A liquid mixture containing 45.0% benzene (B) and 55.0% toluene (T) by mass is fed to distillation column. A product stream leaving the top of the column (the overhead product) contains 95.0 mole %B, and a bottom product stream contains 8.0% of the benzene fed to the column (meaning that 92% of the benzene leaves with the overhead product). The volumetric flowrate of the feed stream is 2000L/h and the specific gravity of the feed mixture is 0.872 . a. Do the degree-of-freedom (DOF) analysis, and verify that all unknown stream flows and compositions can be calculated. b. Determine the mass flow rate of the overhead product stream and the mass flow rate and compositions (mass fractions) c. An analyzer is available to determine the composition of Benzene-Toluene mixtures. The calibration curve for the analyzer is a straight line on a plot on logarithmic axes (i.e. analyzer reading, R. The line passes through the points (R=15,x=0.1) and (R=38,x=0.4). Derive an expression for x as a function of R based on the calibration, and use it to determine the value of R that should be obtained if the top product stream from the distillation column is analyzed. b=[ln(x2/x1)/ln(R2/R1)] Methane is burned with air in a continuous steady-state combustion reactor to yield a mixture of carbon monoxide, carbon dioxide, and water. The reactions taking place are: CH4+23O2CO+2H2OCH4+2O2CO2+2H2O The feed to the reactor contains 7.8 mole %CH4,19.4O2, and 72.8%N2. The percentage a. Carry out a degree-of-freedom analysis on the process. b. Calculate the molar composition of the product stream using Extents of Reactions