Rate Equations and an Ion-pair Mechanism for Batch Dissolution of Gypsum: Repositioning the Shrinking Object Model at the Core of Hydrodynamic Modelling

Abstract

Recent improvements to experiments and modelling of batch dissolution in a turbulent reactor, based upon the shrinking object model, are extended to middle loadings of gypsum, that is, in the region between low and high loadings, which lead, respectively, to high under-saturation or saturation with a great excess of solid left undissolved. Dissolved calcium sulphate concentration was monitored by change in electrical conductivity. This investigation uses an improved, ion-pair model for CaSO 4 0 to allow for the presence of calcium or sulphate added as common ions. The study demonstrates that the full dissolution curve for 5.82 mM loadings of 106-lm particles of gypsum (*1.00 g L -1 ) in de-ionised water barely changed in the presence of either 4.64 or 8.09 mM calcium chloride, or 4.39 mM sodium sulphate. However, this masked a doubling of dissolution rate imposed by comparable increases in ionic strength from sodium chloride. The results are consistent with the ion pair, CaSO 4 0 , being the key species in the rate-determining step of the back-reaction, and perhaps all salt dissolutions, including calcium carbonate. In this case, the rate equation is as follows:where k 1 and k 2 0 are rate constants. The reported observations are interpreted as effects of ionic strength and common ion concentrations upon the formation equilibrium for the ion pair. This rate equation readily transforms mathematically to one involving the product of [Ca 2? ] and [SO 4 2-] in the back-reaction. The parallel of this with the well-known PWP equation used in calcium carbonate dissolution is discussed, with the CaHCO 3 ? ion pair of the equation being replaced by that of CaCO 3 0 . Meanwhile, the earlier use of the product, [Ca 2? ] 9 [CO 32-] , in the back-reaction term of another dissolution rate equation for calcite is shown to be incorrect. Finally, it is argued that the shrinking object model should be repositioned as a logical derivative of the hydrodynamical approach to dissolution.

Unifying Batch-Dissolution Kinetics for Salts: Probing the Back Reaction for Gypsum and Calcite by Means of the Common-Ion Effect

“…This contrasts with earlier results (Truesdale 2011b) that did not completely follow the Solubility Product rule as in Fig. 1 (key empirical finding 3).…”

“…The curves confirm that the same amount of gypsum (0.00582 M) dissolved in the two runs; these runs remained unsaturated. With the c sat values shown in Table 3, the linearised shrinking object model (Truesdale 2011b) fitted well to all of the plots, with the coefficient of determination (r 2 ) between 0.990 and 0.999 for 16-26 df (Table 3). There was a small, but nevertheless discernible, upwards curvature in the linearised data for the two runs at the highest initial calcium concentration, whence the intercepts for the fitted lines were forced about 3% below the origin.…”

“…When comparing solutions with different terminal loadings of solute, c T , it is useful to rationalise this parameter (to a constant loading) to give the more fundamental variable, the shrinking object rate constant, a Ka R (Truesdale 2011b). This is not actually carried out here as all the measurements are made with a constant loading of gypsum.…”

“…The concentration-time data collected from each run were introduced into the linearised version of the shrinking object model (Truesdale 2011b), the gradient of which yielded the shrinking object rate parameter a Ka . In this study, the testing of the viability of the modelling approach is the objective, and not information specific to gypsum.…”

Pilot-scale passive bioreactors for the treatment of acid mine drainage: Efficiency of mushroom compost vs. mixed substrates for metal removal

“…Such a release of sulfate from mushroom compost was also reported in a previous study (31.1 g kg À1 ; Guo et al, 2001). The potential source of sulfate in the mushroom compost could be either cow manure or gypsum (CaSO 4 2H 2 O), or both, since the former is a base material of mushroom compost and the dissolution of the latter can be enhanced through an ion-pair mechanism and the common ion effect (Truesdale, 2011). In a previous study, as much as 7 g kg À1 of sulfate was found to originate from a composted poultry manure substrate (Zagury et al, 2006).…”