In a purification system, a stream of oil containing 1.0 mol% methanol is contacted with a stream of nitrogen to recover the methanol, using a counter-current multistage operation. The liquid solution is fed at 200 kmol/hr. The separation is run at a relatively constant condition of 60C and 1 atm. We may take ideal gas and ideal mixtures assumptions to be valid. a) Suppose the nitrogen inlet is at 300 kmol/hr and contains 0.01 mol% methanol (not pure nitrogen). Determine the number of stages needed give 90% recovery of methanol. In part a), there are 3 factors that are used to determine the number of stages: nitrogen flow rate, % methanol in the nitrogen, and % recovery of methanol. Below, we investigate the limits of each factor, while keeping the other factors constant. b) Suppose the nitrogen inlet is at 300 kmol/hr and contains 0.01 mol% methanol (not pure nitrogen). Determine the minimum and maximum % recovery of methanol. c) If the nitrogen is known to contain 0.01% methanol, determine whether there is a theoretical minimum or maximum flow rate of nitrogen to provide 95% recovery of methanol. d) If the nitrogen inlet is at 300 kmol/hr but with an amount of methanol that is not specified, determine whether there is a theoretical minimum or maximum mol% of methanol in the nitrogen to still allow 95% recovery of methanol.