Consider a packed-bed reactor carrying out an exothermic, first-order reaction that converts A

(reactant) into B (product). A enters the reactor through an inlet pipe (diameter 10 cm) with a

volumetric flow rate of 0.5 m³/s at a concentration of 0.1 M. The first-order reaction's kinetic

constant is k = 10 s¹ and the diffusion coefficient of A in steam is DAB = 5x10³ m²/s at a temperature

of 300 °C. Assume that the reaction is irreversible, that there is zero bulk velocity inside the reactor

(meaning that convection can be neglected or that there is equimolar counter-diffusion), and that

the reactor's temperature is maintained at 300 °C.

A. Draw a simple diagram of the packed-bed reactor and label the inlet flow.

B. Derive a diffusion equation (in a differential equation form) that describes the concentration

profile inside the packed bed reactor. State all assumptions. Do not integrate.

C. What is the molar flux of A (in units of mol/m²-s) entering the reactor?

D. If full conversion is achieved using 0.3 m of the reactor, determine the concentration profile of

A inside the reactor and sketch a plot of concentration of A versus position inside the reactor.

Label the concentrations of A at z = 0, 0.1, 0.2, and 0.3 m.