Page 85 - Academic Press Encyclopedia of Physical Science and Technology 3rd Analytical Chemistry

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Encyclopedia of Physical Science and Technology EN005M-206 June 15, 2001 20:25

Electrochemistry 163

aqueous solution. A highly effective electrolytic moisture The flux of ox that is reduced at the electrode (v c ) has
2
analyzer provides continuous online assays for water in the dimensions of moles per unit area (cm ) per second,
gases.Anotherpracticaldevelopmenthasbeenthevoltam- and
metric membrane electrode for dioxygen (·O 2 ·), which re- v c = d(C ox ) o /Adt = k c (C ox ) o = j c /nF), (7)
sponds linearly to the partial pressure of ·O 2 ·, either in the
3
where (C ox ) o is concentration (mol/cm ) at the electrode
gas phase or in solution. The use of an immobilized en-
2
surface, A is area of the electrode (cm ), and j c is net
zyme (glucose oxidase) on an electrode sensor to assay
2
cathodic (reductive) current density (A/cm ).
glucose in blood is another extension of electrochemistry
At equilibrium ( E = 0),
to practical analysis.

(v c ) E=0 = (C ox ) o [κkT/h]exp − G ‡ RT ,
c E=0
(8)
I. FUNDAMENTALS
where κ is the transmission coefficient within the Ac-
Reductive electrochemistry involves the transfer of elec- tivated Complex Theory, k is the Boltzmann constant,
trons from the electrode surface (cathode) into the double- and h is the Planck constant, which, in combination
layer interface. Within the latter, the electrons react with with Eq. (7), gives an expression for the heterogeneous
the most electrophilic component of the interface; e.g., electron-transfer rate constant when E is zero,
H O(aq) in acidic aqueous solutions and H 2 O(aq) in basic
+
3 (k c ) E=0 = [κkT/h]exp − G ‡ RT . (9)
aqueous solutions. From electrochemistry the respective c E=0
standard reduction potentials in water are In turn, combination of these equations gives expressions
for the flux of ox reduction (v c ) and cathodic current den-
−
◦
+
e + H O [H·] + H 2 O E , −2.10 V vs NHE (1) sity ( j c ) for a potential difference E.
3
◦
−
e + H 2 O [H·] + HO − E , −2.93 V vs NHE (2) ‡
v c = (C ox ) o [κkT/h]exp − G RT
c E=0
and in acetonitrile are
× exp(−αn a EF/RT )
e + H O [H·] + H 2 O E , −1.58 V vs NHE (3)
+
◦
−
3 = (C ox ) o (k c ) E=0 exp(−αn a EF/RT ); (10)
◦
−
e + H 2 O [H·] + HO − E , −3.90 V vs NHE. (4)
j c = (C ox ) o nF(k c ) E=0 exp(−αn a EF/RT ). (11)
The expressions for the reverse anodic process (oxida-
A. Electron-Transfer Dynamics (Kinetics −
tion) of Eq. (5) (red → ox + ne ; k a ) follow from similar
and Thermodynamics)
arguments:
The rate of electron transfer at an electrode/solution in- v a = (C red ) o (k a ) E=0 exp[(1 − α)n a EF/RT ], (12)
terface for the direct reduction of an oxidized species
II
(ox) to its reduced state (red ) [e.g., Cu (bpy) 2+ + e → j a = (C red ) o nF(k a ) E=0 exp[(1 − α)n a EF/RT ]. (13)
−
2
I
+
Cu (bpy) ],
2 When the cathodic current density ( j c ) is equal to the an-
odic current density ( j a ), the net current flow across the
k c
ox + ne − red, (5) electrode/solution interface is zero and the net flux of ox
k a
and red is zero. For this unique condition (zero net current)
is a function of the concentration of the oxidized species
the current densities represent the equilibrium exchange
and its heterogeneous electron-transfer rate constant (k c ;
current density ( j o ),
cathodic process). The latter is a function of the potential
j c = j a = j o , (14)
difference across the electrode/solution interface ( E),
which is directly proportional to the activation energy which is associated with the equilibrium potential differ-
for reduction (− G ). Only a fraction of E is effec-
‡
c ence, E e . Thus,
tive for accelerating the rate of reduction, which is repre-
sented by a symmetry parameter, α [transfer coefficient, j o = j c = (C ox ) o nF(k c ) E=0 exp(−α E e F/RT ) (15)
0.0 <α < 1.0 (usually about 0.5)], j o = j a = (C red ) o nF(k a ) E=0 exp[(1 − α) E e F/RT ].

G ‡ = G ‡ + G ‡ (16)
c total c E=0 c E

= G ‡ + αn a EF, (6) The difference between E and E e is the activation
c E=0
overpotential (η),
where n a = number of electrons in the rate limiting step;
usually one. η = E − E e . (17)