A reaction demonstrating the conversion of an oxidized species to a reduced species without forming any precipitate is shown below:
(5.6) Reaction 5.6 is known as a half-cell reaction; to move from left to right, there should be an electron donor. This electron donor is the hydrogen half-cell reaction:
(5.7) By convention uH ' uH+, and ue- in the SHE are set to 1 (I1Go = 0) and the overall
• • 2(8"')
reactIOn IS
(5.8) This reaction's redox level can be expressed in volts of Eh, which is obtained by
Eh =-I1G/nF (5.9)
236 REDOX CHEMISTRY
where F is Faraday's constant (23.06 kcal per volt gram equivalent) and n is the number of electrons (representing chemical equivalents) involved in the reaction. From Reac- tions 1" (in the boxed section of this chapter) and 5.9,
-tlG/nF = -tlG%F - RT/nF {In[(Fe2+)/(Fe3+)]} (5.10) where T is temperature and R is the universal gas constant (1.987 x 10-3 kcal deg- I mol-I) and
Eh = J!l-2.303 RTlnF{log[(Fe2+)I(Fe3+)]} (5.11) or
Eh = J!l + 0.059 {log[(Fe3+)I(Fe2+)]} (5.12) where J!l is the standard electrode potential for Reaction 5.6. Equation 5.12 can be generalized for any redox reaction at 25°C:
Eh = J!l + {0.059/n} {log(activity of oxidized species/activity of reduced species)}
(5.13) Considering that
tlG~ = tlG~e2+ - tlG~e3+ = -20.30 - (-2.52) = -17.78 kcal mol-I (5.14) and from Equation 5.9,
J!l = 17.78/{ (1)(23.06)} = 0.77 V (5.15)
or
(5.16) This reaction shows that Eh is related to the standard potential (J!l = 0.77 V) and the proportionality of Fe3+ to Fe2+ in the solution phase. A number of J!l values repre- senting various reactions in soils are given in Tables 5.2 and 5.3. Note that Equation 5.16 is analogous to the Henderson-Hasselbalch equation. A plot of Eh versus (Fe3+lFe3+ + Fe2+) would produce a sigmoidal line with midpoint J!l (Fig. 5.2) (recall that the Henderson-Hasselbalch equation gives the pKa at the titration midpoint; see Chapter 1). To the left of J!l (midpoint in the x axis; J!l = 0.77 V) the reduced species (e.g., Fe2+) predominates, whereas to the right of J!l (midpoint in the x axis), the oxidized species (e.g., Fe3+) predominates.
5.3.2 Redox as pe and the Standard Hydrogen Electrode (SHE) In the case of the redox reaction
(5.17)
5.3 REDOX EQUILIBRIA
TABLE 5.2. Reduction Potentials of Selected Half-Cell Reactions in Soil-Water Systems at 25°C
Reaction F2 + 2e-= 2F- CI2 + 2e-= 2Cl-
NO) + 6W + 5e-= 1I2N2 + 3HP 02 + 4H+ + 4e-= 2H20
NO) + 2W + 2e- = N02+ H20 Fe3+ + e- = Fe2+
S04 + lOW + 8e- = H2S + 4Hp CO2 + 4H+ + 4e- = C + 2H20 N2 + 6H+ + 6e- = 2NH3 2H+ + 2e-= H2
Fe2+ + 2e-= Fe Zn2+ + 2e-= Zn A13+ + 3e-= Al Mg2+ + 2e-= Mg
Na+ + e- = Na Ca2+ + 2e-= Ca K++e- = K
1/2NP + e- + W = I!2N2 + 112 H2 NO + e- + W = 1I2N20 + 112HP
112N02 + e- + 312W = lI4N20 + 3/4H20 1/5NO) + e- + 6/5W = lIlON2 + 3/5HP N02: + e-+ 2W =NO + H20
1/4N0:l + e- + 5/4W = 1I8N20 + 5/8HP 1 /6N02: + e- + 4/3W = 1 /6NH! + 1/3HP lI8NO) + e- + 5/4W = lI8NH! + 3/8HP 112N0:l + e- + W = 112N02: + 112H20
1/6NO) + e- + 7/6W = lI6NHzOH + 1/3HP 1/6N2 + e- + 4/3W = 1/3NH!
