Experimental and Theoretical Study of the Surface-Controlled Dissolution of Cylindrical Particles. Application to Solubilization of Potassium Hydrogen Carbonate in Hot Dimethylformamide

Abstract

In this paper we present a mathematical model for the surface-controlled dissolution of cylindrical solid particles. This is employed to interpret experimental data published previously for the dissolution of potassium bicarbonate in dimethylformamide at elevated temperatures. Significant kinetic differences in assuming cylindrical rather than spherical shapes are reported with the former representing a closer approximation to the true shape of the particles as revealed by scanning electron microscopy. From the fits of experimental data to the cylindrical model for the surface-controlled dissolution, the dissolution rate constant, k, for the dissolution of KHCO(3) in DMF was found to be (9.6 +/- 1.6) x 10(-9) mol cm(-2) s(-1) at 100 degrees C, and the activation energy for the dissolution was 34.5 kJ mol(-1) over the temperature range of 60-100 degrees C. Comparison between cylindrical and spherical dissolution theory highlights the importance of considering the particle shapes for realistic modeling of surface-controlled dissolution kinetics.

Comparative solubilisation of potassium carbonate, sodium bicarbonate and sodium carbonate in hot dimethylformamide: application of cylindrical particle surface-controlled dissolution theory

“…In the kinetic treatment of the dissolution of cylindrical solid particles developed in a previous paper, 18 the number of moles of solid remaining undissolved in solution over time is modelled.…”

“…17 are analysed using the model developed for the surface-controlled dissolution of cylindrical particles model. 18 Eqn (2) was solved numerically to develop plots of the number of moles of undissolved solid, n(t)/mol against time/s to compare the cylinder theory with experiment. The following parameters were used: mass of the inorganic solid/g, density of the solid/g cm À3 , molecular weight of the solid/g mol À1 , time/s, k/mol cm À2 s À1 , cylindrical particle diameter number distribution function, f(d), (Fig.…”

“…Table 2 displays the mean values of the dissolution rate constant, k, determined, employing the surface-controlled dissolution of cylindrical particles model, for the dissolution in DMF at 100 1C of the inorganic solids; KHCO 3 , NaHCO 3 , K 2 CO 3 and Na 2 CO 3 . As originally defined 18 for the surfacecontrolled dissolution of the inorganic solids in solution, the rate of change of the number of moles of solid particle remaining undisssolved in solution with time is proportional to the dissolution rate constant, k, and the particle surface area. Clearly the dissolution of K 2 CO 3 is faster, approximately by a factor of ten, than that for the other inorganic solids studied.…”

“…In previous papers we reported the surface-controlled dissolutions of KHCO 3 and K 2 CO 3 in dimethylformamide (DMF) at elevated temperatures. Two theoretical models have been developed, the first for the dissolution of spherical solid particles 16,17 and secondly for the dissolution of cylindrical particles 18 A comparison between the theories was used to show the influence of particle shape on the dissolution kinetics of a solid and hence the importance of knowing the shape of the individual solid particles for realistic modelling of their dissolution. Both surface-controlled dissolution models were successfully applied to experimental results for the dissolution of KHCO 3 in DMF and values for the dissolution rate constant, k, determined.…”

Electrochemical and sonoelectrochemical monitoring of indigo reduction by glucose

“…The surface area of the particulate and highly water insoluble indigo is therefore controlling the rate of dissolution. Dissolution reactions have been treated in the literature for example for spherical [24] or for cylindrical particles [25]. Here, indigo particles are assumed to be spherical and uniformly sized (for simplicity) and the rate law for the reductive dissolution of indigo to leuco-indigo in the presence of excess glucose is given by Eq.…”