Geology Reference
In-Depth Information
a
1
¼
K
1
{H
1
}/({H
1
}
2
þ
K
1
{H
1
}
þ
K
1
K
2
)
(3.59)
a
2
¼
K
1
K
2
/({H
1
}
2
þ
K
1
{H
1
}
þ
K
1
K
2
)
(3.60)
where
a
0
þ
a
1
þ
a
2
¼
1
(3.61)
Graphical representation of log {}vs. pH can again be used to obtain the
equilibrium pH (Example 3.6).
Example 3.6: Graphical illustration of the relationship between (i)
log
{
H
2
CO
3
*
}
, (ii) log
{
H
2
CO
3
}
, (iii) log
{
HCO
3
}
, and (iv) log
{
CO
3
2
}
and pH for a closed aqueous system. Use C
¼
2
10
5
mol L
1
,K
1
¼
5.1
10
7
and K
2
¼
5.1
10
11
.
The presence of dissolved CO
2
is taken into account by the following
equilibrium:
CO
2
ð
aq
Þ
þ
H
2
O
Ð
H
2
CO
3
ð
aq
Þ
K
hydration
¼f
H
2
CO
3
g=f
CO
2
g¼
1
:
54
10
3
We defined {H
2
CO
3
*}
¼
{CO
2
}
þ
{H
2
CO
3
} but {H
2
CO
3
*}
{CO
2
}
because the hydration equilibrium lies far to the left. So K
hydration
¼
{H
2
CO
3
}/{H
2
CO
3
*} and {H
2
CO
3
}
¼
{H
2
CO
3
*}
1.54
10
3
. In this
way the presence of dissolved CO
2
is taken into account while the true
concentration of carbonic acid can still be determined.
By assuming a closed system, the total analytical activity of carbonic
acid, C, is constant [this is not true for an open system (Example 3.7)].
Thus (3.52)-(3.54) can be combined to give (3.55)-(3.57).
For a diprotic acid such as H
2
CO
3
*, the pH range can be divided into
three regions, pH
o
pK
1
,pK
1
o
pH
o
pK
2
, and pH4pK
2
,andtheproce-
dure outlined in Example 3.5, i.e. obtaining logarithmic expressions for
{H
2
CO
3
*}, {HCO
3
},and{CO
3
2
} and differentiating each with respect
to pH, can then be utilized to construct the plot of
log{}against pH.
B
For {H
2
CO
3
*}
log
f
H
2
CO
3
g¼
2 log
f
H
þ
gþ
logC
2 log
f
H
þ
g
¼
log C
d log
f
H
2
CO
3
g=
dpH
¼
0
pH
o
pK
1
:
