Chemical speciation models based upon the Pitzer activity coefficient equations, including the propagation of uncertainties: Artificial seawater from 0 to 45 °C

Matthew P. Humphreys, Jason F. Waters, David R. Turner, Andrew G. Dickson, Simon L. Clegg

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Accurate chemical speciation models of solutions containing the ions of seawater have applications in the calculation of carbonate system equilibria and trace metal speciation in natural waters, and the determination of pH. Existing models, based on the Pitzer formalism for the calculation of activity coefficients, do not yet agree with key experimental data (potentiometric determinations of H+ and Cl− activity products in acidified artificial seawaters) and, critically, do not include uncertainty estimates. This hampers applications of the models, and also their further development (for which the uncertainty contributions of individual ion interactions and equilibrium constants need to be known). We have therefore implemented the models of Waters and Millero (Mar. Chem. 149, 8-22, 2013) and Clegg and Whitfield (Geochim. et Cosmochim. Acta 59, 2403-2421, 1995) for artificial seawater, within a generalised treatment of uncertainties, as a first step towards a more complete model of standard seawater and pH buffers. This addition to the model enables both the total uncertainty of any model-calculated quantity (e.g., pH, speciation) to be estimated, and also the contributions of all interaction parameters and equilibrium constants. Both models have been fully documented (and some corrections made). Estimates of the variances and covariances of the interaction parameters were obtained by Monte Carlo simulation, with simplifying assumptions. The models were tested against measured electromotive forces (EMFs) of cells containing acidified artificial seawaters. The mean offsets (measured – calculated) at 25 °C for the model of Waters and Millero are: 0.046 ± 0.11 mV (artificial seawater without sulphate, 0.280 mol kg−1 to 0.879 mol kg−1 ionic strength); and − 0.199 ± 0.070 mV (artificial seawater, salinities 5 to 45). Results are similar at other temperatures. These differences compare with an overall uncertainty in the measured EMFs of about 0.04 mV. Total uncertainties for calculated EMFs of the solutions were dominated by just a few contributions: mainly H+-Cl−, Na+-Cl−, and H+-Na+-Cl− ionic interactions, and the thermodynamic dissociation constant of HSO4−. This makes it likely that the accuracy of the models can readily be improved, and recommendations for further work are made. It is shown that standard EMFs used in the calibration of the marine ‘total’ pH scale can be accurately predicted with only slight modification to the original models, suggesting that they can contribute to the extension of the scale to lower salinities.
Original languageEnglish
Article number104095
JournalMarine Chemistry
Early online date12 Feb 2022
Publication statusPublished - 20 Jul 2022


  • Activity coefficient
  • Chemical speciation
  • Seawater
  • pH

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