Explanation of pH Buffer Program Output (Simple Buffer)

Here we explain the results of a calculation of the pH of a Tris buffer in a medium of S = 35 artificial seawater at 25 oC.

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 (for the simple buffer) 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 of an Artificial Seawater Buffer     

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

• Calculated pH: 8.059 ± 0.0082        [B]

• Defined pH (from measurements): 8.073 ± 0.0009 (Dickson)        [C]

• Contributions to the uncertainty in calculated pH (%):            [D]

  33.91    ln[K(HSO4)]                    0.01  b psi(Cl,SO4,Mg)
  23.86    BC(H,Cl)                       1.63    ln[K(Tris)]
  22.50    BC(TrisH,Cl)                   1.28    BC(Na,HSO4)
   7.14  a theta(H,Na)                    1.04  c theta(Cl,HSO4)
   0.38  a psi(H,Na,Cl)                   0.04  c psi(Cl,HSO4,Na)
   2.86    BC(Na,SO4)                     0.76    BC(TrisH,SO4)
   2.02  b theta(Cl,SO4)                  0.64    BC(Na,Cl)
   0.07  b psi(Cl,SO4,Na)                 0.61    BC(H,SO4)

• Individual solute species concentrations (mol kg−1 pure water):        [E]

      H =  6.7438E-09                    TRISH =  4.0007E-02
     NA =  4.4618E-01                       CL =  5.6920E-01
     MG =  5.4736E-02                      SO4 =  2.9270E-02
     CA =  1.0750E-02                     HSO4 =  1.9915E-09
      K =  1.0580E-02                       OH =  3.5412E-06
   MGOH =  3.8910E-06                     TRIS =  3.9993E-02
Notes

This, the simplest use of the program, demonstrates: (a) how closely the measured buffer pH can be predicted by the chemical speciation model; (b) the major contributors to the uncertainty in the calculated value.

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(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.


What The Output Means

[A] The properties of the base seawater buffer (input by the user), before adjustment of the composition.

[B] The model-calculated pH for this seawater buffer is 8.059 ± 0.0082. Notice that the pH differs from that defined from measurements (the next item in the output), and the uncertainty is larger. Work needs to be done to improve agreement.

[C] The defined pH for this seawater buffer, based on measurements using Harned cells, is 8.073 ± 0.001. The values in this demonstration program come from Dickson (Deep Sea Res. I, 40, 107-118, 1993) for 30 ≤ S ≤ 40 (and 5 to 40 oC) and from Muller et al. (Front. Mar. Sci. 5, art. 176, 2018) for all other salinities that are within the range 5 ≤ S ≤ 40 (and 5 to 45 oC).

[D] 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 "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 top percentage contributions of different interactions to the total variance in ΔpH (values >0.1% only).

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 (0.38 %) is much less than that of theta(H,Na) (7.14%).

A key feature of the result is that most of the uncertainty is accounted for by just three contributions: the uncertainty in the dissociation constant of HSO4− (ln[K(HSO4)]), and the interactions of Cl− ion with H+ and TrisH+. This result is consistent with comparisons of model-calculated hydrogen ion activities with measured values in acidified artificial seawater. It suggests that the model of the pH buffer can be greatly improved by focusing effort on the top contributions in list.

[E] These are the calculated molalities of the individual chemical species in the buffer. The definition of pH on the total scale is: pH = -log10(mH+ + mHSO4−). In this buffer solution the molality of HSO4− is about 1/3 of that of free H+. (The buffer contains artificial seawater made to the recipe of Dickson (ref. above), with 0.04 mol kg−1 of TrisH+ substituted for Na+, and 0.04 mol kg−1 of Tris added.)