164
Chemical Oceanography, 4th Edition
The fraction of the free cations and anions can be determined for Equations 4.66 and 4.67.
The desired ion- pairing constants for K MX
* are given in Table 4.6.
To start the iteration, one can assume that α M = 1.0 and calculate the values of α X . These
values of α X are used to make an estimate of [X] F = α X [X] T , and the values of α M are estimated. The new α M is used to determine [M] F = α M [M] T , and the process is repeated until
a self- consistent set of α i is found. A sample of the values obtained by various iterations is
given in Table 4.7. It is clear from this table that after three iterations, a self- consistent set of
α i s is obtained. These values can be used to determine the total activity coefficients of the
various ions (Table 4.8). It is also possible to determine the fraction of the various forms of
each metal and anion shown in Figure 4.31 and Figure 4.32.
The validity of these total activity coefficients can be demonstrated by calculating the
dissociation constant for boric acid in seawater. The K* HB is given by
K HB * = K HB γ HB / γ HB = 10 –9.24 × 1.09/(0.688 × 0.351) = 10 –8.54
(4.72)
Table 4.6
Ion- Pairing Constants for the Major Ion Pairs in Seawater
at S = 35 and t = 25°C
Ion
K* HX
K* NaX
K* KX
K* MgX
K* CaX
K* SrX
Cl–
—
—
—
—
—
—
SO 4
2–
31.35
2.15
1.66
10.41
11.04
7.13
HCO 3–
—
0.28 4
—
2.18
2.20
2.14
Br–
—
—
—
—
—
—
CO 3
2–
—
2.38
—
77.06
138.84 135.0
B(OH) 4–
—
0.70
—
8.07
13.28
4.65
F–
880.4
0.10
—
19.6
4.56
2.35
OH–
—
0.37
—
48.88
5.52
1.79
Table 4.7
Calculations of the Fraction of Free Cations
and Anions after Various Iterations
Ion
Iteration
1st
2nd
3rd
4th
H +
1.0000
0.7342
0.7268
0.7266
Na +
1.0000
0.9771
0.9763
0.9763
K +
1.0000
0.9826
0.9820
0.9820
Mg 2+
1.0000
0.8952
0.8918
0.8917
Ca 2+
1.0000
0.8888
0.8851
0.8850
Sr 2+
1.0000
0.9235
0.9209
0.9208
OH –
0.2555
0.2760
0.2767
0.2767
HCO 3–
0.7806
0.7919
0.7923
0.7923
F –
0.4608
0.4875
0.4884
0.4884
B(OH) 4–
0.5199
0.5395
0.5401
0.5402
SO 4
2–
0.3635
0.3768
0.3773
0.3773
CO 3
2–
0.1271
0.1382
0.1386
0.1387
Chemical Oceanography, 4th Edition
The fraction of the free cations and anions can be determined for Equations 4.66 and 4.67.
The desired ion- pairing constants for K MX
* are given in Table 4.6.
To start the iteration, one can assume that α M = 1.0 and calculate the values of α X . These
values of α X are used to make an estimate of [X] F = α X [X] T , and the values of α M are estimated. The new α M is used to determine [M] F = α M [M] T , and the process is repeated until
a self- consistent set of α i is found. A sample of the values obtained by various iterations is
given in Table 4.7. It is clear from this table that after three iterations, a self- consistent set of
α i s is obtained. These values can be used to determine the total activity coefficients of the
various ions (Table 4.8). It is also possible to determine the fraction of the various forms of
each metal and anion shown in Figure 4.31 and Figure 4.32.
The validity of these total activity coefficients can be demonstrated by calculating the
dissociation constant for boric acid in seawater. The K* HB is given by
K HB * = K HB γ HB / γ HB = 10 –9.24 × 1.09/(0.688 × 0.351) = 10 –8.54
(4.72)
Table 4.6
Ion- Pairing Constants for the Major Ion Pairs in Seawater
at S = 35 and t = 25°C
Ion
K* HX
K* NaX
K* KX
K* MgX
K* CaX
K* SrX
Cl–
—
—
—
—
—
—
SO 4
2–
31.35
2.15
1.66
10.41
11.04
7.13
HCO 3–
—
0.28 4
—
2.18
2.20
2.14
Br–
—
—
—
—
—
—
CO 3
2–
—
2.38
—
77.06
138.84 135.0
B(OH) 4–
—
0.70
—
8.07
13.28
4.65
F–
880.4
0.10
—
19.6
4.56
2.35
OH–
—
0.37
—
48.88
5.52
1.79
Table 4.7
Calculations of the Fraction of Free Cations
and Anions after Various Iterations
Ion
Iteration
1st
2nd
3rd
4th
H +
1.0000
0.7342
0.7268
0.7266
Na +
1.0000
0.9771
0.9763
0.9763
K +
1.0000
0.9826
0.9820
0.9820
Mg 2+
1.0000
0.8952
0.8918
0.8917
Ca 2+
1.0000
0.8888
0.8851
0.8850
Sr 2+
1.0000
0.9235
0.9209
0.9208
OH –
0.2555
0.2760
0.2767
0.2767
HCO 3–
0.7806
0.7919
0.7923
0.7923
F –
0.4608
0.4875
0.4884
0.4884
B(OH) 4–
0.5199
0.5395
0.5401
0.5402
SO 4
2–
0.3635
0.3768
0.3773
0.3773
CO 3
2–
0.1271
0.1382
0.1386
0.1387