Problem $5$

Oxygen diffuses through the wall of drug containers and oxidizes many drugs rendering them inactive. It is the oxygen diffusion$/$reaction scenario that limits the shelf$-$life of many pharmaceutical products. To limit the oxidation of drugs, oxygen scavengers, like sodium bisulfite $($ NaHSO$3$ are often added. The reaction to remove oxygen is:

$2HS{O}_3^{-}+O_{2}S{O}_4^{2-}+H_{2}O$

Consider a liquid drug stored in a cylindrical polyethylene container. The container is $15cm$ high and has an inner diameter of $6cm.$ The initial concentration of $NaHS{O}_3$ in the drug formulation is $1\frac{g}{?}$ liter. How thick must the walls of the container be to ensure that $90\%$ of the $NaHS{O}_3$ remains after $1$ year? Neglect diffusion through the top and bottom of the container and assume that the $NaHS{O}_3$ reacts instantly with the $O_2$ so that the $O_2$ concentration in the drug is always $O.$ The effective diffusivity of $O_2$ through polyethylene is $9{10}^{-14}\frac{m^2}{s}$ and you may assume the partition coefficient is $1,P=1$atm,$T=20C,$ and the process operates at steady$-$state. $($Enever$,$ Lewandowski and Taylor$)$

Please include pictures with your solutions and any helpful advice to solve this problem.