ALL ANSWERS SHOULD BE TWO SIGNIFICANT FIGURES - Problem 1. System analysis of a methane to benzene plant. Given the huge quantities of methane being discovered as part of the shale gas boom there are many new utilization routes for methane being touted. One is the non-oxidative conversion of methane to benzene 6CH. CH. +9H, AH = 432kJ / mol ram There are many challenges for this reaction to be part of a viable process. The main item salient to this analysis is that the heat of reaction at standard state is 432 kJ/mol, i.e., highly endothermic. Part a. If I assume that my carbon yield is 90%, i.e, out of every 100 carbon atoms from methane 90 end up on benzene: 1. Set up and solve the material balances to determine how much methane I need to feed to the plant, and how much hydrogen I will produce if the plant is sized to make 250,000 tons per year of benzene. You may assume that the other 10% of methane does not go to either product, i.e., that all of this 10% goes into a byproduct stream. Give me flow rates in tons per day assuming this plant operates 350 days per year, i.e., the benzene flow is 250,000/350 tons per day. 2. How much energy will be required based on the heat of reaction provided? Part b. In part (a) you determined the methane feed rate, hydrogen production rate, and the energy requirements based on the heat of reaction. In this part of the problem, we are going to look at the energy side in a bit more detail 1. If one assumes the heat is supplied via methane combustion with a heat of reaction of -804 kJ/mol, how much methane do I need to burn to provide the heat asked for in number 2 of part a above? Give me this number in tons per day. In this scenario how much carbon dioxide will this process emit (tons per day)? 2. Another way to supply the heat would be to burn the hydrogen, i.e., H2 + 12 O2 == H20. The heat released in this reaction is 285 kJ/mol. How much hydrogen do I need (tons per day)? Do I produce enough hydrogen via the reaction? Your final answer in each of these should contain two significant figures