Response to Comments upon, “Evidence and potential implications of exponential tails to concentration versus time plots for the batch dissolution of calcite”

Abstract

where k2 is the rate constant of the back-reaction to dissolution, csat and c are concentrations of solute at saturation and any time, t, respectively, and the apparent surface area is a time-dependant function of time, A(t). Note that in the calcite experiments of Truesdale (2015), the actual surface area was constant. Note also that the rate constant of the forward reaction, k1, does not appear in the rate equation (Eq. 1) because this is a complex reaction in which the forward reaction and back-reaction are tied together, analogously to a bolas (Truesdale 2015). The discussion paper had three objectives. Firstly, to launch the hypothesis that new and re-worked results, together with an extended Shrinking-Object model, might explain the very long reaction times needed for saturation to be reached in batch dissolutions of calcite. Secondly, to explain that the hypothesis could have been formed around 1975, had the rigour of kinetics of that time (Lewis 1974), defined in Truesdale (2015) as Empirical Kinetics (Fig. 1), been consistently applied to mineral dissolution, generally. Thirdly, to show that the hypothesis might even cover the more complex examples of silicate and alumino-silicate mineral dissolutions as they too had not been investigated under Empirical Kinetics. Such a universal solution is badly needed if modelling of calcite behaviour in the environment at the large scale, e.g. the oceanic water column (e.g. Morse et al. 2007), and the catchment (e.g. Buhmann and Dreybrodt 1985),