Spherical solid particles containing B are roasted at constant temperature in an oven by gas of constant composition. Solids are converted to give firm non-flaking product according to the shrinking core model. From the following conversion data determine the rate controlling mechanism for the transformation of solid.

$$\begin{array}{|c|c|c|} \hline \mathrm{{d p}, {m m}} & \mathrm{X}_{\mathrm{B}} & t,s \\ \hline 1 & 1 & 200 \\ \hline 1.5 & 1 & 450 \\ \hline \end{array}$$

Solution :

Here conversion in case of both spherical particles is complete ($\mathrm {X_B}=1$) so the time given is $\tau $

For $\mathrm {dp_1=1~mm, \quad \tau_1=t_1=200~s}$

For $\mathrm{ dp_1=1.5~mm, \quad \tau_2=t_2=450~s}$

1) Film diffusion controls :

We have $\mathrm {\tau \propto R}$

$\mathrm {r_{1} \propto R_{1}}$ and $\tau_{2} \propto \mathrm …