Kinetic rate equation, contracting area

The (en) compound developed nuclei which advanced rapidly across all surfaces of the reactant crystals and thereafter penetrated the bulk more slowly. Kinetic data fitted the contracting volume equation [eqn. (7), n = 3] and values of E (67—84 kJ mole"1) varied somewhat with the particle size of the reactant and the prevailing atmosphere. Nucleus formation in the (pn) compound was largely confined to the (100) surfaces of reactant crystallites and interface advance proceeded as a contracting area process [eqn. (7), n = 2], It was concluded that layers of packed propene groups within the structure were not penetrated by water molecules and the overall reaction rate was controlled by the diffusion of H20 to (100) surfaces. 

The reaction of Si02 with SiC [1229] approximately obeyed the zero-order rate equation with E = 548—405 kJ mole 1 between 1543 and 1703 K. The proposed mechanism involved volatilized SiO and CO and the rate-limiting step was identified as product desorption from the SiC surface. The interaction of U02 + SiC above 1650 K [1230] obeyed the contracting area rate equation [eqn. (7), n = 2] with E = 525 and 350 kJ mole 1 for the evolution of CO and SiO, respectively. Kinetic control is identified as gas phase diffusion from the reaction site but E values were largely determined by equilibrium thermodynamics rather than by diffusion coefficients. 

The reaction of Ni(OH)2 resembled [39] that of Fe(OH)2 in that the contracting area equation fitted the data and the value of was 95 kJ mol. The rate was appreciably decreased by water vapour. The textural changes that accompany water removal have been studied [41] by electron microscopy which identified rapid initial nucleation at crystallite edges to form a continuous interface. The dehydration is topotactic to yield particles of product which are pseudomorphs of the reactant. These textural changes are consistent with the earlier conclusions based on kinetic evidence. 

A different treatment of TGA based Ajm data accounts for the decrease of the surface area between the growing silica layer and the unreacted fiber, assuming the oxidation process is also rate controlled by diffusion [90]. The kinetic constant, Ks, is derived from the contracting disc rate equation ... 

The reaction of this solid [48] was the first [133] example of Smith-Topley behaviour recognized and studies of this rate process have continued. Flanagan and Kim [133] showed that irradiation decreased the induction period to dehydration and the rate of water evolution rapidly reached a maximum value which was maintained between 0 < nr < 0.4. Water evolution was more rapid than that found for unirradiated salt and the value of , was decreased. Irradiation damage to the crystal promoted nucleation and there was rapid initial establishment of a constant area of reaction interface (the contracting volume equation approximates to zero-order kinetics at low values of nr). There was also evidence [134] that preirradation aided recrystallization during vacuum dehydration. 

The kinetics of decomposition of CuS [50] in the interval 583 to 611 K were fitted by the contracting volume equation with E = 250 kJ mol. Shah and Khalafalla [51] studied the decomposition in nitrogen (618 to 673 K, E = 100 kJ mol ) and concluded that the rate depended on the surface area rather than interface advance. 

Equations relating x and t have been derived for simple geometrical systems assuming (1) the reaction rate is phase-boundary controlled, (2) the reaction rate is proportional to the surface area of the fraction of unreacted material, and (3) the nucleation step occurs virtually instantaneously so that the surface of each particle is covered with a layer of product. The models developed from the foregoing boundary conditions are termed phase boundary or contracting volume kinetic models. For a sphere reacting from the surface inward ( ) the relationship between x and t is... 

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