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ELECTROCHEMICAL CELLS
CHAPTERS ELECTROCHEMICAL CELLS 6.1 Electrochemical CeUs A pair of electrodes immersed in an electrolyte solution constitutes an electrochemical celly which is occasionally called a Galvanic cell after L. Galvani (electrochemist, 1737-1798), as shown in Fig. 6-1. The term of Voltaic cell, which was originally assigned to copper-zinc piles in sulfuric acid (invented by A. Volta, electrochemist, 17457-1827), is occasionally used for electricity-producing cells. When the Fermi level of one electrode ML on the left hand side is higher (the electrode potential is lower) than the Fermi level of the other electrode MR on the right hand side as shown in Fig. 6-1, a positive electric chargeflowsfrom electrode ML through an electrolyte to electrode MR with a simultaneous flow of electrons from electrode ML through an external cell circuit (containing no electric power source) to electrode MR. The electrode from which a positive electric charge flows into the electrolyte is termed the anodes and the electrode to which a positive electric charge flows from the electrolyte is termed the cathode as described in Sec. 4.1.
VA
' ^.CML)
ii 1
^^!^^^ /T\ , ,,1
^
'
fc
PN:
t *e
Fig. 6>1. Electrochemical cell, electric charge flow in a closed cell circuit, and electron levels of two electrodes in an open cell circuit: M = electrode; S s electrolyte solution; o.^ real potential of electrons in electrode, £e*u =electromotive force.
202
CHAP. 6
ELECTROCHEMICAL CELLS
From a practical viewpoint, as shown in Fig. 6-2, electrochemical cells can be classified into two groups: one is a chemical cell in which electricity is produced by consiuning chemical energy of substances; the other is an electrolytic cell in which chemical substances are produced by consimiing electrical energy. In practice, the chemical cell is connected to an external load and the electrolytic cell is connected to an external electric power source.
Fig. 6-2. Chemical cell and electrolytic cell: (a) hydrogen-oxygen fuel cell (chemical cell), (b) water decomposition cell (electrolytic cell).
The hydrogen-oxygen fuel cell is a typical example of the chemical cell and its cell reaction is represented in Eqn. 6-1: 2H^, + 2e 4-Ooga. + 2H*«, + 2e
HoO.
H2,gM + -ft" 02,gM "^ H20.q ,
left electrode, right electrode,
anode, cathode.
AHa/Og = - ^GSijj/Oa ,
(6-1)
where AH2/O2 is the affinity of the reaction and AGii^K>2 is the free enthalpy of the reaction. This cell may also regarded as a cell of water synthesis, which produces electric energy in the course of synthesizing water. On the other hand, a typical electrolytic cell is the cell of water decomposition and its cell reaction is given in Eqn. 6-2:
203
Electrochemical Cells
2H;, + 2 e - H 2 . , „ , H 2 0 ^ - i 0 2 . , „ + 2H;,,
cathode, left electixde, right electrode, anode, (&-2)
H20aq - • H2,ga« + "g" 02.ga« •
This reaction of water electrolysis is the same as, but reverse in its direction to, the reaction of hydrogen-oxygen fuel cell in Eqn. 6-1. Note that the anode and the cathode are reversed in the chemical and the electrolytic cells. The "cell reaction" that occurs when the cell circuit is closed consists of two electrochemical reactions: one at the anode and the other at the cathode. As an example, the foUowing anodic and cathodic ion transfer reactions, Zn -• Zn^i + 2 e ,
anodic reaction,
Cu^ii^ + 2 e -* Cu ,
cathodic reaction,
can be coupled to produce a cell reaction given by Eqn. 6-3: Zn + Cu'i ^ Zn^i + Cu .
(6-3)
According to the convention in lUPAC (International Union of Pure and Applied Chemistry) [Whiffen, 1979], the cell of Eqn. 6-3 is illustrated by the cell diagram shown in Eqn. 6-4: Zn I Zn^,^ : Cu'i | Cu ,
(6-4)
1 Zn 1 Zn^., 1 Cu^*^
Cu
(a) Zn -j^-Zn'^.q j Cu^*«, 4-^ Cu (b) Zn + Cu^^ —• Zn^\q + Cu
(0 Fig. 6-3. Expression of cell diagram and cell reaction (lUPAC convention): (a) cell diagram, (b) flow of electric charge, (c) ceD reaction.
