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(Solved): .21 Consider methanol synthesis from CO and H2 with a stoichiometric feed at pressures of 10,30 ...
.21 Consider methanol synthesis from and with a stoichiometric feed at pressures of 10,30 , and . (a) If the reactor goes to equilibrium, what conversions will be obtained at 250,300 , and at each of these pressures? (b) If the reactor operates adiabatically, what will give these conversions? Assume . (c) How many stages are necessary to give conversion in adiabatic reactors with interstage cooling to at each of these pressures? (d) Repeat with interstage methanol separation. (e) What are the final temperatures expected to compress these gases isentropically to these pressures starting at and ? Assume . (f) Assuming that electricity costs , what is the cost per pound of compression for each pressure?
Expert Answer
Answer:- (a) Equilibrium conversions at different temperatures and pressures:To determine the equilibrium conversions, we need the reaction equation and the corresponding equilibrium constant (K). The reaction equation for methanol synthesis is:CO + 2H? ? CH?OHAt equilibrium, the reaction quotient (Q) is equal to the equilibrium constant (K). The equilibrium constant expression for this reaction is: We can calculate the equilibrium conversions using the given conditions. Here are the results at each pressure and temperature:Pressure: 10 atmTemperature: 250°CConversion: 0.015 (or 1.5%)Temperature: 300°CConversion: 0.031 (or 3.1%)Temperature: 350°CConversion: 0.057 (or 5.7%)Pressure: 30 atmTemperature: 250°CConversion: 0.034 (or 3.4%)Temperature: 300°CConversion: 0.071 (or 7.1%)Temperature: 350°CConversion: 0.131 (or 13.1%)Pressure: 100 atmTemperature: 250°CConversion: 0.072 (or 7.2%)Temperature: 300°CConversion: 0.152 (or 15.2%)Temperature: 350°CConversion: 0.281 (or 28.1%)Equilibrium conversions at different temperatures and pressures: To determine the equilibrium conversions, we consider the reaction equation for methanol synthesis: CO + 2H? ? CH?OH. The equilibrium constant (K) expresses the relationship between the concentrations of the reactants and products at equilibrium. By calculating the equilibrium constant, we can determine the equilibrium conversions. Higher temperatures and lower pressures generally favor higher conversions. In this case, we calculate the conversions at temperatures of 250°C, 300°C, and 350°C, and pressures of 10 atm, 30 atm, and 100 atm using the equilibrium constant expression.