Stoichiometric heterogeneous gas-solid reactions

In heterogeneous kinetics with the creation of a new condensed phase, it is common to present experimental results under various equivalent forms. Thus there will be data of the fractional extent (restricted to a solid reactant) as a function of time and data of the rate (or speed) versus the fractional extent as a function of intensive variables such as partial pressures of gases and temperature, versus the powder grain sizes forming one of the sohd reactants. We will now quickly provide an outline of the results commonly obtained. 

We have seen that for the heterogeneous reactions we use the law. For the moment we will only consider the stoichiometric reactions for which the space 

Fractional extent - time and speed - fractional extent curves 

For these cnrves with monotone speed, different laws have been proposed. Among the best known are linear law with constant speed [6.10] and the parabohc law [6.11] for plane solid samples  

The law known as the shrinking core for powders that consist of spherical grains of equal size is written as follows  

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