Here we explain the results of a calculation of the change in pH of a Tris buffer in a medium of S = 35 seawater at 25 oC, for which the Na+ molality (mol per kg pure water) has been increased by 2.1%, and Mg2+ molality decreased by 3.0%, by the addition/subtraction of the chloride salts. (The molality of Cl− is also altered, of course.)
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 salinity and temperature for the base buffer composition.
• Temperature: 25.00 °C, Salinity: 35.00, Pressure: 1.0 atm (fixed) [A]
• Buffer composition has been altered as follows: [B]
Na by +2.100% by adding NaCl Mg by -3.000% by removing MgCl2 Cl by +1.069% (by changing NaCl, MgCl2)
• This changes the calculated pH from 8.059 ± 0.0082 to 8.060 (ΔpH = 0.00152) [C]
The uncertainty in ΔpH is ± 7.63E-05 [D]
• Contributions to the uncertainty in calculated ΔpH (%): [E]
33.80 a theta(H,Na) 0.19 b psi(Cl,SO4,Na)
2.73 a psi(H,Na,Cl) 0.03 b psi(Cl,SO4,Mg)
15.01 BC(H,Cl) 2.11 lambda(Tris,Na)
15.01 BC(TrisH,Cl) 1.78 BC(Mg,SO4)
10.47 BC(Na,SO4) 1.11 c theta(H,Mg)
5.55 BC(Mg,HSO4) 0.02 c psi(H,Mg,Cl)
4.30 BC(Na,Cl) 0.88 d theta(Cl,HSO4)
4.05 BC(Na,HSO4) 0.12 d psi(Cl,HSO4,Na)
1.91 b theta(Cl,SO4)
• Individual solute species concentrations (mol kg−1 pure water): [F]
H = 6.7217E-09 TRISH = 4.0007E-02
NA = 4.5555E-01 CL = 5.7529E-01
MG = 5.3094E-02 SO4 = 2.9270E-02
CA = 1.0750E-02 HSO4 = 1.9830E-09
K = 1.0580E-02 OH = 3.5392E-06
MGOH = 3.7724E-06 TRIS = 3.9993E-02
Here the program calculates the change of buffer pH caused by a change in the solution composition (relative to that of artificial seawater). This is useful for: (a) measuring pH of natural waters that depart from seawater stoichiometry; (b) extending the pH scale to low salinity waters, and compensating for the effect of the buffer substance itself on H+ in the dilute solution medium.
The list of uncertainty contributions to the calculated ΔpH, show 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 the ion interactions in the speciation model and ln[K(..)] are thermodynamic equilibrium constants. Examples: BC(TrisH,Cl) – the thermodynamic properties of aqueous TrisHCl; 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 the notes regarding the current state of development of the treatment of uncertainties.
[A] The properties of the base seawater buffer (input by the user), before adjustment of the composition.
[B] This is the list of changes to the buffer composition that were selected: first, an increase in Na+ molality by 2.1% (by adding NaCl); second a decrease in Mg2+ molality by the removal of MgCl2. These changes are made by adding/removing salts, rather than individual ions, in order to preserve overall charge neutrality. Consequently, the molality of Cl− has also been affected, and the change is listed. 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 buffer is 8.059 ± 0.008 and for the modified composition it is 8.060, an increase of only 0.00152. This change is very small.
[D] This is the calculated uncertainty in the change in buffer pH brought about by the change in solution composition noted above. Notice how this figure (± 7.63 × 10−5) is much less than the uncertainty in the pH itself (±0.0082 for the base composition). The model is able to calculate the uncertainty of the change in pH arising from an alteration of buffer composition more accurately than the uncertainty in the pH itself (although, of course, the value of ΔpH is very much less than pH).
[E] This section is mainly of interest to chemical speciation modellers. The calculation of pH uses thermodynamic equilibrium constants (chiefly those for of TrisH+/Tris and HSO4−/SO4− in this case), and sets of Pitzer ion interaction parameters that express the influence of the major seawater ions on the activity coefficients of H+, TrisH+, HSO4−, etc. The numbers in this section are the percentage contributions of different interactions to the total uncertainty in ΔpH (values >0.1% only).
For example, the first interaction listed – contributing almost 34% of the total variance – is that of the Na+ ion on H+ (via the parameter theta(Na,H)). This is not suprising: the higher the concentration of the ion, the greater its influence. The letters 'a', 'b', etc. identify groups of co-varying Pitzer interaction parameters. The listed uncertainty contributions are ranked by the total for each group, and all individual contributions are listed. Hence, for example, parameters theta(Na,H) and psi(H,Na,Cl) co-vary (their values are determined simultaneously from data for aqueous HCl/NaCl mixtures), and it can be seen that the contribution of psi(H,Na,Cl) to the total variance (2.73 %) is much less than that of theta(H,Na) (33.8 %).
These calculations illustrate two important points:
First, the majority of the variance in the calculated ΔpH is accounted for by a relatively small number of interactions, about 5 in this case. This means that significant improvements to the model can be made by focusing work on a relatively small number of chemical systems.
Second, a calculation for just the base seawater buffer shows that that largest single contributor to the uncertainty in the calculated pH comes from the thermodynamic dissociation constant of HSO4−. In this calculation, in which the molality of SO42− is not varied, the contributions of an error in the value of K(HSO4−) to ΔpH cancel.
[F] These are the calculated molalities of the individual chemical species in the buffer. The definition of pH on the total scale, and a molality basis, is: pH = -log10(mH+ + mHSO4−). In this buffer solution the molality of HSO4− is about 1/3 of that of free H+.