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V. Uses of pe–pH Thermodynamic Information

V. Uses of pe–pH Thermodynamic Information

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REDOX CHEMISTRY OF SOILS



161



predict that reduction of 0, to H,O would be coupled to oxidation of

C6H1,06 to CO,, and coupling oxidation of H,O to 0, with reduction of

CO, to C6H1206would not be thermodynamically possible. In fact, both

respiration (the predicted reaction) and photosynthesis (the second, “impossible” reaction) occur together, and the balance of the two is responsible

for the existence of the aerobic lifestyle and the persistence of organic

matter in soils. Photosynthesis is made possible via a complex series of

coupled reactions that make an overall thermodynamically impossible

reaction occur rapidly in sunlight.

Similarly, a reaction predicted to be thermodynamically possible may

not occur under natural conditions. The pe for NO, reduction to N, at pH

5 (14.3) is greater than that for HCrO,, reduction to Cr(OH), (10.9), but

this NO, oxidation of Cr( 111) has not been demonstrated in soils or plants,

probably because the reduction of NO, requires enzymatic processes to

lower the energy of activation at such a high pH.

The order of log K values for reduction-half reactions also has been used

to predict the sequence of reduction reactions camed out by respiring soil

microorganisms following saturation of a soil (Ponnamperuma, 1972).

The descending order of preference (pe) for the electron acceptors at pH 7

(proportional to free energy derived from the reduction) is 02/H,0 ( 13.6),

NOJN, (1 1.9), MnO,/MnZ+ (8.8), Fe(OH),/Fe2+(- 1.2), SO,/H,S (- 3 . 9 ,

and C02/CH,, (-4.1). Heterotrophic bacteria are using organic compounds as the electron donors (energy source) in their respiration to produce CO, or organic acids (pe range at pH 7 of - 8.7 to - 3.1 ), so most of

the organic compounds can be used throughout the reduction sequence

following depletion of atmospheric 0,.

The predicted pe values at a given pH are determined by chosen activities of reductant and oxidant, and by the values of Gibbs free energy of

formation (AGa used to calculate log K values. As shown in Table 11, the

sensitivity of calculated pe due to changes or error in log K and activities

varies considerably among reduction half-reactions. Predicted pe values for

O,, NO,, CO, , and SO,, reduction changed less than 0.5 units in response

M . In contrast, an error of only 10

to decreasing activity from lo-‘ to

kcal/mol in the AG,“resultedin changes in the calculated pe values of 3.6,

1.5, 0.3, and 0.9, respectively, for the above half-reactions. This result

indicates that wide variation and error in estimates of activities will have a

smaller effect on pe than will errors in free energy of formation data,

especially for 0, and NO, reduction reactions.

In contrast to these half-reactions involving the reduction or oxidation of

gases, those involving oxides and oxyhydroxides of Mn and Fe are subject

to greater error ( 1 .O to 3.0 units) in estimation of pe due to variation in

and

M. Similar to the gas

activity of Fe2+ or Mn2+ between



Table I

Selected Reduction Half-Reactions Pertinent to Soil, Natural Water, Plant,and Microbial

Systems



Reaction



-



Nitrogen species

iN,O e H+ jN, jH,)

NO e- H+ = j N 2 0 tH,O

+NOT C fH+ = tN20 fHtO

fNO; e- tH+ = &N, fH,O

N q e 2H+ = NO HzO

+NO; e- fH+= tN,O )H,O

&NOT C 3H+ = fNH: jHiO

+NOT h fH+ +NH: + H i 0

tNOT e H+ = 4NOT +HzO

&NO; C )H+ iNH2OH +H20

&N2 e- fH+= JNH:



+ +

+ +

+ +

+ +

+ +

+ +

+ +

+ +

+ +

+ +

+ +



+

+



+

+

+

+

+

+

+



-



+



Oxygen species

j O 3 C H+=jO2 +HZ0

OH. e -OHOr e 2H+ Hz02

+HzOi C H+ = H i 0

C H+-+H,O

j O 2 C H + = jH202

0 2



+ +

+

+ +

+ +

+ +

+ +

+ e- - 0;