ELECTROCHEMICAL CELLS
204
CHAP. 6
where the vertical soUd Une denotes the interface between electrode and electrolyte, and the vertical dotted line denotes the junction of two miscible electrolytes. As shown in Fig. 6-3, it is also in the same lUPAC convention that a positive electric charge flows from the left hand electrode through the electrolyte to the right hand electrode, as the cell reaction proceeds in the direction as written in Eqn. 6-3. This defines the sign of the electromotive force of electrochemical cells. The charge nimiber, /i, which represents the number of electrons involved in a imit advancement of the cell reaction, is also important; in the cell reactions of Eqns. 6-1 and 6-3/1 = 2.
6.2 Electromotive Force of Electrochemical Cells The electromotive force of an electrochemical cell is the difference in electrode potential between the two electrodes in the cell. According to the lUPAC convention, the electromotive force is the potential of the right hand electrode referred to the potential of the left hand electrode. We consider, for example, a hydrogen-oxygen cell shown in Fig. 6-4; the cell reaction is given by Eqn. 6-1 and the cell diagram is given by Eqn. 6-5:
H-i pliiil
£eeU
1^ 2H*
11
HjO^^
S «e,L
Fig. 6-4. Electromotive force -^MU, electron level a^, and electrostatic potential profile for an electrochemical cell: ^ = inner potential.
Electromotive Force ofElectrochemical Cells
205
PtL I H2.g.. I H ; , , H2O I 02,ga. I PtR .
(&-5)
From the electrode reactions in equilibrium at the left hand electrode (anode) and at the right hand electrode (cathode), we obtain the real potential, «•, of electrons in the two electrodes as shown in Eqns. 6-6 and 6-7: ae.L = -^^^^^=^o 2
^ ,
Cte^R =
2
(6-^)
•
^
^
The electromotive force, E^^02, of the cell in Fig. 6-4 is given by the difference in the Fermi level between the two electrodes, (ep. R - EF. L ) = - « -E^HJ/OS . As described in Sec. 4.5, the difference in the Fermi level, (epR-epL), is equivalent to the difference in the real potential of electrons between the two electrodes, (cte.R-cte,L); honce, (ae,R-ae.L) =-e-EH2/02. The electromotive force is then expressed in Eqn. 6-8:
^H2/02 -
e
-
2e
"
= ^H^o.-H-|fhipH. + ^ l n p o , ,
2e (&-8)
where E^i^o^ is the standard electromotive force (1.23 V at 26°C) and p is the fiigacity of hydrogen and oxygen gases. In general, the cell reaction may be written in Eqn. 6-9: 2vii = 0 ,
AG,
(6-9)
where i denotes a particle in the reaction, Vj denotes the stoichiometric coefficient, and AG denotes the free enthalpy of the reaction. The electromotive force Ec^ is then given by Eqn. 6-10: ^^ -
ne
- — n e — " —Tie
nT ^ ^^ ^^^'
where ai is the activity of particle i, n is the charge niraiber of the cell reaction, and EI^ is the standard electromotive force.
ELECTROCHEMICAL CELLS
206
CHAP. 6
The effect of temperatxu^ on the electromotive force can be derived from Eqn. 6-10 to obtain Eqn. 6-11: f a^cdi ] _
1 ( dAG ] _ AS
I dT L "
(6-11)
^^ I dT L ~ ne >
where AS (= bQIT) is the entropy change of the cell reaction, and Q is the heat absorbed in the ceD. The cell reaction is hence endothermic if the temperature dependence of £c«u is positive (AS > 0); whereas, it is exothermic if the temperatm^ dependence of-E^u is negative (AS < 0). The reaction of the hydrogen-o^o^en fiiel cell, which is described in Figs. 6-2 and 6-4 as well as Eqns 6-1 and 6-2, is an exothermic reaction. Such heat generation or absorption in cell reactions is called the "Peltier effect" after C. A. Peltier (physicist, 1785-1845).
6.3 Equilibrium Potential of Electrode Reactions 6.3.1 Equilibrium potential of electron transfer reactioTis The electrode potential of an electrode reaction at equiHbrium can be measured as the electromotive force of an electrochemical cell composed of both the reaction electrode and the normal hydrogen electrode. The potential of the reaction electrode thus measured is taken as the equilibrium potential of the electrode reaction relative to the normal hjdrogen electrode. To illustrate this relationship to the normal hydrogen electrode, we consider an electrode reaction of redox electron transfer as shown in Eqn. 6-12: OX + fi e = RED
/)HJ
(6-12)
I = 1 atm
T
B
i
2^2
I I
S
RED OX
i
^H^^. + O X . , - H ; , + RED^
Pt
Fig. 6-6. Electrochemical cell composed of an electrode of redox electron transfer on the right hand side and a normal hydrogen electrode on the left hand side.
