273
The Carbonate System
–ΔV cal = 48.76 – 0.5304(T – 273.15)
(7.78)
–ΔV arag = 46.0 – 0.5304(T – 273.15)
(7.79)
–10 3 ΔK cal = 11.76 – 0.3692(T – 273.15)
(7.80)
–10 3 ΔK arag = 11.76 – 0.3692(T – 273.15)
(7.81)
The pK’s needed to calculate the parameters of the carbonate system in seawater (S = 35) at
various temperatures are given in Table 7.4. It should be pointed out that all the carbonic
acid constants are on the total scale. The values of the carbonate constants of seawater on
the various pH scales are given in Table 7.5 (Millero, 2010).
The equation used to make conversions with the dissociation constants between pH
scales is as follows (Millero, 2010):
pK i – pK 0 i = A i + B i / T + C i ln(T)
where T is the absolute temperature, and A i , B i , and C i are salinity- dependent constants.
The values for pK 0
1 and pK 0 2 are fitted to the following equations (Millero et al., 2006):
Table 7.4
Dissociation Constants for Carbonate Calculations in Seawater (S = 35)
Temp. (°C)
pK 0
pK 1
pK 2
pK B
pK W
pK cal
pK arg
0
1.202
6.101
9.376
8.906
14.30
6.37
6.16
5
1.283
6.046
9.277
8.837
14.06
6.36
6.16
10
1.358
5.993
9.182
8.771
13.83
6.36
6.17
15
1.426
5.943
9.090
8.708
13.62
6.36
6.17
20
1.489
5.894
9.001
8.647
13.41
6.36
6.18
25
1.547
5.847
8.915
8.588
13.21
6.37
6.19
30
1.599
5.802
8.833
8.530
13.02
6.37
6.20
35
1.647
5.758
8.752
8.473
12.84
6.38
6.21
40
1.689
5.716
8.675
8.416
12.67
6.38
6.23
Table 7.5
Coefficients for the Fits of the Values pK 1 and pK 2 in Seawater as a Function of
Temperature, Salinity, and Ionic Strength on the pH F , pH T , and pH SWS Scales
pK 1
pK 2
pH F Scale
pH T Scale
pH SWS Scale
pH F Scale
pH T Scale
pH SWS Scale
S 0.5
a 0
5.09247
13.4051
13.4038
11.0637
21.5724
21.3728
S
a 1
0.05574
0.03185
0.03206
0.1379
0.1212
0.1218
S 2
a 2
−9.279E-05
−5.218E-05
−5.242E-05
−3.788E-04
−3.714E-04
−3.688E-04
S0.5/T
a 3
−189.879
−531.095
−530.659
−366.178
−798.292
−788.289
S/ T
a 4
−11.3108
−5.7789
−5.8210
−23.288
−18.951
−19.189
S0.5 ln T
a 5
−0.8080
−2.0663
−2.0664
−1.810
−3.403
−3.374
SE
0.0055
0.0053
0.0053
0.0105
0.0108
0.0109
Number
551
551
551
590
590
590
The Carbonate System
–ΔV cal = 48.76 – 0.5304(T – 273.15)
(7.78)
–ΔV arag = 46.0 – 0.5304(T – 273.15)
(7.79)
–10 3 ΔK cal = 11.76 – 0.3692(T – 273.15)
(7.80)
–10 3 ΔK arag = 11.76 – 0.3692(T – 273.15)
(7.81)
The pK’s needed to calculate the parameters of the carbonate system in seawater (S = 35) at
various temperatures are given in Table 7.4. It should be pointed out that all the carbonic
acid constants are on the total scale. The values of the carbonate constants of seawater on
the various pH scales are given in Table 7.5 (Millero, 2010).
The equation used to make conversions with the dissociation constants between pH
scales is as follows (Millero, 2010):
pK i – pK 0 i = A i + B i / T + C i ln(T)
where T is the absolute temperature, and A i , B i , and C i are salinity- dependent constants.
The values for pK 0
1 and pK 0 2 are fitted to the following equations (Millero et al., 2006):
Table 7.4
Dissociation Constants for Carbonate Calculations in Seawater (S = 35)
Temp. (°C)
pK 0
pK 1
pK 2
pK B
pK W
pK cal
pK arg
0
1.202
6.101
9.376
8.906
14.30
6.37
6.16
5
1.283
6.046
9.277
8.837
14.06
6.36
6.16
10
1.358
5.993
9.182
8.771
13.83
6.36
6.17
15
1.426
5.943
9.090
8.708
13.62
6.36
6.17
20
1.489
5.894
9.001
8.647
13.41
6.36
6.18
25
1.547
5.847
8.915
8.588
13.21
6.37
6.19
30
1.599
5.802
8.833
8.530
13.02
6.37
6.20
35
1.647
5.758
8.752
8.473
12.84
6.38
6.21
40
1.689
5.716
8.675
8.416
12.67
6.38
6.23
Table 7.5
Coefficients for the Fits of the Values pK 1 and pK 2 in Seawater as a Function of
Temperature, Salinity, and Ionic Strength on the pH F , pH T , and pH SWS Scales
pK 1
pK 2
pH F Scale
pH T Scale
pH SWS Scale
pH F Scale
pH T Scale
pH SWS Scale
S 0.5
a 0
5.09247
13.4051
13.4038
11.0637
21.5724
21.3728
S
a 1
0.05574
0.03185
0.03206
0.1379
0.1212
0.1218
S 2
a 2
−9.279E-05
−5.218E-05
−5.242E-05
−3.788E-04
−3.714E-04
−3.688E-04
S0.5/T
a 3
−189.879
−531.095
−530.659
−366.178
−798.292
−788.289
S/ T
a 4
−11.3108
−5.7789
−5.8210
−23.288
−18.951
−19.189
S0.5 ln T
a 5
−0.8080
−2.0663
−2.0664
−1.810
−3.403
−3.374
SE
0.0055
0.0053
0.0053
0.0105
0.0108
0.0109
Number
551
551
551
590
590
590