-



+



Sulfur species

t S 0 - e fH+= tH,S jH,O

+so,- Q 2H+ = jS02+ HzO



+ +

+ +



+



Iron lad mpa%lwse compollllds

jMn,O, e 4H+ = fMn2+ 2H20

jMn203 e 3H+ = M d + f H 2 0

Mn3+ e = Mn2+

yMnOOH e 3H+ = M d + 2H,O

0.62Mn0,,1 e- 2.2H+ = 0.62Mn2+ 1.1H20

jFe,(OH), e 4H+ = jFG+ 4H20

jMn02 e 2H+- jMnz+ H,O

[Mn3+(PO,),I3- e- = (Mn'+(FQ,)l14Fe(OH)Z h 2H+ = Fe'+ 2H20

+Fe,04 e 4H+ = f F P 2HI0

Mn02 e 4H+ = Mn3+ 2H20

Fe(OH), C 3H+ = F g + 3Hi0

Fe(OHP+ C H+ = FS+ HzO

iFe20, e-+ 3H+ = FG+ jH,O

FeOOH e 3H+ = FZ+ 2HzO

Fe3+ e = Fe'+ phcnanthroline

Fe'+ e- = FG+

Fe3+ e- = Fe'+acetate

Fe'+ e = F$+ malonate

Fe'+ e- = F P salicylate

Fe)+ e- = FG+ hemoglobin

Fe'+ e- = Fe2+cyl b, (plants)

Fe'+ e- = F P oxalate



+ +

+ +

+

+ +

+ +

+ +

+ +

+

+ +

+ +

+ +

+ +

+ +

+

+ +

+

+

+

+

+

+

+



+

+



+



+

+

+

+



+



+



+



+



+



162



29.8

26.8

23.6

21.1

19.8

18.9

15.1

14.9

14.1

11.3

4.6



22.9

19.8

15.1

14.3

9.8

12.1

8.4

8.6

9. I

5.4

-0.7



20.9

17.8

12.1

11.9

5.8

9.6

5.7

6. I

7. I

3. I

-3.3



35. I

33.6

32.6

30.0

20.8

11.6

-9.5



28.4

33.6

22.6

23.0

15.6

8.2

-6.2



26.4

33.6

18.6

21.0

13.6

6.2

-6.2



5.2

2.9



- 1.0



- 3.5

-11.1



30.7

25.7

25.5

25.4

22. I

21.9

20.8

20.7

20.2

17.8

16.5

15.8

15.2

13.4

13.0

18.0

13.0



-



-7.1

16.7

14.7

25.5

14.4

13.4

7.9

12.8

20.7

10.2

3.9

0.54

4.8

10.2

2.4

2.0



-E



13.0

5.8

4.4 (pH 4)

4.4 (pH 4)



-



-



8.7

8.7

25.5

8.4

8.9

-0.1

8.8

20.7

6.2

-4.1

-7.5

- 1.2

8.2

-3.6

-4.0



-



13.0



-



2.4

0.68

0.034

(conrinued)



Table I (Continued)

peb



Reaction



+

+



FZ+ e- = FP+ pyrophosphatt

Fe3+ e- = FP+peroxidase

Fe3++ e- = Fe? ferredoxin (spinach)

fKFe,(SO,h(OH), Q 2H+ F 9 + + 2 H 2 0+ fS@[Fe(CN),]’- + F = [Fe(CN),]‘-



-



+ +



Carbon species

JCHJOH C H+ = JCH, JH20

toquinone F H+ = *phenol

tpquinone F H+ = thydroquinone

&H,,O6

c H+ fC2HSOH iH2O

Pyruvate + F H+ = lactate

KO, e- H+ = K H , f H 2 0

jCH,O F + H+ = jCH,OH

tHCOOH c H+ KH2O + jH2O

KO, c H+ = hC,jH,,O6 fH2O

+deasc + e- H+ = jasc

KO2 + C + H+= jCH2O + tH2O

KO2 c + H+ = tHCOOH



+ +

+ +

+ +

+ +

+

+ +

+

+ +

+ +

+

+



+



-



+



+



+



Pollutant/nutrient group

CO)+ e- = cd+

JNiO, F 2H+ = /Ni2+ HzO

Puo; e- = Puo2

2H+= tPff + H I 0

jPbOz

PuO2 6 4H+ = Pu3+ 2H20

+HCrO; C /H+ = KNOH), + jH,O

j A ~ ( 3 - F 2H+ tAsOi H2O

Hg2+ e- = fH&

+MOO- F 2H+ = J M d Z H 2 0

jS&6 H+ jw- 4H2O

f S e 0 - e- fH+ = iSe fH2O

f S e 0 - tH+ = tH2& tH,O

tV0;