11203 + e + H+ = 1/202 + 1/2HP OH + e-= OH-
02+ e-+ 2W = HP2 1/2HP2 + e- + H+ = HP 11402 + e- + W = 1I2Hp 11202 + e- + H+ = 1I2HP2 O2 + e-= O2
E' (V) +2.87 +1.36 +1.26 +1.23 +0.85 +0.77 +0.31 +0.21 +0.09 +0 -0.44 -0.76 -1.66 -2.37 -2.71 -2.87 -2.92 +1.76 +1.58 +1.39 +1.24 +1.17 +18.9 +1.12 +0.88 +0.83 +0.67 +0.27 +2.07 +1.98 +1.92 +1.77 +1.23 +0.68 -0.56 Source: Reproduced from Stumm and Morgan (1981) and Sparks (1995).
237
238 REDOX CHEMISTRY
TABLE 5.3. Electrode Potentials of Phenol, Acetic Acid, Ethanol, and Glucose Redox Couple
Phenol-C02
6C02 + 28W + 28e-= C6HsOH + IIHp Acetic acid-C02
2C02 + 8W + 8e = CH3COOH + 2HP Ethanol-C02
2C02 + llW +lle-= CH2CH20H + 3H20 Glucose-C02
6C02 + 24H+ + 24e-= C6H1206 + 6H20
Source: Reproduced from Stumm and Morgan (1981).
J!l (V)
0.102 0.097 0.079 -0.014
the half-cell of the SHE can be omitted because its b.Go = 0, and
rearranging
and taking logarithms on both sides of Equation 5.19, pe = log Keq + {log(Fe3+)I(Fe2+)}
or
1.0r---=---,
Eh (mVolts)
(5.18)
(5.19)
(5.20a)
(5.20b)
Figure 5.2. Relationship between redox electrical potential, Eh, and relative fraction of oxidized species (adapted from Kokholm, 1981).
5.3 REDOX EQUILIBRIA
where Keq (eo) is the equilibrium constant of the Fe3+ (Reaction S.17):
peo = -log Keq = -17.78 kcal mol-1/1.364 = -13.03
Substituting log Keq = 13.03 into Equation S.20b gives pe = 13.03 + log [(Fe3+)/(Fe2+)]
Assuming that (Fe3+)/(Fe2+) is set to 1, Equation S .22 reduces to pe = 13.03
239
(S.21)
(S.22)
(S.23)
TABLE 5.4. Equilibrium Constants of Redox Processes Pertinent in Soil-Water Systems (25°C)
Reaction
(1) 1/40z{g) + W + e-= 112 H20
(2) 1 /5N0:3 + 6/5 W + e-= 1I1ONz(g) + 3/SH20 (3) 1I2Mn02(s) + 1I2HCO} (10-3) + 3/2W + e-=
1I2MnCOis) + H20
(4) 1I2NO} + W + e-= 112N02 + 112H20
(5) 1I2NO} + 5/4W + e- = 1I8NHt + 3/8HP (6) 1I6N02 + 4/3W + e-= 1I6NHt + 1/3HP (7) 1I2CHPH + W + e-= 1I2CH4(g) + 112HP (8) 1I4CHP + W + e-= 1I4CHig) + 1/4H20
(9) FeOOH(s) + HCO} (10-3) + 2W + e-= FeC03(s) + 2HP (10) 1/2CHP + W + e-= 1I2CHPH
(11) + 1 /6S0~-+ 4/3W + e-= 1/6S(s) + 2/3HP
(12) 1I8S0~-+ 5/4W + e-= 1/8H2S(g) + 1I2Hp (13) 1I8S0~-+ 9/8W + e-= 1I8HS- + 1I2HP (14) 1/2S(s) + W + e-= 1I2HzS(g)
(15) 1/8COz(g) + W + e-= 1/8CHh) + 1I4HP (16) 1/6Nz(g) + 4/3W + e-= 1/3NHt
(17) 1I2(NADf>+) + 1/2W + e-= 112(NADPH) (18) W + e-= 1/2Hz(g)
(19) Oxidized ferredoxin + e-= reduced ferredoxin (20) 1I4COz{g) + W + e-= 1124 (glucose) + 1I4H20 (21) 1I2HCOO- + 3/2W + e-= 112CHP + 1I2HP (22) 1I4COz(g) + W + e-= 1/4CHP + 1I4HP (23) 1/2COz(g) + 112W + e-= 1/2HCOO-
Source: Reproduced from Stumm and Morgan (1981).
