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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

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overpotential
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 low overpotential limit
  • The overpotential ηis 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
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 high overpotential limit
  • The overpotential ηis 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
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

voltammetry
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
  • 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.
electrolysis
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.
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