e- /H,O+ = fV(OH),

Cu’+ e- = c u +

PuO, F 3H+ = PuOH2+ H I 0



+

+ +

+

+ +

+ +

+ +

+ +

+

+ +

+ +

+ +

+

+ +

+

+ +



+

+

+

+



-



+



+



+



+



+



M y t i c a l couples

Ce02 e- 4H+ = Ce3+ 2H20

jCI0- 6 H+ = jC- + H i 0

H a 0 + C + j C l 2 + H2O



+ +

+

+ +

+

Kl, + F = a&lor

+ e- + H+ = il- + t H 2 0

)F?(OH), + e- + H+ = tPt + H 2 0

+I2 + e- = ItHg2C12+ F = Hg + C

T

C + H+ = +H2

jPts + e - + H + = +Pt + t H 2 0



iog~4



-2.4



-



+ +K+



8.9



-



9.9



-



4.4



-



2.9

2. I

I.5

-0.21



I .o



-1.2

- 1.9

30.6

29.8

26.0

24.8

9.9

18.9

16.5

15.4

15.0

14.9

14.8

7.62

6.9

2.6

2.9

47.6

29.0

27.6

23.0

18.6

16.6

9. I

4.5

0

-5.0



~ H S



6.9



-



4.9



-



0.I

-2.1

-2.9

- 3.5

-5.9

-3.5

-6.1

-6.7

30.6

21.8

22.0

16.8

-6.1

10.9

6.5

13.4

3.0

9.9

6.3



p ~ 7



-4.6

-7.3

2.9

6. I

2.9

5.9

4.7

- 1.9

-3.1

-4.1

-4.9

- 5.5

-7.9

- 5.5

-8.1

-8.7



2.4

2.6

-8.1



30.6

17.8

22.0

12.8

-14.1

8.2

2.5

13.4

- 1.0

7.9

3.3

-1.7

I .4

2.6

-14.1



31.6

24.0

20.6

25.0

13.6

11.6



23.6

22.0

18.6

25.0

11.6

9.6



11.1



11.1



3.9



3.9

-7

- 12.0



1.o



-5

- 10.0



Calculated for reaction as written according to Eq. (14). Free energy of formation data were taken

from Lindsay (1979) as a primary source, and when not available from that sou-, from Gamls and Christ

( I 965) and Loach ( I 976).

*Calculated Using tabulated log K values, reductant and oxidant = IO-‘ Msoluble ions and molecules,

activities of solid phases = 1; partial pressures for gases that are pertinent to soils: IO-, atrn for trace gases,

0.21 atm for 0,.

0.78 for N,, and 0.00032 for CO,.

Values not listed by h h ( I 976).

163



164



R I C H M O N D J. B A R T L E T T A N D BRUCE R. JAMES

Table I1



Sensitivity of Calculated pe at pH 0 to Variation in ACj nod Activities of Reductant or Oxidant in

Selected Reduetion HIII-ReactionsPertinent to Soils



Column



-Log activity



Couple



AGj



ox



Red



ox



Red



Pe



0.68

2.68

0.68

4

6

4

0

0

0

0

0

0

0

0

0

3.5

3.5

3.5

0

0

0

0

0

0

4

6

4



0

0

0

0.1 1

0.11

0.11

4

6

4

4

6

4

4

6

4

4

6

4

4

6

4

4

6

4

4

4

4



0

0

0



- 56.70

- 56.70



- 26.43



0

0

0



20.6 1

20.11

24.20

20.30

19.90



-26.43

- 36.43

- 306.20

- 306.20

-3 16.20

-111.10

-111.10

- 121.10

- 133.10

- 133.10

- 143.10

-94.26

-94.26

-94.26

- 170.40

- 170.40

- 180.40

- 177.10

- 177.10

- 187.10

- 177.95

- 177.95

- 167.95



-66.70



- 54.40

- 54.40

- 54.40

- 54.40



- 54.40

- 54.40

- 54.40

- 54.40

- 54.40



-2 18.58

- 2 18.58

-228.58

-21.80

-21.80

-21.80

-21.80

-21.80

-21.80

-8.02

- 8.02

- 8.02



18.80



36.70

39.70

33.00

22.80

23.80

19.10

29.40

3 I .40

22.10

-0.91

-0.83

-0.60

19.80

2 I .80

12.40

17.40

19.40

13.70

5.20

5.50

6.10



Ape‘

-0.50

3.59

-0.40

- 1.50



3.00

-3.70

1 .00

-3.70



2 .OO

-7.30

0.08

0.3 1



2.00

-7.40

2.00

-3.70

0.30

0.90



‘Change in calculated pe resulting from change in activity of oxidant or reductant

