Compatibility of activity coefficients estimated experimentally and by Pitzer equations for the assessment of seawater pH

Abstract

Calibration of pH meters is usually performed with reference pH buffer solutions of low ionic strength, I ≤ 0.1 mol kg−1. For seawater pH measurements (I ≈ 0.7 mol kg−1), calibration buffers in high ionic strength matrix are required. The Harned cell, in association with the Nernst equation and a model for estimating the chloride ion activity coefficient, \(\gamma_{{{\text{Cl}}^{ - } }} ,\) is the basis of the primary method for pH assignment to reference pH buffers. The semi-empirical Pitzer model is, in principle, adequate to estimate \(\gamma_{{{\text{Cl}}^{ - } }}\) of complex solutions, namely seawater. Nevertheless, no assessment of the validity of the model for this matrix is known to the authors. This work aims at estimating the adequacy of the Pitzer model by assessing the metrological compatibility of mean activity coefficients, in this case \(\gamma_{ \pm } = \sqrt {\gamma_{{{\text{H}}^{ + } }} \gamma_{{{\text{Cl}}^{ - } }} }\) estimated experimentally with the Harned cell, \(\gamma_{ \pm }^{\text{Exp}} ,\) and using the Pitzer model, \(\gamma_{ \pm }^{\text{Ptz}}\). The measurement uncertainty considered in the compatibility test was estimated using the bottom-up approach, where components were combined by the numerical Kragten method after checking its adequacy. The compatibility of the estimated \(\gamma_{ \pm }\) was assessed for solutions with increasing complexity and an ionic strength of 0.67 mol kg–1. \(\gamma_{ \pm }^{\text{Exp}}\) and \(\gamma_{ \pm }^{Ptz}\) are metrologically compatible for a confidence level of 95 % where the relative standard uncertainty of their difference ranged from 1.1 % to 3.1 % in all chloride solutions to approximately 6.3 % when sodium sulfate was also present. This led to assume the validity of the Pitzer model equations to estimate \(\gamma_{{{\text{Cl}}^{ - } }} ,\) required to define reference pH values of buffer solutions with high ionic strength.