Files:
Coulometry.EXP
Coulometry 2Q.CRV
Abstract
The "electrochemical surface" of a polished platinum
electrode is determined from a chrono coulometry operated on the
electrochemical reduction of complexed ferric ions, in a phosphate
buffer (pH7) solution. The analysis uses the integration of Cottrell
equation which establishes [2] the time evolution profile of the
current versus the surface, the concentration and the diffusion
coefficient of the species for a large potential step at planar
electrode. The integration of the Cottrell equation establishes
that the slope of Q versus sqrt (t) is directly proportional to
the electroactive surface. This is why the electroactive surface
can be determined from a chrono coulometry. The electroactive surface
is calculated and the rugosity, defined as the ratio between the
electrochemical surface and the geometrical surface, is also determined,
close to one.
Sample
Solution{Potassium Hexacyanoferrate III (Ferricyanide)
plus
Potassium Hexacyanofferate II (Ferrocyanide) at
10E2 mol/l in phosphate buffer, pH 7.00}
prepared from redox buffer type BS870, diluted 10 times
in phosphate buffer type PH76B
WORKPlatinum disc electrode
S = 0.196±0.01 cm² (Diameter = 5.0±0.05 mm)
REFCalomel electrode (XR100)
AUXPlatinum wire (XM100)
CP06Electrochemical cell, room temperature.
Settings  Experimental
An OCP and a Potentiostatic pause at OCP are
performed prior to the coulometry at imposed potential = 0 mV versus
REF.
Curve examination
1) Display
: Type = normal X = sqrt(Time) Y1= Quantity(C) Y2 = Current
Q = 2nFSC sqrt{(D*t)/Pi}
This is the “integration” of Cottrell equation. It is valid for
or a large potential step at planar electrode. Considering a reduction
process the slope of Q versus sqrt (t) equals a,
Slope= a = 2nF*S*C*[sqrt(D/Pi)]
and the surface can be calculated as S =  a / {2nF*C*[sqrt(D/Pi]}
With:
a = slope of Q versus sqrt(t)
Q = Total charge from t=0
n = number of electron exchanged = 1
C = Ferricyanid bulk concentration [C= 0.01 mol/l]
F = 96500 C
Pi = Pi number
D= Diffusion coefficient D =0.735e05 cm². s1 from [1]
S = electrochemical surface
The slope is determined from a linear
regression with Q versus sqr(t):
X min.: 3.975
X max.: 5.79
Mode : y=f(x)
Coefficient : 0.999868
Result : y(mC/cm²) = 0.609*x(sqrt ) + 0.703
x(y=0) = 1.15307
The measured slope = 0.609
The electrochemical surface is calculated, S = 0.206 cm²
Conclusion
The electroactive surface determined (0.206 cm2)
is just slightly larger than the geometrical surface of the polished
platinum electrode (0.196 cm2). The rugosity is very low.
Notes and references
[1] D
=0.735e05 cm². s1 from handbook of Chemistry and physics 79th
Ed. 199899 p 594
[2] Integration
of the Cottrell equation versus time in "Electrochemistry, principles,
methods and applications" Christopher M.A. Brett & Ana Maria
Oliveira Brett  Oxford science publication p206 Oxford University
Press, 1993