(column I or 2) or resulting from use of A G j 10 kcal/mol different from the published value

(first row, column 3 or 4).



group, pe values for the oxide group showed considerable change due to

error in free energy of formation, ranging from 3.7 to 7.4 pe units. Differences between MnOOH, Mn,O,, and MnO, also were large, and similar

differenceswere found for the Fe oxides. This indicates that correct identification of Mn oxide mineralogy significantly affects pe- pH relationships



REDOX CHEMISTRY OF SOILS



16.5



and predicted energy changes associated with these reductions in soils at

certain pH values.

These observations of the sensitivity of predicted pe values due to variation in activities and due to error in free energy of formation indicate that

exact pe values for the reduction of a particular oxidant are difficult to

obtain, and ranges of values may be more accurate. The use of such ranges

also recognizes the heterogeneity of soii minerals, gaseous composition,

and ion activity in space and time.

Values for log K for reduction half-reactions are especially sensitive to

changes in activity of oxidant or reductant if oxygen atoms are transferred

from the oxidant to H20, e.g., in the reduction of MnOOH to Ma”, in

contrast to the reduction of Mn3+ to Mn2+. The formation of H20 is

favorable because it increases entropy of aqueous systems (Cotton and

Wilkinson, 1980)and thereby tends to lower calculated AGro.Water molecules formed as a product of a reduction half-reaction are balanced by H+

on the left side of the equation, resulting in a larger ratio of H+ to econsumed. This increases the slope of the pe-pH relationship, resulting in

a greater error in the estimation of pe due to an error in pH measurement.



VI. USES OF p - p H DIAGRAMS

Individual pe-pH relationships can be defined by the equation for a

straight line [Eq. ( 1 l)] in which log A’ and the activities of the oxidant and

reductant determine the y intercept, and the ratio of H+ to e- consumed

determines the slope. When such lines are plotted together, they predict

whether the oxidation - reduction reaction can occur “spontaneously,”

that is, with AG;
clearly shown, so that the interactions of pe and pH as master variables are

delineated.



A. OXYGEN

SPECIES

Whereas the pe for reduction of 0, to H,O ranges from 20.8 at pH 0 to

13.6 at pH 7 (Fig. 1 and Table I), the intermediates associated with

one-electron transfers show a wide fluctuation in their oxidizing power, a

property of 0, that is pertinent to understanding the transition in soils

from “aerobic” to “anaerobic” conditions. Anaerobic respiratory enzymes

are produced when Po, reaches approximately 1% of atmospheric levels

(0.2 kPa or 0.002 1 atm). The data in Table I1 also indicate that the pe for



166



R I C H M O N D J. BARTLETT AND BRUCE R. JAMES



a,



a



PH

Figure 1. A pe-pH diagram for 0, reduction reactions, including partially reduced

intermediates:superoxide (Oi), hydroxyl free radical (OH .), and hydrogen peroxide (H202).

Reduction of 0,to O2is also included for comparison with 0, reduction reactions. Activity

of oxygencontaining ionic or molecular species is 1 6 ‘ M.except that Pa is 2 1 Wa.



reduction of 0, is relatively insensitive to the 0, partial pressure in this

range.

and the hydroxyl free radical (OH-)are the most powerful

Ozone (0,)

oxidants among the oxygen species (Table I), and the latter may be formed

during stepwise, four-electron reduction of 0, to Oy, H,O,, and H,O

(Fridovich, 1978). The low and high positions of the pe-pH lines for

superoxide (0;) reduction to H,O, and for superoxide oxidation to 0,

indicate that both a powerful oxidlzing and reducing agent is formed in the

first step of reduction of 0,. The enzyme superoxide dismutase scavenges

0; in living cells using 0, as the terminal electron acceptor, but relatively

little is known about its reactivity in biological and chemical processes in

soils that may be pertinent to our understanding of the formation of highly

reduced components (e.g., soil organic matter) and highly oxidized species

(e.g., NO;) that coexist in soil at chemical equilibrium or quasi-equilibrium.



B. NITROGEN

SPECIES

Most reduction reactions of N species (Fig. 2 and Table I) are not

reversible, and therefore are not well defined by thermodynamic pe-pH



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