Download 22A The effect of current on cell potential

Chapter 22
Bulk Electrolysis: Electrogravimetry and
Coulometry
22A The effect of current on cell potential
When there is a net current in an electrochemical cell, the measured
potential across the two electrodes is no longer simply the difference
between the two electrode potentials as calculated from the Nernst
equation.
Two additional phenomena, IR drop and polarization, must be considered.
The following electrolytic cell for the determination of Cadmium (II) in HCl
solutions can be considered:
Ag|AgCl(s), Cl-(0.2M), Cd+2(0.005M)|Cd
The right-hand electrode is the working electrode and operates as a
cathode.
The left-hand electrode or the reference electrode is a silver/silver chloride
electrode whose electrode potential remains nearly constant during the
analysis.
Figure 22-1 An electrolytic cell for determining Cd2+. (a) Current 5 0.00
mA. (b) Schematic of cell in (a) with internal resistance of cell represented
by a 15.0-V resistor and Eapplied increased to give a current of 2.00 mA.
Ohmic Potential: IR Drop
Ohm’s law describes the effect of this resistance on the magnitude of the current
in the cell.
The product of the resistance R of a cell in ohms (V) and the current I in
amperes (A) is called the ohmic potential or the IR drop of the cell.
In order to generate a current of I amperes in this cell, a potential that is IR volts
more negative than the thermodynamic cell potential must be applied.
Eapplied = Ecell – IR
Polarization Effects
I
Figure 22-2
cell.
Ecell  Eapplied
R

E applied
R

Ecell
R
Experimental current/voltage curve for operation of the
The term polarization refers to the deviation of the electrode potential from
the
value predicted by the Nernst equation on the passage of current.
Cells that exhibit nonlinear behavior at higher currents exhibit polarization,
and the degree of polarization is given by an overvoltage, or overpotential,
which is symbolized by .
Eapplied = Ecell – IR – 
Factors that influence polarization are
(1) electrode size, shape, and composition;
(2) composition of the electrolyte solution;
(3) temperature and stirring rate;
(4) current level; and
(5) physical state of the species participating in the cell reaction.
Polarization phenomena can be divided into two categories:
concentration polarization and kinetic polarization.
Concentration polarization occurs because of the finite rate of mass transfer
from the solution to the electrode surface.
It occurs when reactant species do not arrive at the surface of the electrode
or product species do not leave the surface of the electrode fast enough to
maintain the desired current.
Reactants are transported to the surface of an electrode by three
mechanisms:
diffusion, migration, and convection.
Products are removed from electrode surfaces in the same ways.
Figure 22-3 Pictorial diagram (a) and concentration versus distance
plot (b) showing concentration changes at the surface of a cadmium
electrode.
Figure 22-4 Current-potential curve for electrolysis showing the linear or
ohmic region, the onset of polarization, and the limiting current plateau.
In the limiting current region, the electrode is said to be completely
polarized since its potential can be changed widely without affecting the
current.
rate of diffusion to cathode surface = k’([Cd2+] - [Cd2+]0)
Convection is the transport of ions or molecules through a solution as a
result of stirring, vibration, or temperature gradients.
22 B The selectivity of electrolytic methods
22C Electrogravimetric methods
They are of two general types:
(1) the potential of the working electrode is uncontrolled, and the applied cell
potential
is held at a more or less constant level that provides a large enough current to
complete
the electrolysis in a reasonable length of time.
(2) the controlled-potential or potentiostatic method the potential of the working
electrode is maintained at a constant level versus a reference electrode, such as a
SCE.
Figure 22-6
control.
Apparatus for electrodeposition of metals without cathode-potential
Figure 22-7 (a) Current. (b) IR drop and cathode potential change during
electrolytic deposition of copper at a constant applied cell potential. The current (a)
and IR drop (b) decrease steadily with time.
Figure 22-9 Changes in cell potential (A) and current (B) during a
controlled-potential deposition of copper. The cathode is maintained at 20.36
V (versus SCE) throughout the experiment.
Figure 22-10 A mercury cathode for the electrolytic removal of metal ions from
solution.
22 D Coulometric methods
In coulometric methods, the quantity of electrical charge required to convert
a sample of an analyte quantitatively to a different oxidation state is measured.
The proportionality constant between the quantity measured and the analyte
mass
is calculated from accurately known physical constants.
Electrical charge is the basis of the other electrical quantities, current, voltage,
and power.
The charge on an electron (and proton) is defined as 1.6022  10-19 coulombs
(C).
A rate of charge flow equal to one coulomb per second is the
definition of one ampere (A) of current.
The charge Q that results from a constant current of I amperes
operated for t seconds is
Q = It
For a variable current i,
t
Q   idt
0
The faraday (F ) is the quantity of charge that corresponds to one mole or
6.022  1023 electrons.
Each electron has a charge of 1.6022  10-19 C, hence, the faraday equals
96,485 C.
Faraday’s law relates the number of moles of the analyte nA to the charge Q
nA 
Q
nF
Two methods have been developed that are based on measuring the quantity
of
charge:
1. controlled-potential (potentiostatic) coulometry and
2. controlled-current coulometry, or coulometric titrimetry.
1. In controlled-potential coulometry, the potential of the working electrode is
maintained at a constant level such that only the analyte is responsible for
conducting charge across the electrode/solution interface.
The charge required to convert the analyte to its reaction product is then
determined by recording and integrating the current-versus-time curve during
the electrolysis.
The instrumentation for potentiostatic coulometry consists of an electrolysis
cell, a
potentiostat, and a device for determining the charge consumed by the
analyte.
Figure 22-11 Electrolysis cells for potentiostatic coulometry. Working
electrode: (a) platinum-gauze, (b) mercury-pool.
Coulometric titrations are performed with a constant-current source
(galvanostat), which senses decreases in current in a cell and responds by
increasing the potential applied to the cell until the current is restored to its
original level.
Figure 22-14
A typical coulometric titration cell.
Figure 22-15
base.
A cell for the external coulometric generation of acid and
Applications of Coulometric Titrations
1. Neutralization titrations
2. Precipitation and Complex-formation reactions
3. Oxidation/reduction titrations