1. You are going to solve problem 1 in homework 2 with one change in the given information which is assuming the diffuses through the ceiling in one dimension only (z-dimension). The maximum concentration and the diffusion coefficient of water in the ceiling material are 0.458gm/cm3 and 5.9109m2/s, respectively. The thickness of the ceiling is L is 30cm. Assume that the ceiling was totally dry before the rain. Consider this a molecular diffusion process in a semi-infinite medium. Answer the following questions: i. State the assumptions that the solution covered in the textbook is based on. Are these assumptions valid in this problem? Why? ii. What is the maximum diffusion time that will make the diffusion in a semi-infinite medium assumption valid? iii. Use Microsoft Excel or Matlab to plot the concentration profiles of water as a function of z at time =1% and 5% of the time calculated from part (ii). (Plot both profiles on the same graph, add all necessary information on the plot to make it understandable) iv. Calculate the time needed for the concentration of water to reach 23% of the maximum