207
EqiUlibnum Potential of Electrode Reactions
Figure 6-5 shows an electrochemical cell of the redox reaction involving electron transfer coupled with a normal hydrogen electrode reaction. The cell diagram and cell reaction can be written, respectively, in Eqns . 6-13 and 6-14: PtL
H* iRED.„OX.
H 2, gas
Pt]R
(&-13)
>
(6-14)
AGiREDOX
"o~ H2,ga8 + OXaq = fl H"iq + RED^
where4GREix)x = (^^H* + ^RED-0-5^^H2""JAOX) is thefreeenthalpy of the reaction. In the normal hydrogen electrode, it is conventional to assign a value of zero to the energy levels of both the hydrated proton and the gaseous hydrogen molecule, respectively; ^IH* = 0 and JXH2 = 0- The electromotive force of this cell gives the equilibrium potential J^REDOX of the redox reaction as shown in Eqn. 6-15: £ ]REDOX
-AG - "
REDOX
ne
.
-AGi REDOX ne
Mli^^^m. ORED ne
= E°REDOX' kTL]^.3o^ ORED ne
(6-15)
where EKRJX>X is the standard redox potential at which the activities of the reductant and oxidant particles are equal to unity.
TABLE 6 - 1 . Hie standard equilibrium potentials for redox electrode reactions of hydrated redox particles at 26'*C: -^NHE = relative electrode potential referred to the normal hydrogen electrode. [Handbooks of electrochemistry.] Electrode ^ 2 ^
..
Co^/Co^ Ce**/Ce^ Mn**/Mn**
cycr MnOg/Mn^ O^^ljO Fe**/Fe=*
02^02 Cu^/Cu' Sn^^/Sn"^
^ ^ ^
Ti^rre* Cr**/Ci^
Reaction F2 + 2 e - 2 F " Co**+e-Co^ Ce** + e - C e * * Mn**+e-» M n ^ CI2 + 2 e - 2 CI" MnOg + 4 H * + 4 e - Mn^ + 2 HgO 02-»-4H* + 4 e - 2 H 2 0 Fe**+e-Fe** 02 + 2 i r + 2 e - H 2 0 2 Cu^ + e - C u * Sn** + 2 e - * S n ^ 2HV2e-H2 T[»- + e - T i ^ Cr'^ + e - C i ^
n
•Eo/VNHE
2 1 1 1 2 2 4 1 2 1 2 2 1 1
2.87 1.82 1.61 1.51 1.359 1.23 1.229 0.771 0.682 0.153 0.15 0.00 -0.37 -0.41
208
ELECTROCHEMICAL CELLS
CHAP. 6
Table 6-1 shows the standard equiUbrium potentials of several redox reactions of hydrated redox particles. 6.3.2 Equilibrium potential of ion transfer reactions Next, we consider a transfer reaction of metal ions across the interface of metal electrodes as in Eqn. 6-16: M^^^M 2+
(&-16)
where M^ is the metal ion in the state of metallic bonding in metal electrodes, and M^ is the hydrated metal ion in aqueous solution. Figure 6-6 shows the cell in which the transfer reaction of metal ions is coupled with the normal hydrogen electrode reaction; the cell reaction is written in Eqn. 6-17 as: H 2,gaa + M t = 2H* + M N
AGM 3 * / M
(6-17)
1
= 1 aim
PHJ
H2
1
^ 1 2e^ 2^^
^ 2H* I OH*
=1j
1i^g..-HM^:,-2H;, +
M^w
Fig. 6 - ^ Electrochemical cell composed of an electrode of metal ion transfer and a normal h3^drogen electrode: M^ = metal ion in metallic bonding and in hydrated state.
The electromotive force of this cell gives the equilibrium potential SM^^/M for the transfer reaction of metal ions as shown in Eqn. 6-18: ^M^*/M
2i
2^
+ "27""^^M^* - ^M3+/M + "27""^^M3* »
(6-18)
where E^2.^ is the standard equilibrium potential and 0^2+ is the activity of hydrated metal ions. Equation 6-18 indicates that the equiUbriiun potential depends on the activity of hydrated metal ions. Table 6-2 shows the standard equiUbrium potentials of the transfer reactions of metal ions at metal electrodes in aqueous solutions.
