Electrode equilibria
相關概念:
電極(electrode)
電流(current)
電化學電池(electrochemical cell)
電位差(electric potential difference, E)
電動勢(electromotive force)
標準電極電位(standard electrode potential, Eo)
熱力學(thermodynamics)
Gibbs 能變化(Gibbs energy change, G)
平衡(equilibria)
參考電極(reference electrode)
鹽橋(salt bridge)
指示電極(indicator electrode)
第一類電極(first kind electrode)
第二類電極(second kind electrode)
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---An electrochemical cell (2.3.1, 2.3.3)
: a voltaic cell : a galvanic cell
: is a device in which a chemical reaction
occurs with the production of an electric potential
difference (referred to as the electromotive force,
emf) between two electrodes.
: results a flow of current, if the two
electrodes are connected to an external circuit,
and leads to the performance of mechanical work.
The voltaic cell can be depicted as
reference electrode | salt bridge | interested electrode
[a salt bridge may be denoted as ||]
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By convention, a potential difference
corresponding to an external flow of electrons
from the left-hand electrode to the right-hand
electrode is said to be a positive potential
difference.
According to the International Union of Pure
and Applied Chemistry (IUPAC) convention: the
hydrogen electrode is placed on the left-hand side,
and the emf of the other electrode is taken to be
that of the cell
Under standard conditions, such emf
values are known as standard electrode
potentials or standard reduction potentials and
are given the symbol Eo.
---The standard hydrogen electrode:
Pt, H2 (1 bar) | H+ (1 M)||
[Eo = 0.00 V]
its emf is arbitrarily assigned the value of zero
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---Thermodynamics of electrochemical cells
(2.3.6)
James Prescott Joule
found in 1840 that the heat generated in a
wire is q = IVt
concluded not correctly in 1852 that there is
a correspondence between the heat of reaction of
a cell and the electric work
Willard Gibbs
drew the correct conclusion in 1878 that the
work done in an electrochemical cell is equal to
the decrease in Gibbs energy
Go = - zFEo
= -RT ln Ko
Eo = (RT/zF) ln Ko
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---Nernst equation (2.3.4)
For a reaction aA + bB = yY + zZ
G = Go + RT ln (aYyaZz/aAaaBb)u
- zFE = - zFEo + RT ln (aYyaZz/aAaaBb)u
E = Eo - (RT/zF) ln (aYyaZz/aAaaBb)u
If unit activity coefficients, then
E = Eo - (RT/zF) ln ([Y]y[Z]z/[A]a[B]b)u
a relation given by Nernst in 1889
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---Applications of emf measurements
The voltaic cell for potentiometry is depicted as
reference electrode | salt bridge | analyte solution | indicator electrode
---Metallic indicator electrodes (2.3.2, 2.3.5):
* A first-kind electrode is a pure metal electrode
that is in direct equilibrium with its cation in the
solution.
Xn+(aq) + ne- = X(s)
Eind = EXn+o - (RT/nF) ln(1/aXn+)u
* A second-kind electrode is a pure metal
electrode serves as an indicator electrode for the
activities of anions that form sparingly soluble
precipitates or stable complexes with the metal
cation.
AgCl(s) + e- = Ag(s) + Cl-1(aq)
Eind = EAgClo – (RT/F) ln (aCl-)u
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---Types of electrochemical cells
Chemical cells: due to a chemical reaction
Concentration cells: due to a dilution process
Concentration cells
Pt, H2|HCl(c1)||HCl(c2)|H2, Pt
left-hand: (1/2) H2  H+ (c1) + eright-hand: H+ (c2) + e-  (1/2) H2
net process: H+ (c2)  H+ (c1)
G = RT ln (c1/c2) = -zFE
E = (RT/F) ln (c2/c1)
Redox cells : important in biological systems
both the oxidized and reduced
species are in solution
Pt, H2 | H+(1 M) || Fe2+, Fe3+ | Pt
left-hand: (1/2) H2  H+ + eright-hand: Fe3+ + e-  Fe2+
net process: Fe3+ + (1/2) H2  H+ + Fe2+
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E = Eo - (RT/F) ln([Fe2+]/[Fe3+])
Pt, H2 | H+(1 M) || F2-, S2-, H+(cH+) | Pt
-OOCH=CHCOO- + 2H+ + 2e-  -OOCH2-CH2COO-
fumarate
succinate
net process: F2- + 2H+ (cH+) + H2  S2- + 2H+ (1 c)
E = Eo - (RT/2F) ln ([S2-]/[F2-]cH+2)
= Eo - (RT/2F) ln ([S2-]/[F2-])
+ (RT/F) ln cH+
[pH  -log cH+ = - (1/2.303) ln cH+]
= Eo - 0.05916 pH - (RT/2F) ln([S2-]/[F2-])
at 298.15 K
= Eo' - (RT/2F) ln([S2-]/[F2-])
---Other standard electrodes:
[with a KCl salt bridge]
* the standard sliver-silver chloride electrode
Ag | AgCl(s) | Cl-1 (1 M)||
Eo = 0.2224 V
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* the calomel electrode:
Hg | Hg2Cl2 (s) | Cl-1 (0.1 M)|| Eo = 0.3338 V
Hg | Hg2Cl2 (s) | Cl-1 (sat'd)||
Eo = 0.2145 V
* the glass electrode:
devised in 1906 by the German biologist M.
