165
Ionic Interactions
This calculated value can be compared to the measured value of 10 –8.60 measured by
Hansson (1973). The results of similar calculations for other acids are shown in Table 4.9.
The calculated values are in good agreement with the measured values and demonstrate the reliability of the model.
The speciation of minor components of seawater can be made using the concentrations
of free cations and anions given in Table 4.8. These calculations can be made without making any iterations since minor components do not affect the speciation of the major components. A sample calculation for the PO 4
3– ion is
α PO
NaPO
F
MgPO
F
CAPO
K
Na
K
Mg
K
C
4
4
4
4
1
= +
+
+
(
[ ]
[
]
[
*
*
*
a a F
] )
.
−
=
1
0 0016
(4.73)
Since the value of γ F = 0.0252 for PO 4
3− , the value of γ T = 4 × 10 −5 .
For the calculation of the fraction of free trace metals in seawater, one needs reliable values of K* MX for the metal with the major anions at an ionic strength of 0.7.
Reliable values of K* MX are not normally available. Whitfield and coworkers (Turner,
Whitfield, and Dickson, 1981) have made these calculations using the best available
data. Their results are given in Table 4.10. Since reliable values of K* BMX are available for
Cu 2+ (Table 4.11), it is possible to demonstrate how the method is used. The function of
free Cu 2+ is given by
α Cu
CuSO
F
CuHCO
F
CuCO
K
SO
K
HCO
K
= +
+
+
(
[
]
[
]
*
*
1
4
3
3
4
3
* *
*
(
)
*
(
[
]
[
]
[
]
CO
K
CO
K
OH
K
F
CuCO
F
Cu OH
F
Cu O
3
3
2
2
+
+
+
H H
F
OH
)
*
[
] )
2
2 1
−
(4.74)
Table 4.8
Values for [i] T , [i] F, α i , γ F (i), and γ T (i) for the Major Ionic
Components of Seawater at S = 35 and t = 25°C
Ion
[i] T
α i
[i] F
γ F (i)
γ T (i)
H+
—
0.7266
—
0.947
0.688
Na+
0.48610 0.9763
0.47458 0.707
0.690
K+
0.01058 0.9820
0.01037 0.628
0.616
Mg 2+
0.05474 0.8917
0.04878 0.286
0.255
Ca 2+
0.01066 0.8850
0.00943 0.258
0.228
Sr 2+
0.00009 0.9208
0.00008 0.251
0.231
Cl–
0.56577 1.0000
0.56577 0.628
0.628
OH –
—
0.2769
—
0.853
0.236
F –
0.00007 0.4883
0.00003 0.681
0.333
Br –
0.00087 1.0000
0.00087 0.646
0.646
HCO 3–
0.00193 0.7924
0.00153 0.677
0.536
B(OH) 4–
0.00009 0.5403
0.00005 0.650
0.351
SO 4
2–
0.02927 0.3771
0.01097 0.224
0.085
CO 3
2–
0.00020 0.1386
0.00003 0.207
0.029
H 2 PO 4–
—
0.7860
—
0.502
0.395
HPO 4
2–
—
0.2968
—
0.167
0.050
PO 4
3–
—
0.00147
—
0.0284 0.000042
Ionic Interactions
This calculated value can be compared to the measured value of 10 –8.60 measured by
Hansson (1973). The results of similar calculations for other acids are shown in Table 4.9.
The calculated values are in good agreement with the measured values and demonstrate the reliability of the model.
The speciation of minor components of seawater can be made using the concentrations
of free cations and anions given in Table 4.8. These calculations can be made without making any iterations since minor components do not affect the speciation of the major components. A sample calculation for the PO 4
3– ion is
α PO
NaPO
F
MgPO
F
CAPO
K
Na
K
Mg
K
C
4
4
4
4
1
= +
+
+
(
[ ]
[
]
[
*
*
*
a a F
] )
.
−
=
1
0 0016
(4.73)
Since the value of γ F = 0.0252 for PO 4
3− , the value of γ T = 4 × 10 −5 .
For the calculation of the fraction of free trace metals in seawater, one needs reliable values of K* MX for the metal with the major anions at an ionic strength of 0.7.
Reliable values of K* MX are not normally available. Whitfield and coworkers (Turner,
Whitfield, and Dickson, 1981) have made these calculations using the best available
data. Their results are given in Table 4.10. Since reliable values of K* BMX are available for
Cu 2+ (Table 4.11), it is possible to demonstrate how the method is used. The function of
free Cu 2+ is given by
α Cu
CuSO
F
CuHCO
F
CuCO
K
SO
K
HCO
K
= +
+
+
(
[
]
[
]
*
*
1
4
3
3
4
3
* *
*
(
)
*
(
[
]
[
]
[
]
CO
K
CO
K
OH
K
F
CuCO
F
Cu OH
F
Cu O
3
3
2
2
+
+
+
H H
F
OH
)
*
[
] )
2
2 1
−
(4.74)
Table 4.8
Values for [i] T , [i] F, α i , γ F (i), and γ T (i) for the Major Ionic
Components of Seawater at S = 35 and t = 25°C
Ion
[i] T
α i
[i] F
γ F (i)
γ T (i)
H+
—
0.7266
—
0.947
0.688
Na+
0.48610 0.9763
0.47458 0.707
0.690
K+
0.01058 0.9820
0.01037 0.628
0.616
Mg 2+
0.05474 0.8917
0.04878 0.286
0.255
Ca 2+
0.01066 0.8850
0.00943 0.258
0.228
Sr 2+
0.00009 0.9208
0.00008 0.251
0.231
Cl–
0.56577 1.0000
0.56577 0.628
0.628
OH –
—
0.2769
—
0.853
0.236
F –
0.00007 0.4883
0.00003 0.681
0.333
Br –
0.00087 1.0000
0.00087 0.646
0.646
HCO 3–
0.00193 0.7924
0.00153 0.677
0.536
B(OH) 4–
0.00009 0.5403
0.00005 0.650
0.351
SO 4
2–
0.02927 0.3771
0.01097 0.224
0.085
CO 3
2–
0.00020 0.1386
0.00003 0.207
0.029
H 2 PO 4–
—
0.7860
—
0.502
0.395
HPO 4
2–
—
0.2968
—
0.167
0.050
PO 4
3–
—
0.00147
—
0.0284 0.000042