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This paper continues the search for a reliable, solution-based, rate equation for mineral dissolution, as the one dominant for over 40 years has recently been challenged by the Shrinking Object (SO) model. This study is needed to remedy several major environmental problems of immense social and economic importance including climate change, ocean acidification and industrial waste disposal. This paper describes the preliminary investigation of how reactors open and closed to CO2, which are used to study calcite dissolution, ought to be used with the SO model to gain maximum advantage. The open reactor is re-conceptualised as a constant head device for dissolved inorganic carbon, to give the kineticist a mechanistic description of it, to flesh out the thermodynamic categorisation. Application of this reveals that the recent experiments conducted in a reactor blown with CO2-free N-2, which were central to the establishment of the concept of non-ideal dissolution of calcite, would have exaggerated the effect. Although this current study was still unable to determine conditions where the effect was absent, it does seem that it will be possible to skirt around this in the future, by approximating the classic works on the variation with pH of the initial rate of dissolution to full reaction curves from the SO model, which are exponential. To guide workers towards a further round of laboratory investigation on this, practical work on the dissolution of calcite crystallites in 0.311 M Tris buffer at pH 8 or 9, under various partial pressures of CO2, in different reactors, and under various stirring and filtration strategies, is presented. Improved data runs, with unparalleled, strategically-spaced samplings, which show up the finer details of dissolution, can now be anticipated.