209
Equilibrium Potential of Electrode Reactions TABLE 6 - 2 . The standard equilibrium potentials for transfer reactions of metal ions at metal electrodes at 25*'C. [Handbooks of electrochemistry.]
Electrode
Eo 1 VNHE
Electrode
-EQ/VNHE
1.50 0.987 0.799 0.521 0.337
Cd^^/Cd Fe^/Fe Ga^'/Ga Cr**/Cr Zn^/Zn Mn*^/Mn Zr**/Zr
-0.403 -0.44 -0.53 -0.74 -0.763 -1.18 -1.53 -1.63 -1.66 -2.37 -2.714 -3.045
Au^'/Au Pd^/Pd AgVAg Cu7Cu Cu'^/Cu
0.0
irm. Fe**/Fe
-0.036 -0.126 -0.136 -0.250 -0.277 -0.342
Pb^/Pb Sn^/Sn Ni^/Ni Co'^/Co In^/ln
Ti^/n A1**/A1 Mg**/Mg Na7Na LiTU
Further, we consider an ion transfer reaction at a multiphase silver-silver chloride electrode in an aqueous chloride solution as shown in Fig. 6-7. The ion transfer reactions at the AgCl/Cr.q interface and at the Ag/AgCl interface are, respectively, given in Eqn. 6-19: CI AgCl • ^ Cl'aq ,
(6-19)
Ag*Aga^Ag"Ag.
1
PHS = 1 atna
[iiiiiiii
\ 1 , 3
\ \
Aga
'
'^*1
r|M|;!
OH- = 1
H\
pt 1
r*- e j
a-* -a*
Fig. 6 - 7 . Electrochemical cell composed of a silver-silver chloride multiphase electrode of ion transfer and a normal h3rdrDgen electrode: Ag = silver metal; AgCl = silver chloride.
210
ELECTROCHEMICAL CELLS
CHAP. 6
The overall cell reaction is given in Eqn. 6-20: i H2.g.. + AgClAgd = H^, + AgAg + Cl-«,,
^GAgci/ci-.
(6-20)
Then, the equilibrium potential Ej^gcuci- is obtained as shown in Eqn. 6-21; J.
_ -^GAgCUCl-
EA^ua-
2i
~^QAgCl/Cl- . kT
=
2^
A^^
+ ^^inod-
= ^Agcvci- + - 2 ^ ^CLci-»
(6-21)
where the activities of sohd Ag and AgCl are assigned a value of unity. The standard equilibrium potential calculated from Eqn. 6-21 is ^Ago/a- = + 0.224 V at25^C. 6.4 Electrochemical Reference Level for Hydrated Ions In electrochemistry, the chemical potential of hydrated ions has been determined from the equilibrium potential of ion transfer reactions referred to the normal hydrogen electrode. For the reaction of metal ion transfer (metal dissolution-deposition reaction) of Eqns. 6-16 and 6-17, the standard equiUbrium potential £M2*/M is give in terms of the standard chemical potential, ^^, by Eqn. 6-22:
M2*/M
2e
"
2
6
'
where the chemical potentials of gaseous hydrogen molecule and of solid metal in the standard state have been assigned a value of zero following the convention in Sec. 6.3.1(^1^2 = 0,^^ = 0). It follows from Eqn. 6-22 that the standard chemical potential of hydrated ions determined from the standard equihbriimi potential of the ion transfer reaction is a relative value that is to the standard chemical potential of hydrated protons at unit activity, which, by convention in aqueous electrochemistry, is assigned a value of zero on the electrochemical scale of ion levels. The reaction equiUbrium of the normal hydrogen electrode, H2,g«» = 2 H*aq + 2 envHa* where en^/Ha ^^ the equiUbrium redox electron, can be obtained by the equiUbration of the free enthalpy of the reactants and that of the products as foUows: 2 a^. + 2 a^ H^/H^ = 2 ^^. + 2 e XS + 2 ji° ^.^^ - 2 e Xs = ^H,» where a^ is the standard real potential and Xs is the surface potential of aqueous solution. Hence, we obtain Eqn. 6-23:
References
2 < , + 2
211
(6-23)
If we set >AH2 at a value of zero according to the conventional chemical thermodynamic energy scale, the standard chemical potential of a hydrated proton, ^H* , is given by Eqn. 6-24: \il. = a^. - 6 Xs = - cx° H.^^ - e xs .
