Here we explain the results of a calculation of the changes in pH, and log(K0-2*), in standard seawater for which the Na+ concentration has been decreased by 5% by the removal of NaCl from the solution, and the SO42− concentration increased by 20% by the addition of Na2SO4.
The output of the demonstration program is shown in the box. The letters [A] – [E] 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 salinity and temperature for the base seawater composition.
• Temperature: 25.00 °C, Salinity: 35.00, Pressure: 1.0 atm (fixed) [A]
• Seawater composition has been altered as follows: [B]
Na by -2.592% by removing NaCl (and changing Na2SO4) Cl by -4.296% (by changing NaCl) SO4 by +20.000% by adding Na2SO4
• This changes the calculated pH from 8.100 ± 0.0136 to 8.081 (ΔpH = -0.01895)
The uncertainty in ΔpH is ± 8.48E-04 [C]
• Calculated changes in the stability constants: [D]
Δlog(K0*): +0.00090 ± 4.79E-04, Δlog(K1*): +0.02388 ± 8.52E-04,
Δlog(K2*): +0.01770 ± 8.87E-04
Uncertainty contributions Uncertainty contributions to Δlog(K0*) (%): to Δlog(K1*) (%): 59.63 a theta(Cl,HCO3) 67.81 ln[K(HSO4)] 5.35 a psi(Cl,HCO3,Na) 13.90 BC(H,Cl) 16.54 BC(Na,HCO3) 7.11 a theta(Cl,HCO3) 6.81 BC(Mg,Cl) 0.64 a psi(Cl,HCO3,Na) 4.37 theta(Cl,CO3) 3.32 b theta(H,Na) 3.45 BC(Na,CO3) 0.28 b psi(H,Na,Cl) 3.29 BC(Na,Cl) 2.96 BC(Na,Cl) 0.30 theta(Na,Mg) 1.88 c theta(Cl,SO4)
Uncertainty contributions Calculated stability constants to Δlog(K2*) (%): at S = 35.000 (standard seawater) 62.59 ln[K(HSO4)] log(K0*) = -3.56165 ± 2.12E-05 12.83 BC(H,Cl) log(K1*) = -13.46357 ± 2.98E-04 6.56 a theta(Cl,HCO3) log(K2*) = -20.64487 ± 1.19E-03 0.59 a psi(Cl,HCO3,Na) 5.57 BC(Mg,Cl) 3.07 b theta(H,Na) 0.26 b psi(H,Na,Cl) 2.73 theta(Cl,CO3)
• Individual solute species concentrations (mol kg−1 solution): [E]
H = 6.1722E-09 CL = 5.2272E-01 BOH3 = 3.1748E-04 NA = 4.5707E-01 SO4 = 3.3902E-02 CO2 = 9.5037E-06 MG = 5.2700E-02 HSO4 = 2.1300E-09 HF = 1.4391E-10 CA = 1.0257E-02 OH = 3.5967E-06 MGCO3 = 1.1266E-04 K = 1.0213E-02 BR = 8.4259E-04 CACO3 = 2.8726E-05 MGOH = 4.0484E-06 HCO3 = 1.7157E-03 SRCO3 = 1.7557E-07 SR = 9.0570E-05 CO3 = 1.0065E-04 MGF = 2.9943E-05 BOH4 = 9.7924E-05 CAF = 1.7490E-06 F = 3.6657E-05
The program calculates the change in seawater pH, and in the three log(K*) of the carbonate system, caused by a change in the solution composition (relative to that of standard seawater at the input salinity). This is useful for determining the influence of natural water composition on carbonate equilibria, and for the calculation of pCO2 and saturation with respect to calcium carbonate minerals.
The list of the main individual uncertainty contributions to each calculated Δlog(K*) shows where research effort should be focused to improve the model and make it more accurate for this particular composition. The chemical symbols, in parentheses, indicate relevant 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.
The literature values of each of the measured log(K*) for the input T and S are also shown.
The calculated individual species concentrations include a number of ion pairs (e.g., MgOH+) that are defined within the seawater model that is used.
See the notes regarding the current state of development of the treatment of uncertainties.
First, here is a reminder of the definitions of the three K* values for the equilibria of the carbonate system in seawater, and between gas phase and dissolved CO2:
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).
[A] The base standard seawater (input by the user), before adjustment of the composition.
[B] This is the list of changes to the buffer composition that were selected: a decrease in Na+ molality by 5% (by removing NaCl), and an increase in SO42− molality by 20% by the addition of Na2SO4. These changes are made by adding/removing salts, rather than individual ions, in order to preserve overall charge neutrality. The molality of Cl− is affected, and this change is listed. The net change in Na+ molality from the subtraction of NaCl and the addition of Na2SO4 is -2.592%. This approach to varying solution composition was chosen, for this demonstration program, because of its simplicity.
[C] The model-calculated pH for the base (unaltered) seawater is 8.100 ± 0.0136, and for the modified composition it is 8.081. Notice that, although the uncertainty in the calculated pH value is about 0.014, the uncertainty in the calculated change in pH is very much less, only about ± 8.5 × 10−4.
[D] This section lists, first, the calculated changes in log(K0-2*) going from the base standard seawater to the altered composition. The estimated uncertainty in each Δlog(K*) is also given. Beneath these values are the top contributions to each of the estimated uncertainties, expressed as percentages of the total variances. This information is useful for speciation model development: it identifies those elements of the model (ion-ion interactions, thermodynamic equilibrium constants) which, if improved and made more accurate, will do most the reduce the overall uncertainty in predicted values of the log(K*).
For example, the first quantity listed for both Δlog(K1*) and Δlog(K2*) is the thermodynamic equilibrium constant for HSO4−. This is not surprising: the SO42− concentration is being altered, and the [H+] term in the equations for K1* and K2* above is a total value equal to the sum of the concentrations of free H+ and HSO4−. The letters 'a', 'b', etc. identify groups of co-varying Pitzer interaction parameters (note that uncertainty contributions of all members of the groups are plotted, even where some individual values may be small). For example, the interaction parameters theta(H,Na) and psi(H,Na,Cl) are treated as co-varying, because their values are determined simultaneously from data for aqueous HCl/NaCl mixtures.
The last group of values in this section is the set of log(K*) for standard seawater at the T, S, and P that were input. The equations for these values are taken from chapter 5 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).
This example calculation illustrates an important point: The majority of the variances in the calculated Δlog(K*) are accounted for by the contributions of relatively small numbers of interactions and equilibrium constants. This means that significant improvements in the model can be made by focusing work on a small number of chemical systems.
[E] These are the calculated concentrations (in mol per kg of solution) of the individual chemical species in the seawater of altered composition. 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).