Rate law Avrami-Erofeev

Table 8.1 Values of a as a Function of Time for a Reaction Following an Avrami-Erofeev Rate Law with n = 3 and k = 0.020 min-1.

The experimental data of aqueous leaching under constant pH were fitted with Avrami-Erofeev rate law (IS) for reactions in the solid state. The reactions of metal dissoluticm, desorption and transport were combined into one reaction, uhich is expressed as... 

The overall rate of ZnO aqueous leaching might be controlled by mass transfer in the boundary layer solid-liquid (16). At this layer, a constant low pH in the aqueous phase suggests a saturation of dissolved Zr. Kakovskii et al. (16) have reported, that at high acid concentrations the rate of ZnO dissolution is controlled by diffusion of Zn away from the siuface. This local saturation appears to influence eq. 4 and suggests a pH dependent dissolution-desorption step. This step was estimated with the Avrami-Erofeev rate law applying the results of the aqueous leaching data. 

The general form of the rate law that is used to describe nucleation processes is known as the Avrami (or Avrami—Erofeev) rate law. 

In order to provide a practical example of the type of behavior exhibited by a reaction that follows an Avrami-Erofeev rate law, the data presented in Table 7.1 were derived. In performing the calculations, it was assumed that the reaction follows an Avrami-Erofeev rate law with an index of 2 (the A2 rate law) and that k is 0.025 min . ... 

Having a set of a,t) data available, a graph was prepared to illustrate the type of plot that can be expected when a reaction follows an Avrami-Erofeev rate law. The result is shown in Figure 7.2, and the sigmoidal curve is characteristic of a reaction that follows a nucleation rate law. In Chapter 2, it was shown that a sigmoidal rate plot results from autocatalysis, but for reactions in the solid state such plots are more likely to indicate that the reaction is controlled by some type of nucleation process. 

These reactions take place in the range of 47 to 63°C and 70.5 to 86°C, respectively. Both reactions appear to follow an Avrami—Erofeev rate law with an index of 2 over a range of a from 0.1 to 0.9 (see Ng, et al., 1978). 

FIGURE 7.5 Arrhenius plot for the dehydration-anation reaction of [Co(NH3)5H20]Cl3 when the Avrami-Erofeev rate law with = 1.5 is used. 

Incorporation of a diffusion term in nucleation and growth reaction models has been proposed by Hulbert [68]. Interface advance is assiuned to fit the parabolic law and is proportional to but the nucleation step is uninhibited. The overall rate expressions have the same form as the Avrami-Erofeev equation ... 

Care should be taken in defining the procedure for calculating values of k fi om the experimental data. There is always the possibihty that the apparent is a compound term containing several individual rate coefficients for separable processes (such as nucleation and growth). It is important that the dimensions of k (and hence of A) should be (time). For example, the power law (Table 3.3.) should be written as = kt and not as ar = k t. Similarly the Avrami-Erofeev equation (An) is [-ln(l - a)Y = kt. The use of k in place of A in the Arrhenius equation will produce an apparent activation energy /i, which is n times the conventional activation energy obtained using k. 

Many reactions in the solid state follow a rate law of the Avrami-Erofeev type. For example, the dehydration of CuS04 5H20 is a process where the first two steps can be represented as... 

When the data are presented in this way, the unmistakable sigmoidal nature of the rate plots for dequation-anation of [Co(NH3)5H20]Cl3 suggests that the process obeys an Avrami—Erofeev type of rate law. In... 

It will be noted that through the Erofeev law, we find the same result as the Avrami one when k t is smaller compared to 1 (equation [A.9.25]), if we put q=, which corresponds well to the assumption of Avrami when we have only a single rate-determining step in nucleation. 

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