(6-24)
Pro°i "e.H*/H2 = - ^-S ^V and Xs = 0.13 V, we obtain \i^. = - 4.37 eV, which is assigned a value of zero on the electrochemical scale of ion levels in aqueous electrochemistry.
References [WhifFen, 1979]: D. H. WhiflFen, Manual of Symbols and TerminologyforPhysicochemical Quantities and Units, p. 28, Pergamon Press, Oxford, (1979).
VA
' ^.CML)
ii 1
^^!^^^ /T\ , ,,1
^
'
fc
PN:
t *e
Fig. 6>1. Electrochemical cell, electric charge flow in a closed cell circuit, and electron levels of two electrodes in an open cell circuit: M = electrode; S s electrolyte solution; o.^ real potential of electrons in electrode, £e*u =electromotive force.
202
CHAP. 6
ELECTROCHEMICAL CELLS
From a practical viewpoint, as shown in Fig. 6-2, electrochemical cells can be classified into two groups: one is a chemical cell in which electricity is produced by consiuning chemical energy of substances; the other is an electrolytic cell in which chemical substances are produced by consimiing electrical energy. In practice, the chemical cell is connected to an external load and the electrolytic cell is connected to an external electric power source.
Fig. 6-2. Chemical cell and electrolytic cell: (a) hydrogen-oxygen fuel cell (chemical cell), (b) water decomposition cell (electrolytic cell).
The hydrogen-oxygen fuel cell is a typical example of the chemical cell and its cell reaction is represented in Eqn. 6-1: 2H^, + 2e 4-Ooga. + 2H*«, + 2e
HoO.
H2,gM + -ft" 02,gM "^ H20.q ,
left electrode, right electrode,
anode, cathode.
AHa/Og = - ^GSijj/Oa ,
(6-1)
where AH2/O2 is the affinity of the reaction and AGii^K>2 is the free enthalpy of the reaction. This cell may also regarded as a cell of water synthesis, which produces electric energy in the course of synthesizing water. On the other hand, a typical electrolytic cell is the cell of water decomposition and its cell reaction is given in Eqn. 6-2:
203
Electrochemical Cells
2H;, + 2 e - H 2 . , „ , H 2 0 ^ - i 0 2 . , „ + 2H;,,
cathode, left electixde, right electrode, anode, (&-2)
H20aq - • H2,ga« + "g" 02.ga« •
This reaction of water electrolysis is the same as, but reverse in its direction to, the reaction of hydrogen-oxygen fuel cell in Eqn. 6-1. Note that the anode and the cathode are reversed in the chemical and the electrolytic cells. The "cell reaction" that occurs when the cell circuit is closed consists of two electrochemical reactions: one at the anode and the other at the cathode. As an example, the foUowing anodic and cathodic ion transfer reactions, Zn -• Zn^i + 2 e ,
anodic reaction,
Cu^ii^ + 2 e -* Cu ,
cathodic reaction,
can be coupled to produce a cell reaction given by Eqn. 6-3: Zn + Cu'i ^ Zn^i + Cu .
(6-3)
According to the convention in lUPAC (International Union of Pure and Applied Chemistry) [Whiffen, 1979], the cell of Eqn. 6-3 is illustrated by the cell diagram shown in Eqn. 6-4: Zn I Zn^,^ : Cu'i | Cu ,
(6-4)
1 Zn 1 Zn^., 1 Cu^*^
Cu
(a) Zn -j^-Zn'^.q j Cu^*«, 4-^ Cu (b) Zn + Cu^^ —• Zn^\q + Cu
(0 Fig. 6-3. Expression of cell diagram and cell reaction (lUPAC convention): (a) cell diagram, (b) flow of electric charge, (c) ceD reaction.
ELECTROCHEMICAL CELLS
204
CHAP. 6
where the vertical soUd Une denotes the interface between electrode and electrolyte, and the vertical dotted line denotes the junction of two miscible electrolytes. As shown in Fig. 6-3, it is also in the same lUPAC convention that a positive electric charge flows from the left hand electrode through the electrolyte to the right hand electrode, as the cell reaction proceeds in the direction as written in Eqn. 6-3. This defines the sign of the electromotive force of electrochemical cells. The charge nimiber, /i, which represents the number of electrons involved in a imit advancement of the cell reaction, is also important; in the cell reactions of Eqns. 6-1 and 6-3/1 = 2.
