#### Diffusion and Reaction in Porous Catalysts: Example Problems

Try to solve these problems before watching the solutions in the screencasts.

##### Example Problem 1

The first-order reaction A → B takes place in a spherical catalyst pellet. The effectiveness factor due to diffusion limitations in the catalyst pores is 0.80, When the same reaction is carried out in a catalyst pellet whose diameter is four times larger, how much larger is the total rate of reaction?

##### Example Problem 3 (optional)

The molecule A diffuses from the gas phase, which only contains A and B, through a porous layer that covers a flat catalyst surface. The reaction A → 2B is essentially instantaneous on the catalyst surface. The product B diffuses through the porous layer back into the bulk, where diffusion is fast.

- Calculate the concentration profile for A in the porous layer.
- Calculate the flux of A into the layer.

##### Example Problem 2

Consider a long porous catalyst cylinder. Because of a particular arrangement of catalyst within the pores, the concentration gradient of reactant A is

\[C_A = C_{As} \frac{r^2}{R^2}\]

What is the total amount of A reacting in any 1-cm length of the cylinder if the radius is 3 cm, the effective diffusivity is 10^{-3} cm^{2}/s, and the concentration at the external surface (C_{As}) is 0.001 mol/cm^{3}?