Geology Reference
In-Depth Information
Chapter 4), is the dissociation of diprotic acids such as carbonic acid,
H
2
CO
3
. The hydration of dissolved CO
2(aq)
in natural waters gives rise
to carbonic acid. The dissociation of carbonic acid not only influences
the pH of the water but also provides ligands which can complex trace
metals. Example 3.6 illustrates the relationship between log {}and pH
for a closed aqueous system which contains dissolved CO
2
(the presence
of mineral phases has been ignored). By assuming that a system is closed
to the atmosphere, it is possible to treat carbonic acid as a non-volatile
acid and to consider only the hydration reaction which converts CO
2(aq)
to H
2
CO
3
.H
2
CO
3
* is used to represent the sum of the activities of
CO
2(aq)
and H
2
CO
3
, i.e. to take account of the presence of CO
2(aq)
,
which is in equilibrium with H
2
CO
3
. The dissociation of carbonic acid
can then be described by (3.50)-(3.51) and the equilibrium constants, K
1
and K
2
, are defined by (3.52)-(3.53).
H
2
CO
3
HCO
3
þ
H
1
"
(3.50)
HCO
3
CO
2
3
þ
H
1
"
(3.51)
K
1
¼
{HCO
3
}{H
1
}/{H
2
CO
3
}
(3.52)
K
2
¼
{CO
2
3
}{H
1
}/{HCO
3
}
(3.53)
The analytical activity of dissolved inorganic carbon species can be
written as the sum of undissociated and dissociated acid species (3.54).
For a closed system, the value of C is constant over the entire pH
range.
C
¼
{H
2
CO
3
}
þ
{HCO
3
}
þ
{CO
2
3
}
(3.54)
Combining (3.52)-(3.54), an expression for each of these (H
2
CO
3
*,
HCO
3
, and CO
3
2
) is obtained.
{H
2
CO
3
}
¼
C ({H
1
}
2
/({H
1
}
2
þ
K
1
{H
1
}
þ
K
1
K
2
))
(3.55)
{HCO
3
}
¼
C (K
1
{H
1
}/({H
1
}
2
þ
K
1
{H
1
}
þ
K
1
K
2
))
(3.56)
{CO
2
3
}
¼
C (K
1
K
2
/({H
1
}
2
þ
K
1
{H
1
}
þ
K
1
K
2
))
(3.57)
The dissociation fractions, a
0
, a
1
, and a
2
, are obtained by dividing each
of (3.55)-(3.57) by the analytical activity, C (cf. (3.42)-(3.43)).
a
0
¼
{H
1
}
2
/({H
1
}
2
þ
K
1
{H
1
}
þ
K
1
K
2
)
(3.58)