+20.75 +21.05
+14.15 +14.90 +15.14 +9.88 +6.94 +3.99 +6.03 +5.25 +4.25 +2.89 +2.87 +4.68 -2.0
0.0 -7.1 -0.20 +2.82 -1.20 -4.83
+13.75 +12.65 +8.9b +7.15 +6.15 +5.82 +2.88 -0.06 -0.8b -3.01 -3.30 -3.50 -3.75 -4.11 -4.13 -4.68 -5.5 -7.00 -7.1 -7.20 -7.68 -8.20 -8.33
aValues for peo(W) apply to the electron activity for unit activities of oxidant and reductant in neutral water, that is, at pH = 7.0 for 25°C.
h-rhese data correspond to (HeO}) = 10-3 M rather than unity and so are not exactly peo(W); they represent typical aquatic conditions more nearly than peo(W) values do.
240 REDOX CHEMISTRY
Equation 5.23 demonstrates that as long as Fe3+ and Fe2+ are present in the system at equal activities, pe is fixed at 13.03. If electrons are added to the system, Fe3+ will become Fe2+, and if electrons are removed from the system, Fe2+ will become Fe3+.
Equation 5.22 can be generalized for any redox reaction at 25°C,
pe = (lIn)Keq + (lInHlog(activity of oxidized species)/(activity of reduced species)}
(5.24)
TABLE 5.5. Equilibrium Constants for a Few Redox Reactions (25°C)
Reaction Log Keq FJ (Y)
Na+ + e-= Na(s) -47 -2.71
Zn2+ + 2e-= Zn(s) -26 -0.76
Fe2+ + 2e-= Fe(s) -14.9 -0.44
C02+ + 2e-= Co(s) -9.5 -0.28
y3+ + e-= y2+ -4.3 -0.26
2W + 2e-= H2(g) 0.0 0.00
S(s) + 2W + 2e-= H2S +4.8 +0.14
Cu2+ + e-= Cu+ +2.7 +0.16
AgCl(s) + e-= Ag(s) + Cl- + 3.7 +0.22
Cu2+ + 2e-= Cu(s) +11.4 +0.34
Cu+ + e-= Cu(s) +8.8 +0.52
Fe3+ + e-= Fe2+ +13.0 +0.77
Ag+ + e-= Ag(s) +13.5 +0.80
Fe(OHMs) + 3W + e-= Fe2+ + 3H2O +17.1 +1.01
103 + 6W + 5e-= 1/212(s) + 3HP +104 +1.23
Mn02(S) + 4H+ + 2e-= Mn2+ + 2H2O +43.6 +1.29
Clig) + 2e-= 2Cl- +46 +1.36
C03+ + e-= C02+ +31 +1.82
1I2Ni02 + e- + 2W = 112Ni2+ + Hp 29.8 +1.76
PUO/ + e-= PU02 26.0 +1.52
1I2Pb02 + e- + 2H-= 112Pb2+ = H2O 24.8 +1.46
Pu02 + e- + 4H+ = Pu3+ + 2H2O 9.9 +0.58
1I3HCrQ + e- + 4/3W = 1I3Cr(OHh + 1I3Hp 18.9 +1.12
112As01 + e- + 2W = 112As02 + Hp 16.5 +0.97
Hg2+ + e-= 1I2H~+ 15.4 +0.91
1I2Mo~-+ e- + 2W = 1I2Mo02 + HP 15.0 +0.89
1I2SeO~-+ e- + W = 112SeOj-+ 1/2Hp 14.9 +0.88
1I4SeO~-+ e- + 3/2W = 1I4Se + 3/4HP 14.8 +0.87 I /6SeO~-+ 4/3W = 1/6H2Se + 112H2O 7.62 +0.45
1I2YO! + e- + i/2HP+ = 1/2Y(OHh 6.9 +0.41
PU02 + e- + 3H+ = PuOH2 + HP 2.9 +0.17
Source: Reproduced from Stumm and Morgan (1981) and Sparks (1995).
5.3 REDOX EQUILIBRIA
ã10 o
pe
5 10 15 20
I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 1 1 1 " 1 1 II I I I f l 1 t l
-0.5 o 0.5
Eh (volts)
1.0
Figure 5.3. Relationship between pe and Eh (adapted from Drever, 1982).
