Evidence and Potential Implications of Exponential Tails to Concentration Versus Time Plots for the Batch Dissolution of Calcite

Abstract

Calcite batch dissolution kinetics behaviour has been described as complex for more than half a century. The dissolution of 100-to 250-lm particles of natural calcites at 20-35°C in Tris buffer or alkali at pHs 8-10.6 reveals that the non-ideal, long tails to the plot of calcium concentration versus time, are probably exponential. Equivalent alternative evidence from elsewhere for both calcite and gypsum is supplied. Inadequate kinetics templating of earlier results is believed to have obscured this exponential character, but rectification could induce a renaissance for batch dissolution study of calcite as well as for silicate and aluminosilicate minerals, too. The work extends a programme of study of the shrinking object (SO) model which has already considered a variety of substances such as sucrose, sodium chloride, gypsum, and silica gel, through which it has operationally defined ideal dissolution as an exponential rise in concentration with time, at high solids loadings. The SO model is limited to a constant surface area of the solid during dissolution. However, the possibility of explaining non-ideal dissolution of calcite by including a reduction in the apparent surface area during a dissolution, is explored here. In this the model shifts from an initial mode under one reaction rate constant to a terminal mode under a second rate constant, and by this the SO model is shown to share properties with a decelerating bolas-the South American hunting tool. The bolas model is consistent with earlier suggestions elsewhere that non-ideality arises from the surface being either poisoned or otherwise changed during dissolution. This current investigation derives from Empirical Kinetics, which is defined here as the wisdom of kinetics collected by the middle of the last half of the twentieth century. With the preliminary success gained with the exponential tails, the paper overcomes much confusion in the literature by differentiating direct measurements of rates of dissolution made for the purposes of chemical kinetics, from those needed for biogeochemical field purposes.

Dissolution Processes at Step Edges of Calcite in Water Investigated by High-Speed Frequency Modulation Atomic Force Microscopy and Simulation

“…In previous studies, several dissolution models [5][6][7][8][9] have been proposed to explain the experimental results obtained by the macroscopic elemental analyses 5,6 and nanoscale step flow measurements 7,8,[10][11][12] . Based on these models and semi-empirically determined parameters, Monte Carlo simulations successfully predicted dissolution processes under various conditions 9,12,13 .…”

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

“…My discussion paper, Truesdale (2015), seized on the possibility of extending the Shrinking-Object model rate equation to Eq. 1:…”

“…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, k 1 , does not appear in the rate equation (Eq.…”

“…Note also that the rate constant of the forward reaction, k 1 , 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.…”