Jander rate equation

Furusaki et al. [49] reported that the kinetic characteristics of the conversion of LaCr04 (monazite structure) to LaCrOj (perovskite structure) depended onp 0- and that the rate decreased with increasing availability of oxygen. In N2, the reaction (908 to 938 K) fitted the contracting volume expression with , = 198 kJ mol. The rate limiting step for reaction in Oj is the diffusion of oxygen across the product layer, the Jander rate equation applies with about 506 kJ mol. ... 

Diffusion). For a model in which a sphere of a reactant B exists in another reactant A (Fig. 18), a rate equation for reaction between A and B at the interface was derived by Jander in... 

S. Miyagi, A Criticism on Jander s Equation of Reaction Rate Considering the Statistical Distribution of Particle Size of Reacting Substance, J. Japan. Ceram. Soc. 59 132-35 (1951). 

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... 

This deceleratory reaction obeyed the parabolic law [eqn. (10)] attributed to diffusion control in one dimension, normal to the main crystal face. E and A values (92—145 kJ mole-1 and 109—10,s s-1, respectively) for reaction at 490—520 K varied significantly with prevailing water vapour pressure and a plot of rate coefficient against PH2o (most unusually) showed a double minimum. These workers [1269] also studied the decomposition of Pb2Cl2C03 at 565—615 K, which also obeyed the parabolic law at 565 K in nitrogen but at higher temperatures obeyed the Jander equation [eqn. (14)]. Values of E and A systematically increased... 

Although we have shown several kinetic models for reacting solids, none specifically applies to a reaction between two solids. A rate law that was developed many years ago to model reacting powders is known as the Jander equation, and it is written as... 

Figure 103. Effect of water content on degradation of propantheline bromide in the presence of sodium aluminum gel. The values of the rate constant (in units of h-" ) calculated according to the Jander equation at 37°C. , Moisture equilibrium water added. (Reproduced from Ref. 454 with permission.)...

The question arises as to what type of rate law can be used to model reactions between two solids. Probably the most widely employed rate law is that known as the Jander equation. 

The solids were suspended in dodecane, and the mixture was sonicated using a pulsed source. At specific times, samples of the soHds were separated from the reaction mixture and analyzed to determine the amount of CdS formed. The extent of reaction was found to vary with sonication time, although the data showed considerable scatter. Although the results did not represent a highly sophisticated kinetic study, they indicated that the Jander equation represents a rate law that should be considered when a model for a reaction between two soHds is being sought. 

Equation (2.16), referred to as the Jander equation, suffers from two oversimplifications that limit its applicability and the range over which it adequately predicts reaction rates. First, the parabolic growth law assumed for the thickness of the reaction layer is valid for one-dimension reaction across a planar boundary and not for a system witli spherical geometry. At best, it is expected to be valid only for the initial stages of the powder reaction when y r. Second, any change in molar volume between the reactant and the product is neglected. These two oversimplifications have been taken into account by Carter (37), who derived the following equation ... 

Equation (5) is the well-known Jander equation relating the fraction of reaction completed to time, where kj is the rate constant. In order to determine the rate constant for an isothermal solid-state reaction, the fraction of material reacted must be determined as a function of time, and then, according to the Jander model, a plot is made of [1 — (1 — versus time. 

This plot, often referred to as u Jander analysis, should give a straight line whose slope is the rate constant kj. If the Jander model applies to the system being studied, the rate constant should not drift as the reaction proceeds. If the rate constant does drift with time, another model must be sought. The empirical equation developed from the Jander physical model for solid-state reactions states that the rate constant is proportional to the diffusion coefficient of the species being transported and inversely proportional to the square of the radius. 

In interpreting their results these authors also suggested that reaction (5.2.3a) constituted the rate-controlling step and were able to represent their results adequately by using either Jander s or Gnistling s equation [viz., Eq. (5.2.4) or (5.2.5)]. 

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