241
A number of half-cell redox reactions pertinent in soil-water systems are given in Tables 5.4 and 5.5. Note that at 25°C, pe = 16.9 Eh and Eh = 0.059 pe. Graphically, the relationship between pe and Eh is shown in Figure 5.3.
5.3.3 Redox as Eh in the Presence of Solid Phases
The discussion in Sections 5.3.1 and 5.3.2 was based on the electrochemical cell shown in Figure 5.1, which included a platinum and a hydrogen electrode. This electrode pair gave us an understanding of pe and Eh, but one should keep in mind that the electrode potential in cell I is independent of the SHE and platinum electrode. The redox potential is determined only by the redox couple under consideration (e.g., Fe3+, Fez+) when both members are present in solution or in contact with solution. In natural soil-water systems, more often than not, several redox pairs maybe present (e.g., Fe3+, Fez+; SO~-, HzS; NO;, NO;"). In such situations, each pair will produce its own pe or Eh, but the three values mayor may not be the same. When a chemical equilibrium between the three redox pairs is met, the three pe or Eh values will be the same (Drever, 1982). In nature, redox couples may also involve solution and solid phases, for example, Fez+, Fe(I1)(OH)3; Mnz+, Mn(III)(OOH); Fe(I1)CO;, Fe(I1)(OH)3; their role in determining redox potential is demonstrated below.
Consider a reaction where two solid phases are involved. Thus, in addition to electron transfer (redox process), one of the solid phases decomposes while the other one forms. For example,
FeC03(s) + 3HzO ~3 Fe(OH)3(s) + HCO; + 2H+ + e- (5.25) Reaction 5.25 is a half-cell reaction. In order for this half-cell reaction to move from left to right, there should be an electron sink. In soils, a most common electron sink is 0z' although other soil minerals, as we shall see later in this chapter, can act as electron sinks (see also Chapter 6). The equilibrium expression (Keg) for Reaction 5.25 is
(5.26) In this case, H+ activity cannot be set to 1 because the two solids, Fe(OH)3(s) and FeC03(s)' cannot persist at such low pH. Unit activity, however, is assigned to all other
242 REDOX CHEMISTRY
pure phases, Fe(OH)3(s)' HCO;-, FeC03(s)' and H20. The above reaction's redox level can be expressed in units of volts of Eh obtained from the relationship
Eh = -I1GfnF (5.27)
where F is Faraday's constant (23.06 kcal per volt gram equivalent) and n is the number of electrons (representing chemical equivalents) involved in the reaction. From the classical thermodynamic relationships (outlined in Reactions A to J" in the boxed section) and Reaction 5.26 [considering that activity of the pure phases (Fe(OHh(s)' Fe(OH)3(sằ)' H20, and HCO;- is set to 1],
(5.28) where R is the universal gas constant (1.987 X 10-3 kcal deg- I morl). If I1G~ (Garrels and Christ, 1965) is as follows:
and
then
FeC03(S) = -161.06 kcal morl H20 = -56.69 kcal mol-I Fe(OH)3(s) = -166.0 kcal morl
HCO;-= -140.31 kcal mol-I
I1G~eaction = I1G~roducts - I1G~eactants (5.29)
I1G~ = -166.0 + (-140.31) - (-161.06) - (3x -56.69) = 24.82 kcal morl (5.30) For natural systems, a more accurate representation is HCO;-= 10-3 M. From Equation 5.27, f!J = - 24.82 kcal mol-If{ (I)(23.06)} = - 1.08 V. By replacing the -I1GfnFterms of Equation 5.28 with Eh terms (see Equation 5.27),
Eh = f!J - RTfnF {In(W)2} (5.31) and
Eh = -1.08 -RTfnF {In(Jr)2} (5.32) Equation 5.32 can be converted to base 10:
Eh = -1.08 - 2.303 RTfnF {log(W)2} (5.33) Using R, standard temperature (25°C), n = 1, and Faraday's constant gives
5.3 REDOX EQUILIBRIA 243 (5.34) or
Eh = -1.08 + 0.118 pH (5.35)
A plot of pH versus Eh will give a straight line with slope 0.118 and y intercept of -1.08. Equation 5.35 shows that as long as FeC03(s) and Fe(OH)3(s) are present in the system, EfJ is fixed at -1.08 V. If electrons are added to the system, Fe(OH)3(s) will become FeC03(s)' and if electrons are removed from the system, FeC03(S) will become Fe(OH)3(s)'