Encyclopedia of Environmental Science and Engineering, Volume I and II

WATER CHEMISTRY 1267

This treatment of electrons is no different from that of

many other species such as hydrogen ions and silver ions,

which do not actually exist in aqueous solution as free and

unhydrated species but which are expressed as H^ ^ and Ag^ ^

in reactions. For example, the H^ ^ really takes the form of

hydrated protons (H 9 O 4 ) or hydrogen complexes (acids

such as HCl).

Redox Intensity

By introducing the definition pH  log[H^ ^ ], which under

idealized conditions is formulated as

pH  log{H^ ^ }, (28)

Sørenson (1909) established a convenient intensity parame-

ter that measures the relative tendency of a solution to donate

or transfer protons. In an acid solution this tendency is high

and in an alkaline solution it is low.

Similarly, Jørgensen (1945) has established an equally

convenient redox intensity parameter,

p  log{e}, (29)

that measures the relative tendency of a solution to donate

or transfer electrons. In a highly reducing solution the ten-

dency to donate electrons, that is, the hypothetical “electron

pressure” or electron activity, is relatively large. Just as the

activity of hypothetical hydrogen ions is very low at high

pH, the activity of hypothetical electron is very low at high

p. Thus a high p d indicates a relatively high tendency for

oxidation. In equilibrium equations H^ ^ and e are treated in

an analogous way. Thus oxidation or reduction equilibrium

constants can be defined and treated similarly to acidity con-

stants as shown by the following equations:

For protolysis:

HA  H^ ^  A^ ^ (30)

{H^ ^ }{A^ ^ }/{HA}  K HA , or

pH  log K HA  log({A^ ^ }/{HA}). (31)

For the oxidation of Fe^2 ^ to Fe^3 ^ :

Fe^2 ^  Fe^3 ^  e (32)

{e}{Fe^3 ^ }/{Fe^2 ^ }  K ox , or

p  log K ox  log({Fe^3 ^ /Fe^2 ^ }). (33)

As seen from Eq. (33) p increases with the ratio of the activ-

ities (or concentrations) of oxidized to reduced species. †

† The sign convention adopted here is that recommended by IUPAC

(International Union of Pure and Applied Chemistry).

From the following general reduction reaction:

aA  bB  ne  cC  dD

the generalized expression for any redox couple is given by

ppεε



0

1

23

a

n

b

n

c

n

d

n

n

G

RT

ppppABCD

.

(34)

where p X  log[ X ] and

p

n

K

n

K

n

G

nRT

ε  

11 1

23

log log

ox red.

K ox and K red are the equilibrium constants for the oxidation

and reduction reactions; n is the number of electrons trans-

ferred in the reaction. G represents the free energy change

for the reduction. Thus it is seen that p is a measure of the

electron free energy level per mole of electrons.

Equation (34) permits the expression of the redox

intensity by p for any redox couple for which the equi-

librium constant is known. Numerical illustrations of the

calculation of p values (25C) are given for the following

equilibrium systems in which the ionic strength, I, ‡ is

assumed to approach O:

a) An acid solution 10^ ^5 M in Fe^3 ^ and 10^ ^3 M in

Fe^2 ^.

b) A natural water at pH  7.5 in equilibrium with

the atmosphere (Po 2  0.21 atm.).

c) A natural water at pH  8 containing 10^ ^5 M

Mn^2 ^ in equilibrium with g MnO 2 (s).

“Stability Constant of Metal-Ion Complexes” gives the

following equilibrium constants ( K red ):

a) Fe^3 ^  e  Fe^2 ^ ;

KK





{}

{}{}

; log.

Fe

Fe e

2

3 12 53

b) 1/2 O 2 ( g )  2H^ ^  2e;

H 2 O(1)

‡ Ionic strength, I, is a measure of the interionic effect resulting pri-

marily from electrical attraction and repulsions between the various

ions; it is defined by the equation t = 1/2 (^) iCiZ^2 i. The summation is
carried out for all types of ions, cations and anions, in the solution.
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