two half-cells with the half cell reactions
described by Eq (27.8) and (27.7). The free energy change for the overall
reaction in Eqs (27.8) in equal to the sum of the free energy changes for the
two half-cell reactions :
RUMUS
Since tables of standard redox potential
tabulate Eo in terms of a reduction reaction, it is convenient to
express the free-energy for the oxidation reaction ∆G in terms of a reduction reaction (-∆G), which has the opposite sign. Using this convention, one would
express the half-cell reactions for Eq (27.8) as follows :
RUMUS
So that,
RUMUS
Substitutions of Eq (27.4) and division by -
gives
;
gives
;
RUMUS
Because the electrode to be considered as the
anode is written as the left half-cell in the schematic diagram of an
electrochemical cell. Eq (27.3) can be expressed in more general term as :
RUMUS
Equation (27.24) is the convention
established by IUPAC for the calculation of cell potentials. In this convention
the half-cells are not specifically identified as being the anode or cathode.
This is advantageous in that the true identity of the anode is generally not
known until the result of the calculation is known or the cell is actually
constructed and its potential measured. Thus, couching the calculation of Ecell
in the framework of Eright a Eleft for a schematically
represented call is generally less confusing than dealing with Ecathode and Eanode, which may have to be
reassigned after the result of the calculation are known.
The potential of a cell is easily calculated
by the first calculating the potential of each half-cell, both written in terms
of reduction reactions. For example, the appropriate expressions for Eright
and Eleft for the general case considered in Eqs (27.18-27.20) would
be ;
RUMUS
Where Eo is the standard electrode
potential for each half-cell. Once Eright and Eleft are
calculated Eq (27.24) is applied to calculate the cell potential.
TABLES OF STANDARD ELECTRODE POTENTIALS
As described in the previous section, the
potential of an electrochemical cell can be calculated by taking the difference
in the potentials of two half-cells. For the purpose of calculating half-cell
potentials, it is useful to have a table of standard electrode potentials, Eo,
for various redox systems. One difficulty of a fundamental nature in obtaining
data for such a table is the inability to measure the potential difference
between two half-cells! The question “what is the potential of the half –cell
Cu2+ (0,1M)/Cu?” is somewhat analogous to the question :How far away
is Cincinnati?” In answering the latter question one must ask “How far away is
Cincinnati from where : Lubbock, Durham, the planet Jupiter?” In other words
one must establish a point of reference from which the distance is to be
measured. The same is true of the first question, which should also be
rephrased : “What is the potential of the half cell Cu2+ (0,1M)/Cu
with respect to some other half-cell?” In the case of electrochemical cells, it
is useful to select a half-cell against which other half-cells can be measured
or referenced. Such a half-cell is called a reference electrode.
A short tabulation of Eo values
for representative half-cell reactions is shown in Table 27.2. The half –cell
reaction for the reduction of H+ is assigned a value of 0V. As such,
this couple is the “reference electrode” for the table and is called the
standard hydrogen electrode (SHE) . The measurement of half-cell potentials for
other redox couples consist of preparing the half cell for each redox couple
under the conditions of standard state. The potential of the cell is then
measured with respect to the SHE. By convention, the potential is assigned a
positive sign if the half-cell functions as a cathode versus the SHE. A
negative sign is given if the half-cell functions as an anode. Also by
convention, all of the half-cell reactions in the table are written as
reductions. The sign tell how the redox
couple reacts with the respect to the SHE. A positive sign indicates
that the reaction for the redox couple is the reduction when connected to the
SHE, where as a negative sign denotes that an oxidation would take place.
Some formal electrodes potentials, Eo
are also given in the table. Note that the electrolyte concentration must be
stipulated for each value of Eo.
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