Germer
the silver-silver chloride reference electrode in
a 0.1 M HCl buffer solution
thin glass membrane is permeable to hydrogen
ions
useful for measuring pH values
pH determinations
Activity coefficients
For the cell:
Pt, H2 (1 bar) | HCl(aq) | AgCl(s) | Ag
The overall process:
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(1/2) H2 + AgCl  Ag + H+ + ClG = Go + RT ln (a+a-)u
E = Eo - (RT/F) ln (a+a-)u
a+a- = c+c- = c22
E = Eo - (RT/F) ln (c22)u
= Eo - (2RT/F) ln cu - (2RT/F) ln 
E + (2RT/F) ln cu = Eo - (2RT/F) ln
Equilibrium constants
For the cell:
Pt, H2 (1 bar) | HA(c1), NaA(c2), NaCl(c3) | AgCl(s) | Ag
The overall process:
(1/2) H2 + AgCl  Ag + H+ + ClE = Eo - (RT/F) ln(aH+aCl-)u
= Eo - (RT/F) ln(cH+H+cCl-Cl-)u
= Eo - (RT/F) ln(cH+cCl-)u
- (RT/F) ln(H+Cl-)
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But there also exists an equilibrium
HA = A- + H+
Ka = (cH+cA-/cHA)(H+A-/HA)
E = Eo - (RT/F) ln (cHAcCl-/cA-)u
- (RT/F) ln (HACl-/A-) - (RT/F) ln Kao
{(E - Eo)(F/RT) + ln(cHAcCl-/cA-)u} vs I plot
the intercept = - ln Kao
Solubility products
For the cell:
Cl2 (1 bar) | HCl(aq) | AgCl(s) | Ag
The overall process:
AgCl(s)  Ag + (1/2) Cl2
But AgCl(s) = Cl- + Ag+
The reaction may be written as
Cl- + Ag+  Ag + (1/2) Cl2
E = Eo + (RT/F) ln(aAg+aCl-)u
= Eo + (RT/F) ln Kspo
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Potentiometric titrations
Problem 21 Electrochemical energy conversion
Fuel cells:
For a hydrogen-oxygen fuel cell with a concentrated
KOH electrolyte, the electrode half-reactions are
21-1 Cathode: O2 (g) + 2 H2O + 4 e-  4 OH- (aq)
21-2 Anode: H2 (g) + 2 OH- (aq)  2 H2O + 2 eNet: 2 H2 (g) + O2 (g)  2 H2O
21-3 With a H3PO4 electrolyte,
Cathode: O2 (g) + 4 H+ (aq) + 4 e-  2 H2O
E = 1.23 V
Anode: H2 (g)  2 H+ (aq) + 2 eNet: 2 H2 (g) + O2 (g)  2 H2O
21-4 G0 = -nFE
= -4(96487)(1.23) = -474,716 J
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In The Netherlands, the reaction of natural gas is
exothermic and the energy is utilized indirectly (35-40%),
CH4 (g) + 2 O2 (g)  CO2 (g) + 2 H2O (g) + energy
21-5 In a high-T ceramic fuel cell based on a solid
oxide-ion (O2-) conducting electrolyte, natural gas can be
utilized directly (75%), and the net reaction is
CH4 (g) + 2 O2 (g)  CO2 (g) + 2 H2O (g)
Anode:
CH4 (g) + 2 (O2-, electrolyte)  CO2 (g) + 2 H2O (g) + 4 e-
Cathode: O2 (g) + 4 e-  2 (O2-, electrolyte)
21-6 Another hight-T fuel cell utilizes molten carbonate as
the ionically conducting electrolyte. H2, O2, CO2
Cathode: O2 (g) + 4 e-  2 (O2-, carbonate)
Anode: H2 (g) + (O2-, carbonate)  H2O + 2 eNet: 2 H2 (g) + O2 (g)  2 H2O (g)
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