Repeat Exercise 6.10 using intercoolers instead of cold shots and an unknown number of reaction stages. The feed to the first reactor is at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\). Throughout the reactors, the temperature must be held below \(300^{\circ} \mathrm{C}\). What is the conversion of \(\mathrm{CO}\) in the first reactor? How many reaction stages and intercoolers are necessary to operate between 25 and \(300^{\circ} \mathrm{C}\) ?

Data From Exercise 6.10:-

Divide the methanol reaction operation in Example 6.6 into five consecutive stages in series. Feed the \(\mathrm{CO}\) reactant entirely into the first operation at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\). Divide the \(\mathrm{H}_{2}\) reactant into five cold shots and vary the temperature of \(\mathrm{H}_{2}\) before dividing it into cold shots. Assuming that the reaction operations are adiabatic, determine the maximum temperature in the flowsheet as a function of the temperature of the cold shots. How does this compare with the adiabatic reaction temperature?

Data From Example 6.6:-

To demonstrate the advantages of running the reactions at intermediate temperatures, show the rate constants for the three competing reactions as a function of temperature.