Ginstling-Brounshtein equation

Fig. 3. Reduced time plots, tr = (t/t0.9), for the contracting area and contracting volume equations [eqn. (7), n = 2 and 3], diffusion-controlled reactions proceedings in one [eqn. (10)], two [eqn. (13)] and three [eqn. (14)] dimensions, the Ginstling— Brounshtein equation [eqn. (11)] and first-, second- and third-order reactions [eqns. (15)—(17)]. Diffusion control is shown as a full line, interface advance as a broken line and reaction orders are dotted. Rate processes become more strongly deceleratory as the number of dimensions in which interface advance occurs is increased. The numbers on the curves indicate the equation numbers.

Equations (7) and (8) both apply to a sphere. j3 is the ratio of product volume to reactant volume in the layer of product through which diffusion takes place. When 3 = 1, (8) reduces to eqn. (7). This should be the case if reduced material retains its gross geometry, with pores produced in it to account for the entire decrease in volume upon reaction. Equation (7) is known as the Ginstling—Brounshtein equation eqn. (8) is Carter s modification of it [88] and must be used if there is a volume increase on reaction. This does not often happen in reductions, but can occur in other types of reaction [89]. 

When z approaches unity, equation (3.9) reduces to the Ginstling-Brounshtein equation [65] ... 

D, [l-(2/3)a]-(l- ) = Af Three-dimensional diffusion, spherical symmetry, Ginstling-Brounshtein equation... 

The kinetics of the reaction between strontium carbonate and anatase were found to be described by the Ginstling-Brounshtein equation. 

Isothermal TG studies [33] of the thermal decompositions in Nj of BaOj (763 to 883 K) and SrOj (653 to 803 K) showed overall deceleratory kinetics described by the Ginstling-Brounshtein diffiision model (low a) and the first-order equation at higher nr values, is, values were 185 5 kJ mol for BaOj and 119 2 kJ mol for SrO. Non-isothermal kinetic analyses gave similar is, values for both decompositions (165 5 kJ mol ). It is suggested [33] that the rate of removal of oxygen from the peroxide by diffusion could be drastically altered by the formation of a crystalline layer of oxide on the reactant surface. 

On the basis of TG-curves, Coats-Redfem calculation procedure and the equation of Ginstling-Brounshtein calculated the kinetics parameters, characterizing nonisothermal degradation of rice husks in air or nitrogen atmosphere [70], and the obtained data are summarized in Table 13.2. 

The applicability of the Ginstling-Brounshtein rate equation to this reaction indicates that the mechanism of the reaction consists of the formation of a coherent product layer around one of the reactants with unidirectional diffusion of the other reactant as the rate-controlling step. To determine the mobile species in the reaction an inert marker study was made ( ). Disks of the reactant materials were pressed and platinum markers placed in the anatase so that they were flush with the surface of the disk. Strontium... 

Answer During an actual firing schedule the rate constant / is a function of time. What this means is that all of the solid-state rate equations (Jander, Ginstling-Brounshtein, etc.) which are normally applied for constant k can be used, but the product kt must be replaced by an average product designated kt and given by the equation... 

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