Explanation of Standard Seawater Program Output (Simple Case)

Here we explain the results of a calculation of the pH and carbonate K* values in a medium of S = 35 seawater at 25 oC.

The output of the demonstration program is shown in the box. The letters [A] – [F] on the right hand side refer to explanatory notes, below. You may find it helpful to compare results such as these with those for the same initial salinity and temperature but with an altered composition in which the molalities of some of the major seawater ion(s) have been changed.


     pH & Carbonate Stability Constants, in Standard Seawater     

• Temperature: 25.00 °C,  Salinity: 35.00,  Pressure: 1.0 atm (fixed)        [A]

• Calculated pH (total scale): 8.100 ± 0.0136        [B]

• Calculated stability constants:        [C]

log(K0*) = -1.53955 ± 1.77E-02            log(K1*) = -5.84814 ± 1.18E-02        [D]

Uncertainty contributions (%)    Uncertainty contributions (%)

  30.78    BC(Na,HCO3)                   26.71    BC(Na,HCO3)
  25.77  a theta(Cl,HCO3)                22.36  a theta(Cl,HCO3)
   1.49  a psi(Cl,HCO3,Na)                1.29  a psi(Cl,HCO3,Na)
  17.05    ln[K(MgCO3)]                  15.58    ln[K(HSO4)]
   7.69    ln[K(HCO3)]                   11.49    BC(H,Cl)
   6.33    BC(Na,CO3)                    10.07    ln[K(CO2)]
   4.08    ln[K(CO2)]                     6.67    ln[K(HCO3)]
   2.98    BC(Mg,Cl)                      4.13  b theta(H,Na)

log(K2*) = -8.94876 ± 1.84E-02        [E]

Uncertainty contributions (%)        Literature values

  36.40    ln[K(MgCO3)]                log(K0*) =  -3.56165 ±  2.12E-05
  13.52    BC(Na,CO3)                  log(K1*) = -13.46357 ±  2.98E-04
  10.89    BC(Na,HCO3)                 log(K2*) = -20.64487 ±  1.19E-03
   9.12  a theta(Cl,HCO3)
   0.53  a psi(Cl,HCO3,Na)
   6.36    ln[K(HSO4)]
   6.33    BC(Mg,Cl)
   4.69    BC(H,Cl)

• Individual solute species concentrations (mol kg−1 of solution):        [F]

   H = 6.1727E-09       CL = 5.4587E-01      BOH3 = 3.1782E-04
  NA = 4.6897E-01      SO4 = 2.8235E-02       CO2 = 9.5967E-06
  MG = 5.2670E-02     HSO4 = 1.7704E-09        HF = 1.4427E-10
  CA = 1.0251E-02       OH = 3.5520E-06     MGCO3 = 1.1306E-04
   K = 1.0208E-02       BR = 8.4211E-04     CACO3 = 2.8958E-05
MGOH = 3.9875E-06     HCO3 = 1.7139E-03     SRCO3 = 1.7674E-07
  SR = 9.0518E-05      CO3 = 1.0060E-04
 MGF = 3.0225E-05     BOH4 = 9.7347E-05
 CAF = 1.7734E-06        F = 3.6311E-05
Notes

This, the simplest use of the program, demonstrates: (a), how closely the measured K* of the carbonate system can be predicted by the chemical speciation model; (b), the major contributors to the uncertainties in the calculated values.

The literature values of each of the measured log(K*) for the input T and S are also shown. Generally, the log(K*) are predicted quite accurately, especially close to 25 °C which is the temperature for which there are most thermodynamic data. Uncertainties will be greater at lower T (this is not yet included in the model).

The list of uncertainty contributions shows where research effort should be focused to improve the model and make it more accurate. The chemical symbols, in parentheses, indicate the ion interactions in the speciation model and ln[K(..)] are thermodynamic equilibrium constants. Examples: BC(HCl) – the thermodynamic properties of aqueous HCl; ln[K(MgCO3)] – the thermodynamic association constant for the ion pair MgCO3(aq); theta(H,Na) – the interaction of these two cations; ln[K(HSO4)] – the thermodynamic dissociation constant of the bisulphate ion (HSO4−). Letters 'a', 'b', etc. identify pairs or groups of co-varying parameters. All contributions of each group are listed.

See also our description of the current state of development of the treatment of uncertainties.


What The Output Means

The three K* values, definining the equilibria of the carbonate system in seawater, and between gas phase and dissolved CO2, are:

K0* = [CO2*] / ƒ(CO2)

K1* = [H+] . [HCO3−] / [CO2*]

K2* = [H+] . [CO32−] / [HCO3−]

For further details see, for example, chapter 2 of the Guide to Best Practices for Ocean CO2 Measurements (PICES Special Publication 3, IOCCP REPORT No. 8), eds. A.G. Dickson, C.L. Sabine, and J.R. Christian (2007).

In this example program, all concentrations are in mol per kg of seawater, and the concentration of H+ ion is on the 'total' scale, so that: [H+] = [H+](free) + [HSO4−].

[A] The salinity, temperature, and pressure input by the user.

[B] The model-calculated pH for this standard seawater is 8.10 ± 0.014. (Note that the individual contributions to the uncertainty in the pH can also be calculated, and this is very useful for model development. For simplicity, the results are omitted here.)

[C–E] Here we list the model calculated values of the logarithms of the three carbonate equilibrium constants, their estimated total uncertainties, and the largest individual contributions to those uncertainties (expressed as percentages of the total variance). The letters 'a', 'b', etc. identify groups of co-varying Pitzer interaction parameters. The listed uncertainty contributions are ranked by the total for the group, and all contributions are listed. Hence, for log(K0*) there are values for the group consisting of theta(Cl,HCO3) and psi(Cl,HCO3,Na) (even though the latter value is small).

[D] On this line are the model-calculated values of log(K0*) and log(K1*), and their estimated uncertainties. Beneath these values are the top contributions to the total for each equilibrium constant. These contributions are either the thermodynamic values of various equilibrium constants (e.g., ln[K(HCO3−)] in the list for log(K0*)) or the Pitzer ion interactions in the model that determine the values of activity coefficients of H+ and the species of the carbonate system (CO2*, HCO3−, CO32−).

The following thermodynamic equilibrium constants that appear in the list are defined internally within the model as:

K(CO2)  :  2H+ + CO32− − H2O = CO2*

K(HCO3−)  :  H+ + CO32− = HCO3−

An important feature of the results is that most of the uncertainty is accounted for by just a few contributions, generally about five. This suggests that the model of seawater pH and the carbonate system can be improved significantly by focusing effort on just the first few items in the lists.

[E] The model-calculated values of log(K2*), and its estimated uncertainty, is on this line. Literature values of all three equilibrium constants are shown on the right (they come from sources cited in chapter 5 of the PICES Guide to Best Practices for Ocean CO2 Measurements).

[F] These are the calculated concentrations (in mol per kg of solution) of the individual chemical species in the seawater. The definition of pH on the total scale is: pH = -log([H+] + [HSO4−]). The solution contains seawater to the recipe given in Table 4 of Millero et al. (Deep Sea Res. I, 55, 50-72, 2008).