Write the differential equation for steady-state diffusion and homogeneous chemical reaction at constant reaction rate K in a cylindrical rod. Determine the solution for the HC1 concentration in the rod.

Engineering by Geoffrey

Transport phenomena

3. Poly (vinyl chloride), PVC, is a common polymer used for fluid pipes and many consumer products, such as inflatable mattresses. It degrades at high temperatures and forms hydrochloric acid, a highly corrosive acid:
(C2113COn —, (C2112)7, + HCl

This occurs at a constant rate K, which is independent of HC1 concentration. Consider a PVC rod of radius R that is held at high temperatures for a long time so that the concentration of HC1 reaches a steady state. On the surface, the rod reaches equilibrium with its surroundings at a fixed HC1 concentration, CHci,s. You would like to know the concentration profile of HC1 in the rod.

a) Write the differential equation for steady-state diffusion and homogeneous chemical reaction at constant reaction rate K in a cylindrical rod. Determine the solution for the HC1 concentration in the rod.

b) What is the maximum concentration of HC1? KR2 DCH c) Consider the dimensionless quantity .

How is this quantity related to the ,,
uniformity of the HC1 concentration in the rod? PVC rod