1 inside a spherical pellet radius r pellet density ph surface area sg

Question

1. Inside a spherical pellet (radius = R, pellet density= Ph surface area =Sg, effectivediffusivity = D), irreversible first-order reaction (rate constant = k) occurs. The concentrationof reactant A against the pellet radius can be expressed by the following equation: C_{A}(r)=C_{0} \frac{R \sinh (\omega r)}{r \sinh (\omega R)}, \quad \omega^{2}=\frac{\rho_{b} S_{g} k}{D_{e}} Note that Co is the concentration of reactant A at the external surface of spherical pellet and ris the distance from the pellet center. A) Using the above equation, derive the mathematical function of the internal effectivenessfactor against Thiele modulus. [3 point] B)Make a plot on the basis of your solution in Problem A. Also, explain the effect ofintraparticle diffusion on the reaction rate when Thiele modulus is large and small,respectively. [1 point]