Encyclopedia of Environmental Science and Engineering, Volume I and II

WATER CHEMISTRY 1269

† With dilute solutions it is convenient to express concentrations on

a minus log concentration scale, e.g., pNa  log[Na].

observed voltage gives E H. p is then readily computed by

dividing E H by a constant factor according to Eq. (27):

pε

E

RT F

H

(. )

,

23 ^

where

F  the Faraday constant (96,500 coulombs per

equivalent),

R  the gas constant (8.314 volt-coulombs per

degree—equivalent),

and

T  the absolute temperature in degrees Kelvin.

At 25C, (2.3 T / F )  0.059 volt.

Both conceptually and computationally, it is more conve-

nient to use the dimensionless p rather than the more directly

measured E H , as a measure of the redox intensity. Every ten-

fold change in the activity ratio of Eq. (34) causes a change in

p of one unit divided by the number of electrons transferred

in the redox reaction. The fact that one electron can reduce one

proton is another reason for expressing the intensity parameter

for oxidation in a form equivalent to that used for acidity.

Incidentally, pH is also not measured directly. It is deter-

mined by measuring the potential (in volts) of an indicator

electrode (e.g., a glass electrode) with respect to a reference

electrode. If the hydrogen electrode is used or referred to as

the reference electrode, the resulting potential difference is

called the acidity potential. The pH is calculated by dividing

the acidity potential by 2.3 RT / F.

The Peters-Nernst Equation

Since much literature still describes the electron activity in

volts rather than on a scale^ †^ similar to that for other reagents,

the Peter-Nernst equation is still of utility. It is easily

expressed by substituting Eq. (37) into Eq. (34):

EE

RT

nF reduced

G

nF

HH





0 23. log{}

{}

,

oxidized

(38)

where

ERTF

G

H nF

0

0

 23



(. ) ;pε. (39)

Measurement of E H

It is essential to distinguish between the concept of a poten-

tial and the measurement of a potential. Redox or electrode

potentials (as listed in “Stability Constants of Metal-Ion

Complexes” and other references) have been derived from

equilibrium data, thermodynamic data, the chemical behav-

ior of a redox couple with respect to known oxidizing and

reducing agents, and from direct measurements of electro-

chemical cells.

Direct measurement of E H for natural water environments

involves complex theoretical and practical problems in spite

of the apparent simplicity of the electrochemical technique.

For example, the E H of aerobic (dissolved oxygen contain-

ing) waters, measured with a platinum or gold electrode,

does not agree with that predicted by Eq. (38). Even when

reproducible results are obtained, they often do not represent

reversible Nernst potentials. Among the considerations hin-

dering the direct measurement of E H are the rates of electron

exchange at certain electrodes and the occurrence of mixed

potentials. A mixed potential results when the rate of oxida-

tion of one redox couple is compensated by the rate of reduc-

tion of a different couple during the measurement. Although

aqueous systems containing oxygen or similar oxidizing

agents will usually give positive E H values and anaerobic

systems will usually give negative ones, detailed quantita-

tive interpretation with respect to concentrations of redox

species is generally unwarranted.

Since natural waters are normally in a dynamic rather

than an equilibrium condition, even the concept of a single

oxidation–reduction potential characteristic of the aqueous

system as a whole cannot be justified. At best, measurement

can give rise to an E H value applicable to a particular redox

reaction or to redox species in partial chemical equilibrium

and even then only if these redox agents are electrochemi-

cally reversible at the electrode surface at a rate that is rapid

compared with the electron drain or supply by the measuring

electrode system.

p – pH Diagrams

A p –pH stability field diagram shows in a panoramic way

which species predominate at equilibrium under any condi-

tion of p (or E H ) and pH. The primary value of a p –pH dia-

gram is its simultaneous representation of the consequences

of the equilibrium constants of many reactions for any com-

bination of p and pH. Figure 9 shows stability fields for

the various species pertinent to the chlorine system. These

diagrams are readily constructed from thermodynamic data

such as those listed in Table 4.

Log Concentration—p Diagrams

The predominant redox species are depicted as a function

of p or redox potential in p -log concentration diagrams.

Upper or lower bounds of p values for the occurrence of

specific redox reactions are immediately evident from these

double log-arithmetic diagrams. Such diagrams, constructed

from the data in Table 4 with pH  7, are shown in Figure 10

for a few elements in the biochemical cycle.

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