1. The problem is to understand the shrinking core model, which describes the reaction of a solid particle with a fluid where the unreacted core shrinks over time. 2. The key formula relates the time $t$ to the radius of the unreacted core $r$ and the initial radius $r_0$ of the particle. For a spherical particle, the volume of the unreacted core decreases as the reaction proceeds. 3. The shrinking core model equation for a spherical particle controlled by diffusion through the product layer is: $$t = \frac{\rho_B r_0^2}{2 C_{A} D_e} \left[1 - \left(\frac{r}{r_0}\right)^2\right]$$ where $\rho_B$ is the density of the solid, $C_A$ is the concentration of reactant in the fluid, and $D_e$ is the effective diffusivity. 4. Important rules: - The unreacted core radius $r$ decreases from $r_0$ to 0 as reaction proceeds. - The time $t$ increases as the core shrinks. 5. Intermediate work involves substituting known values for $r_0$, $r$, $\rho_B$, $C_A$, and $D_e$ to find $t$ or vice versa. 6. This model helps predict reaction time and conversion in solid-fluid reactions by tracking the shrinking core radius over time. Final answer: The shrinking core model equation for diffusion control is $$t = \frac{\rho_B r_0^2}{2 C_{A} D_e} \left[1 - \left(\frac{r}{r_0}\right)^2\right]$$ which relates time to the shrinking unreacted core radius.