WATER CHEMISTRY 1257
express the net proton deficiency and net proton excess of
the systems with repect to specific proton reference levels
(equivalance points). The definitions can be readily ampli-
fied to account for the presence of buffering components
other than carbonates. For example, in the presence of borate
and ammonia the definition for alkalinity becomesAlk HCO CO B OHNH OH H[]⎡⎣ ⎤⎦ ⎡⎣ ⎤⎦ ⎡⎣ ⎤⎦[]⎡⎣ ⎤⎦ ⎡⎣ ⎤ 332
432()⎦⎦(4)Although individual concentrations or activities, such as
[H 2 CO 3 * ] and pH, are dependent on pressure and tempera-
ture, [Alk], [Acy], and C T are conservative properties that are
pressure and temperature independent. (Alkalinity, acidity,
and C T must be expressed in terms of concentration, e.g., as
molarity, molality, equivalents per liter or parts per million as
CaCO 3 ). Note that 1meq/l 5 50 ppm as CaCO 3.
The use of these conservative parameters facilitates the
calculation of the effects of the addition or removal of acids,
bases, carbon dioxide, bicarbonates, and carbonates to
aqueous systems. As shown in Figure 2, each of these con-
servative quantities remains constant for particular changes
in the chemical composition. The case of the addition or
removal of dissolved carbon dioxide is of special interest.
Respiratory activities of aquatic biota contribute carbon diox-
ide to the water whereas photosynthetic activities decrease
the concentration of this weak acid. An increase in carbon
dioxide increases both the acidity of the system and C T ,
the total concentration of dissolved carbonic species, and
it decreases the pH, but it does not affect the alkalinity.
Alternatively, acidity remains unaffected by the addition
or removal of CaCO 3 (s) or Na 2 CO 3 (s). C T , on the other
hand, remains unchanged in a closed system upon addition
of strong acid or strong base. For practical purposes, sys-
tems may be considered closed if they are shielded from
the atmosphere and lithosphere or exposed to them only for
short enough periods to preclude significant dissolution of
CO 2 or solid carbonates.Dissolution of Carbon DioxideThough much of the CO 2 which dissolves in solution may ion-
ize to form HCO 3 CO 32 , depending upon the pH, only a small
fraction (0.3% at 25C) is hydrated as H 2 CO 3. Hence, the
concentration of the unhydrated dissolved carbon dioxide,
CO 2 (aq), is nearly identical to the analytically determinable
concentration of H 2 CO 3 * ( [CO 2 (aq)] [(H 2 CO 3 ]).
The equilibrium of a constituent between a gas phase and a
solution phase can be characterized by a mass law relationship.
Table 1 gives the various expressions and their interrelations
for the characterization of the CO 2 dissolution equilibrium.
A water that is in equilibrium with the atmosphere (Pco 2
10 3.5 atm) contains at 25C approximately 0.44 milligram per
liter (10^ ^5 M) of CO 2 ; K H (Henry’s Law constant) at 25C is
10 1.5 mole per liter-atm.Dissolved Carbonate EquilibriaTwo systems may be considered: (1) a system closed to
the atmosphere and (2) one that is in equilibrium with the
atmosphere.
Closed Systems In this case H 2 CO 3 * is considered a non-
volatile acid. The species H 2 CO 3 * , HCO 3 , CO 32 and are
interrelated by the equilibria: †[][ ][ *]HHCO HCO323 K (^1)
[][ ][ ]HCO HCO
3
2
32 K
where K 1 and K 2 represent the equilibrium constants (acidity
constants).
The ionization fractions, whose sum equals unity (see
Eq. (3)), can be defined as follows:
a^023 [*]HCOCT (7)
a 13 []HCOCT
(8)
a^23
[]CO^2 C
T (9)
From Eqs. (3) to (9) the ionization fractions can be expressed
in terms of [H^ ^ ] and the equilibrium constants:
a01 12
([] []) 1 KKKHH ^21 (10)
a^112
([HH]KK 1 [ ])^1 (11)
a^2
2
12 2
([ ] KK [ ]K 1 ] HH^1 (12)
Values for K 1 and K 2 are given in Tables 2A and 2B. Because
HCO^3
and CO 32 may form complexes with other ions in
the systems (e.g., in sea water, MgCO 3 , NaCO 3 , CaCO, 3
MgHCO 3 , it is operationally convenient to define a total
concentration of the species to include an unknown number
of these complexes. For example,
[][][ ]
[][ ]
CO CO MgCO
CaCO NaCO
3
2
3
2
3
33
TT
(^) (13)
The distribution of carbonate species in sea water as a func-
tion of pH is given in Figure 3.
Systems Open to the Atmosphere A very elementary
model showing some of the characteristics of the carbonate
system in natural waters is provided by equilibrating pure
water with a gas phase (e.g., the atmosphere) containing CO 2
at a constant partial pressure. Such a solution will remain in
† To facilitate calculations the equilibria are written here in terms of
concentration quotients. The activity corrections can be considered
incorporated into the equilibrium “constants” which therefore vary
with the particular solution. Such constants for given media of con-
stant ionic strength, as well as the true thermodynamic constants,
are listed in Tables 2A and 2B.
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