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A New Analytic Integration of the Rate Equation for Batch Dissolution of Salts in the Presence of Common Ion

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Abstract

Following a recent suggestion of a new rate equation specifically for the batch dissolution of salts in solutions containing a common ion, this paper describes an analytic solution to its integration. The equation has been tested by dissolving 250 μm gypsum- rock particles in water (26.7 g l−1) containing various mixtures of sodium and calcium chlorides, all at an ionic strength of 0.060 M. The model fitted the experimental curves very well and showed that the dissolution slowed slightly overall when the initial calcium concentration was increased from 0 to 0.020 M. The dissolution curves were also modelled as a simple exponential, whence the fit was comparable to that with the new equation, with the exponential rate constant varying between 0.025 and 0.019 (±0.0004) for 0 and 0.020 M initial calcium concentration, respectively. Conventional Electrolyte theory from thermodynamics is used to show that the new equation is an inevitable consequence of modelling the net rate of dissolution in terms of a back reaction that is first order with respect to the dissolved substance, as per the recently described Shrinking Object model. Moreover, it is shown how the simple exponential model (which is a well-used plot in dissolution kinetics) provides the linear end-member to an infinite number of curvilinear plots of rate of dissolution versus reaction progress developed by the new model—it is the special case where common ion is absent. The results are now judged good enough to identify a generic batch dissolution rate equation for all salts dissolving without significant complication from either contaminants or their own gaseous species, as in calcium carbonate dissolution.

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Acknowledgments

Thanks go to Professors Heinz Gamsjäger and Mike Whitfield for long-standing discussions of the thermodynamics within this project. Stephen Casterton, Regional Technical Services Manager, BPB, Newark, UK, who supplied the gypsum rock, is also thanked greatly. We thank the referees for their efforts in improving the original manuscript.

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  1. School of Life Sciences, Oxford Brookes University, Gipsy Lane, Headington, Oxford, OX3 0BP, UK

    Victor W. Truesdale

  2. Faculty of Technology, Design and Environment, Oxford Brookes University, Wheatley Campus, Oxford, OX33 1HX, UK

    Cristiana Sebu

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  1. Victor W. Truesdale
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Correspondence to Victor W. Truesdale.

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Truesdale, V.W., Sebu, C. A New Analytic Integration of the Rate Equation for Batch Dissolution of Salts in the Presence of Common Ion. Aquat Geochem 19, 39–56 (2013). https://doi.org/10.1007/s10498-012-9177-0

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  • DOI: https://doi.org/10.1007/s10498-012-9177-0

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