6.2 Electromotive Force of Electrochemical Cells The electromotive force of an electrochemical cell is the difference in electrode potential between the two electrodes in the cell. According to the lUPAC convention, the electromotive force is the potential of the right hand electrode referred to the potential of the left hand electrode. We consider, for example, a hydrogen-oxygen cell shown in Fig. 6-4; the cell reaction is given by Eqn. 6-1 and the cell diagram is given by Eqn. 6-5:
H-i pliiil
£eeU
1^ 2H*
11
HjO^^
S «e,L
Fig. 6-4. Electromotive force -^MU, electron level a^, and electrostatic potential profile for an electrochemical cell: ^ = inner potential.
Electromotive Force ofElectrochemical Cells
205
PtL I H2.g.. I H ; , , H2O I 02,ga. I PtR .
(&-5)
From the electrode reactions in equilibrium at the left hand electrode (anode) and at the right hand electrode (cathode), we obtain the real potential, «•, of electrons in the two electrodes as shown in Eqns. 6-6 and 6-7: ae.L = -^^^^^=^o 2
^ ,
Cte^R =
2
(6-^)
•
^
^
The electromotive force, E^^02, of the cell in Fig. 6-4 is given by the difference in the Fermi level between the two electrodes, (ep. R - EF. L ) = - « -E^HJ/OS . As described in Sec. 4.5, the difference in the Fermi level, (epR-epL), is equivalent to the difference in the real potential of electrons between the two electrodes, (cte.R-cte,L); honce, (ae,R-ae.L) =-e-EH2/02. The electromotive force is then expressed in Eqn. 6-8:
^H2/02 -
e
-
2e
"
= ^H^o.-H-|fhipH. + ^ l n p o , ,
2e (&-8)
where E^i^o^ is the standard electromotive force (1.23 V at 26°C) and p is the fiigacity of hydrogen and oxygen gases. In general, the cell reaction may be written in Eqn. 6-9: 2vii = 0 ,
AG,
(6-9)
where i denotes a particle in the reaction, Vj denotes the stoichiometric coefficient, and AG denotes the free enthalpy of the reaction. The electromotive force Ec^ is then given by Eqn. 6-10: ^^ -
ne
- — n e — " —Tie
nT ^ ^^ ^^^'
where ai is the activity of particle i, n is the charge niraiber of the cell reaction, and EI^ is the standard electromotive force.
ELECTROCHEMICAL CELLS
206
CHAP. 6
The effect of temperatxu^ on the electromotive force can be derived from Eqn. 6-10 to obtain Eqn. 6-11: f a^cdi ] _
1 ( dAG ] _ AS
I dT L "
(6-11)
^^ I dT L ~ ne >
where AS (= bQIT) is the entropy change of the cell reaction, and Q is the heat absorbed in the ceD. The cell reaction is hence endothermic if the temperature dependence of £c«u is positive (AS > 0); whereas, it is exothermic if the temperatm^ dependence of-E^u is negative (AS < 0). The reaction of the hydrogen-o^o^en fiiel cell, which is described in Figs. 6-2 and 6-4 as well as Eqns 6-1 and 6-2, is an exothermic reaction. Such heat generation or absorption in cell reactions is called the "Peltier effect" after C. A. Peltier (physicist, 1785-1845).
6.3 Equilibrium Potential of Electrode Reactions 6.3.1 Equilibrium potential of electron transfer reactioTis The electrode potential of an electrode reaction at equiHbrium can be measured as the electromotive force of an electrochemical cell composed of both the reaction electrode and the normal hydrogen electrode. The potential of the reaction electrode thus measured is taken as the equilibrium potential of the electrode reaction relative to the normal hjdrogen electrode. To illustrate this relationship to the normal hydrogen electrode, we consider an electrode reaction of redox electron transfer as shown in Eqn. 6-12: OX + fi e = RED
/)HJ
(6-12)
I = 1 atm
T
B
i
2^2
I I
S
RED OX
i
^H^^. + O X . , - H ; , + RED^
Pt
Fig. 6-6. Electrochemical cell composed of an electrode of redox electron transfer on the right hand side and a normal hydrogen electrode on the left hand side.
207
EqiUlibnum Potential of Electrode Reactions
Figure 6-5 shows an electrochemical cell of the redox reaction involving electron transfer coupled with a normal hydrogen electrode reaction. The cell diagram and cell reaction can be written, respectively, in Eqns . 6-13 and 6-14: PtL
H* iRED.„OX.
