Consider now the following membrane configuration P. = 10 bar Por = 0.1 bar *co2 = 0.9 = 0,1 *202 = 0 Xwe=1 Were the transport of CO2 through the membrane can be described by the following equations: d?p002 dcco2 = 0 = PCO2 dt - k'p02 dx2 Where pco2, are the partial pressures of CO2 (in bar), and co2 its concentrations (in mol m). Qc02 =1 x 10' mol m's bar corresponds to the permeability of CO2, and k is an absorption rate (in mol m s bar). i. ii. (10 points) Use the finite difference method to write a set of equations that describe the partial pressures of CO2 inside of the membrane. Make sure to include the boundary conditions. (30 points) Write a matlab function that solves the system of equations in part (i). Make sure to calculate pco2 for at least 100 points within the slab. Generate a plot of pco2 VS. x for k' = 10mol m's bar-2 and L=100 x10-6 m. (60 points) After multiple runs at different concentrations of CH4, the company realized that CH4 was also absorbed by the particles and the transport process through the membrane could be described by the following equations: iii. dcco2 = 0 = 0 C02 dx2 dt dpcH4 - k" PcH4 dCCH4 0 = PcH4 dt dpco2 k'poz PCH4 dx2 Use the finite difference method to write a set of equations that describe the partial pressures of CO2 and CH4 through the membrane, and write a matlab script that solves the set of equations. Assume the same configuration as of part i and ii, and generate a plot of pcO2 and PCH4 VS. X. Assume that the @ch4 = 2 x 10? mol m's bar and that k'=k = 10 mol m? s bar