Spectrophotometric determination of bicarbonate dissociation constants (K2) for freshwater, estuarine, and marine waters over a wide range of temperatures

This study presents the first spectrophotometric determination of K₂ at estuarine conditions (0 ≤ S_P ≤ 20; where S_P is practical salinity) and over a broad range of temperatures (275.15 ≤ T ≤ 308.15 K; where T is temperature in Kelvin). Spectrophotometric data from Schockman and Byrne (2021) and Schockman et al. (2024) were combined with data obtained in the present study to produce a set of pK₂ (i.e., pK₂ = – log K₂) values for the salinity range 0 ≤ S_P ≤ 41 and temperature range 275.15 ≤ T ≤ 308.15 K. The resulting set of pK₂ values was fitted as a function of S_P and T to obtain a new pK₂ parameterization on the total pH scale:

pK₂ = 5.1703 + 2136.77 T⁻¹ – 177788 T⁻² – 0.4457 S_P^0.5/(1 + 1.11 S_P^0.5) + 0.0674 S_P/lnT – 0.0008238 S_P^0.5 T.

The random uncertainty in this work is 0.0071 based on the standard deviation of the best-fit pK₂ parameterization. Residuals in the fit (i.e., measured minus parameterized pK₂ values) are approximately two times smaller in magnitude than the residuals obtained in past studies for similar S_P and T ranges. The total combined standard uncertainty of pK₂ in this work is 0.0145. Assessments of high-quality total dissolved inorganic carbon (C_T), total alkalinity (A_T), and pH data obtained on oceanic research cruises indicate that internal consistency of CO₂ system calculations (comparing measured and calculated values; e.g., comparing measured pH with pH calculated from C_T and A_T) is improved when calculations use this K₂ parameterization, especially for the Coastal Ocean Data Analysis Product in North America (CODAP-NA) data set (0.117 ≤ S_P ≤ 36.980). As such, this new pK₂ parameterization provides an improved characterization of bicarbonate dissociation constant behavior that encompasses freshwater, estuarine, and open ocean conditions.