Page 103 - 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 181

Electrochemical measurement of pH a via Eq. (116) senses Substitution of Eq. (122) into Eq. (116) gives
hydronium-ion activity rather than its concentration.
E Pt = 0.059 log (K a ) sol + 0.059 log [HA(sol)]/[A (sol)]
−
Hence, electrochemical evaluations of dissociation con-
stants (K HA ) yield thermodynamic quantities − (0.059/2) log P H 2 . (124)
−
+
HA + H 2 O H O + A This equation in conjunction with voltammetric measure-
3 K HA
ments of half-wave potentials (E 1/2 ) for the reduction of

K HA = H O [A ]/[HA]. (119)
+
−
3 Bronsted acids at a platinum electrode in any solvent per-
mits the evaluation of (K a ) sol [pK a (sol)],
+
1. Hydronium-Ion (H O) Reduction
3
−
E 1/2 = 0.059 log (K a ) sol + 0.059 log κ A κ H 2 κ HA
Although the NHE is fundamental to electrochemistry,
=−0.059 pK a + ε, (125)
it does not represent the primary electron-transfer step
for hydronium-ion reduction at an inert (glassy-carbon) where κ A , κ H 2 , and κ HA are parameters that relate to diffu-
−
electrode, sion coefficients, activity coefficients, and P H 2 for a given
GC experimental system. Because solvent has such a major
H O(aq) + e − H·(aq) E , −2.10VvsNHE,
+
◦
+
3 and selective effect on the activity of H O(aq), the differ-
3
(120) ences between concentration-based dissociation constants
(pK) and activity-based constants (pK a ) are dramatic. For
where GC means a glassy-carbon electrode. The −2.10-V
example, phenol in MeCN (pK, 26.6; pK a , 16.0) and in
◦
difference in standard potential (E ) between the latter
Me 2 SO (pK, 16.4; pK a , 20.8) exhibits a reversal; it disso-
and that for the NHE [Eq. (115)] is due to the platinum
ciates more in Me 2 SO than in MeCN, but is more acidic
electrode, which stabilizes the hydrogen atom (H·) via +
[greater H O(aq) activity] in MeCN. Other examples in-
3
formation of a Pt–H covalent bond,
clude (Et 3 NH)Cl in MeCN (pK, 18.5; pK a , 10.0) and in
◦
+
H O(aq) + Pt (s) + e − Pt–H (s) E , 0.000 V Me 2 SO (pK, 10.5; pK a , 12.7) (again, greater dissociation
3
in Me 2 SO and greater acidity in MeCN); PhC(O)OH in
(− G BF ) = [0.00 − (−2.10)] 96.48 kJ mol −1 (eV) −1
MeCN (pK, 20.7; pK a , 7.9), in Me 2 SO (pK, 11.1; pK a
−1
= 203 kJ mol −1 = 48 kcal mol , (121) 13.6), in DMF (pK, 11.6; pK a , 11.5), and in H 2 O(pK, 4.2;
pK a , 3.2); and H 2 O in MeCN (pK a , 30.4) and in Me 2 SO
where − G BF is the free energy of bond formation.
(pK, 31.4; pK a , 36.7).
In this system the platinum electrode surface does not
consist of free platinum atoms, but must undergo ho- 3. Oxidation of Dissolved Dihydrogen (H 2 )
molytic Pt–Pt bond breakage [ H DBE , 24 kcal mol −1
−1
per Pt· (est)] before a Pt–H bond is formed. Thus, the Molecular hydrogen (H 2 ; H DBE , 104 kcal mol ) is re-
Pt–H bond-formation energy (− G BF ) is estimated to be sistant to electrochemical oxidation at inert electrodes
72 kcal mol −1 on the basis of the electrochemical data [for (glassy carbon or passivated metals; Ni, Au, Hg, Cu). At
the gas-phase Pt–H molecule, H DBE ≤ 80 kcal mol −1 or passivatedPtandPd,dissolvedH 2 onlyexhibitsbroad,dif-
−1
(− G BF ≈ 72 kcal mol )]. Determination of the reduc- fuse, anodic voltammetric peaks with irreproducible peak
+
tion potential for H O(aq) at other metal electrodes (M) currents that are not proportional to the partial pressure of
3
provides a convenient means to estimate M–H bond ener- dissolved H 2 (P H 2 ). However, with freshly preanodized Pt
gies [ (− G BF )]. and Pd electrodes, well-defined oxidation peaks for H 2 are
obtained, which have peak currents that are proportional
. The surface conditioning produces a fresh reactive
to P H 2
2. Brønsted-Acid (HA) Reduction and Evaluation II
metal-oxide surface [Pt (OH) 2 (s)], which upon exposure
of pK a(sol)
to H 2 becomes an oxide-free metal surface (Pt ). In turn,
∗
Brønsted acids (HA) undergo dissociation in any solvent the clean surface reacts with a second H 2 to form two Pt–H
+
to yield the solvated aqua-hydronium ion [(sol) n H O(aq)] bonds,
3
{from residual H 2 O; or [(sol) n Hsol ] for basic solvents}, fast
+
−1
∗ 2Pt–H (s) K eq , ∼1 atm .
+
which further dissociates to H O(aq) and the solvated 2Pt (s) + H 2 P H 2
3
−
conjugate base [A (sol) n ] (126)
+
−
HA (sol) + H 2 O H O(aq) + A (sol) The value of K eq is estimated on the basis of the Pt–H
3 (K a ) sol
(122) bond-formation energy from metallic platinum
and [ (− G BF ), 48 kcal mol ] and the dissociative
−1
−1
−
H O(aq) = (K a ) sol [HA (sol)]/[A (sol)]. (123) bond energy for H 2 ( G DBE , ∼96 kcal mol ).
+
3