H 2, gas
Pt]R
(&-13)
>
(6-14)
AGiREDOX
"o~ H2,ga8 + OXaq = fl H"iq + RED^
where4GREix)x = (^^H* + ^RED-0-5^^H2""JAOX) is thefreeenthalpy of the reaction. In the normal hydrogen electrode, it is conventional to assign a value of zero to the energy levels of both the hydrated proton and the gaseous hydrogen molecule, respectively; ^IH* = 0 and JXH2 = 0- The electromotive force of this cell gives the equilibrium potential J^REDOX of the redox reaction as shown in Eqn. 6-15: £ ]REDOX
-AG - "
REDOX
ne
.
-AGi REDOX ne
Mli^^^m. ORED ne
= E°REDOX' kTL]^.3o^ ORED ne
(6-15)
where EKRJX>X is the standard redox potential at which the activities of the reductant and oxidant particles are equal to unity.
TABLE 6 - 1 . Hie standard equilibrium potentials for redox electrode reactions of hydrated redox particles at 26'*C: -^NHE = relative electrode potential referred to the normal hydrogen electrode. [Handbooks of electrochemistry.] Electrode ^ 2 ^
..
Co^/Co^ Ce**/Ce^ Mn**/Mn**
cycr MnOg/Mn^ O^^ljO Fe**/Fe=*
02^02 Cu^/Cu' Sn^^/Sn"^
^ ^ ^
Ti^rre* Cr**/Ci^
Reaction F2 + 2 e - 2 F " Co**+e-Co^ Ce** + e - C e * * Mn**+e-» M n ^ CI2 + 2 e - 2 CI" MnOg + 4 H * + 4 e - Mn^ + 2 HgO 02-»-4H* + 4 e - 2 H 2 0 Fe**+e-Fe** 02 + 2 i r + 2 e - H 2 0 2 Cu^ + e - C u * Sn** + 2 e - * S n ^ 2HV2e-H2 T[»- + e - T i ^ Cr'^ + e - C i ^
n
•Eo/VNHE
2 1 1 1 2 2 4 1 2 1 2 2 1 1
2.87 1.82 1.61 1.51 1.359 1.23 1.229 0.771 0.682 0.153 0.15 0.00 -0.37 -0.41
208
ELECTROCHEMICAL CELLS
CHAP. 6
Table 6-1 shows the standard equiUbrium potentials of several redox reactions of hydrated redox particles. 6.3.2 Equilibrium potential of ion transfer reactions Next, we consider a transfer reaction of metal ions across the interface of metal electrodes as in Eqn. 6-16: M^^^M 2+
(&-16)
where M^ is the metal ion in the state of metallic bonding in metal electrodes, and M^ is the hydrated metal ion in aqueous solution. Figure 6-6 shows the cell in which the transfer reaction of metal ions is coupled with the normal hydrogen electrode reaction; the cell reaction is written in Eqn. 6-17 as: H 2,gaa + M t = 2H* + M N
AGM 3 * / M
(6-17)
1
= 1 aim
PHJ
H2
1
^ 1 2e^ 2^^
^ 2H* I OH*
=1j
1i^g..-HM^:,-2H;, +
M^w
Fig. 6 - ^ Electrochemical cell composed of an electrode of metal ion transfer and a normal h3^drogen electrode: M^ = metal ion in metallic bonding and in hydrated state.
The electromotive force of this cell gives the equilibrium potential SM^^/M for the transfer reaction of metal ions as shown in Eqn. 6-18: ^M^*/M
2i
2^
+ "27""^^M^* - ^M3+/M + "27""^^M3* »
(6-18)
where E^2.^ is the standard equilibrium potential and 0^2+ is the activity of hydrated metal ions. Equation 6-18 indicates that the equiUbriiun potential depends on the activity of hydrated metal ions. Table 6-2 shows the standard equiUbrium potentials of the transfer reactions of metal ions at metal electrodes in aqueous solutions.
209
Equilibrium Potential of Electrode Reactions TABLE 6 - 2 . The standard equilibrium potentials for transfer reactions of metal ions at metal electrodes at 25*'C. [Handbooks of electrochemistry.]
