Transcript Lecture 24 - University of Windsor

Overpotential
• When the cell is producing current, the electrode
potential changes from its zero-current value, E, to a
new value, E’.
• The difference between E and E’ is the electrode’s
overpotential, η.
η = E’ – E
• The ∆Φ = η + E,
• Expressing current density in terms of η
ja = j0e(1-a)fη
and
jc = j0e-afη
where jo is called the exchange current density, when ja = jc
The low overpotential limit
• The overpotential η is very small, i.e. fη <<1
• When x is small, ex = 1 + x + …
• Therefore ja = j0[1 + (1-a) fη]
jc = j0[1 + (-a fη)]
• Then j = ja - jc = j0[1 + (1-a) fη] - j0[1 + (-a fη)]
= j0fη
• The above equation illustrates that at low overpotential limit, the
current density is proportional to the overpotential.
• It is important to know how the overpotential determines the property
of the current.
Calculations under low overpotential
conditions
• Example: The exchange current density of a
Pt(s)|H2(g)|H+(aq) electrode at 298K is 0.79 mAcm-2.
Calculate the current density when the over potential is
+5.0mV.
Solution:
j0 = 0.79 mAcm-2
η = 6.0mV
f = F/RT =
j = j0fη
The high overpotential limit
• The overpotential η is large, but could be positive or
negative!!!
• When η is large and positive
j0e-afη = j0/eafη becomes very small in comparison
to ja
Therefore j ≈ ja = j0e(1-a)fη
ln(j) = ln(j0e(1-a)fη ) = ln(j0) + (1-a)fη
• When η is large but negative
ja is much smaller than jc
then j ≈ jc = j0e-afη
ln(j) = ln(j0e-afη ) = ln(j0) – afη
• Tafel plot: the plot of logarithm of the current density
against the over potential.
Calculations under high overpotential
conditions
• The following data are the anodic current through a
platinum electrode of area 2.0 cm2 in contact with an
Fe3+, Fe2+ aqueous solution at 298K. Calculate the
exchange current density and the transfer coefficient for
the process.
η/mV 50
100 150 200 250
I/mA 8.8
25
58
131 298
Solution: calculate j0 and a
Note that I needs to be converted to J
The general arrangement for
electrochemical rate measurement
Voltammetry
• Voltammetry: the current is monitored as the potential of the lectrode
is changed.
• Chronopotentiometry: the potential is monitored as the current
density is changed.
• Voltammetry may also be used to identify species and determine
their concentration in solution.
• Non-polarizable electrode: their potential only slightly changes when
a current passes through them. Such as calomel and H2/Pt
electrodes
• Polarizable electrodes: those with strongly current-dependent
potentials.
Concentration polarization
• Concentration polarization: The consumption of electroactive
species close to the electrode results in a concentration gradient
and diffusion of the species towards the electrode from the bulk may
become rate-determining. Therefore, a large overpotential is needed
to produce a given current.
• Eqns 29.42 to 29.53 will be discussed in class
• Example 29.3: Estimate the limiting current density at
298K for an electrode in a 0.10M Cu2+(aq) unstirred
solution in which the thickness of the diffusion layer is
about 0.3mm.
Experimental techniques in
voltammetry
Experimental techniques in
voltammetry
Experimental techniques in
voltammetry
Electrolysis
• Cell potential: the sum of the overpotentials at the two
electrodes and the ohmic drop due to the current through
the electrolyte (IRs).
• Electrolysis: To induce current to flow through an
electrochemical cell and force a non-spontaneous cell
reaction to occur.
• Estimating the relative rates of electrolysis.