Kviv s4LE Mathematical Modeling in Chemical Engineering Spring 2023 Homework 1 1. Draw the centrol volume, write the conservation law (do shell balance) and write the boundarics (nok conditions) for the following problems: a) b) A drug molecule dissohes in A gas miture is flowing thregh a borosilicate pipe. The wharion in spherical coondinutes. pipe alloes coly the diffrsion of gas A through its wall wo you want to obteain the coecentration that it keparates gat A from the mixure. Yoe want to Cinuli) in the polution. obtain the coscentration CA(t) throegh the pipe wall 2. A stream of ideal gas mixture A and B flows slowly over the top of the tube as shown in the figure to keep the mole fraction of Ax. constant at yLA is in liquid form at the bottom of the tube (blue shaded volume), and there is flow of gas A upward in the y-direction frum the gas-liquid interface to the top of the tube. The mole fraction of A at the liquid-gas interface is x. The species B is stationary. The molar flux of A in the tube is given by. NAy=1xAcDALdydxA Here, c is the constant concentration of the gas mixture, Dudiffusion constant and x is the mole fraction of A. a) Do steady-state mass balance in molar units to derive the differential equation to solve x in the y-direction. b) Write the boundary conditions to solve the differential equation for xadis. c) Solve for x(0)