Electrode
Eo 1 VNHE
Electrode
-EQ/VNHE
1.50 0.987 0.799 0.521 0.337
Cd^^/Cd Fe^/Fe Ga^'/Ga Cr**/Cr Zn^/Zn Mn*^/Mn Zr**/Zr
-0.403 -0.44 -0.53 -0.74 -0.763 -1.18 -1.53 -1.63 -1.66 -2.37 -2.714 -3.045
Au^'/Au Pd^/Pd AgVAg Cu7Cu Cu'^/Cu
0.0
irm. Fe**/Fe
-0.036 -0.126 -0.136 -0.250 -0.277 -0.342
Pb^/Pb Sn^/Sn Ni^/Ni Co'^/Co In^/ln
Ti^/n A1**/A1 Mg**/Mg Na7Na LiTU
Further, we consider an ion transfer reaction at a multiphase silver-silver chloride electrode in an aqueous chloride solution as shown in Fig. 6-7. The ion transfer reactions at the AgCl/Cr.q interface and at the Ag/AgCl interface are, respectively, given in Eqn. 6-19: CI AgCl • ^ Cl'aq ,
(6-19)
Ag*Aga^Ag"Ag.
1
PHS = 1 atna
[iiiiiiii
\ 1 , 3
\ \
Aga
'
'^*1
r|M|;!
OH- = 1
H\
pt 1
r*- e j
a-* -a*
Fig. 6 - 7 . Electrochemical cell composed of a silver-silver chloride multiphase electrode of ion transfer and a normal h3rdrDgen electrode: Ag = silver metal; AgCl = silver chloride.
210
ELECTROCHEMICAL CELLS
CHAP. 6
The overall cell reaction is given in Eqn. 6-20: i H2.g.. + AgClAgd = H^, + AgAg + Cl-«,,
^GAgci/ci-.
(6-20)
Then, the equilibrium potential Ej^gcuci- is obtained as shown in Eqn. 6-21; J.
_ -^GAgCUCl-
EA^ua-
2i
~^QAgCl/Cl- . kT
=
2^
A^^
+ ^^inod-
= ^Agcvci- + - 2 ^ ^CLci-»
(6-21)
where the activities of sohd Ag and AgCl are assigned a value of unity. The standard equilibrium potential calculated from Eqn. 6-21 is ^Ago/a- = + 0.224 V at25^C. 6.4 Electrochemical Reference Level for Hydrated Ions In electrochemistry, the chemical potential of hydrated ions has been determined from the equilibrium potential of ion transfer reactions referred to the normal hydrogen electrode. For the reaction of metal ion transfer (metal dissolution-deposition reaction) of Eqns. 6-16 and 6-17, the standard equiUbrium potential £M2*/M is give in terms of the standard chemical potential, ^^, by Eqn. 6-22:
M2*/M
2e
"
2
6
'
where the chemical potentials of gaseous hydrogen molecule and of solid metal in the standard state have been assigned a value of zero following the convention in Sec. 6.3.1(^1^2 = 0,^^ = 0). It follows from Eqn. 6-22 that the standard chemical potential of hydrated ions determined from the standard equihbriimi potential of the ion transfer reaction is a relative value that is to the standard chemical potential of hydrated protons at unit activity, which, by convention in aqueous electrochemistry, is assigned a value of zero on the electrochemical scale of ion levels. The reaction equiUbrium of the normal hydrogen electrode, H2,g«» = 2 H*aq + 2 envHa* where en^/Ha ^^ the equiUbrium redox electron, can be obtained by the equiUbration of the free enthalpy of the reactants and that of the products as foUows: 2 a^. + 2 a^ H^/H^ = 2 ^^. + 2 e XS + 2 ji° ^.^^ - 2 e Xs = ^H,» where a^ is the standard real potential and Xs is the surface potential of aqueous solution. Hence, we obtain Eqn. 6-23:
References
2 < , + 2
211
(6-23)
If we set >AH2 at a value of zero according to the conventional chemical thermodynamic energy scale, the standard chemical potential of a hydrated proton, ^H* , is given by Eqn. 6-24: \il. = a^. - 6 Xs = - cx° H.^^ - e xs .
(6-24)
Pro°i "e.H*/H2 = - ^-S ^V and Xs = 0.13 V, we obtain \i^. = - 4.37 eV, which is assigned a value of zero on the electrochemical scale of ion levels in aqueous electrochemistry.
References [WhifFen, 1979]: D. H. WhiflFen, Manual of Symbols and TerminologyforPhysicochemical Quantities and Units, p. 28, Pergamon Press, Oxford, (1979).