Close to 12.2 billion metric tons of ethylene glycol (EG) were produced in 2000, which ranked it the twenty-sixth most produced chemical in the nation that year on a total mass basis.  About one-half of the ethylene glycol is used for antifreeze, while the other half is used in the manufacture of polyesters.           

It is desired to produce 200 million pounds per year of EG by the reaction shown below.  A solution containing water and ethylene oxide (EO) is fed to a 150m³ reactor at a rate of 10m³/min_.  The reaction rate is described by r=kC_EO where k is 0.311 min^-1. 

a. Determine the conversion of EO for a CSTR.

b. Determine the conversion of EO in a 150m³ batch reactor after 15 minutes and compare your answer to part a and b. 

c. Non-dimensionalize the balance equation for the CSTR to show that the important dimensionless number (named the Damkohler number) is kV/ν₀ for a first order irreversible reaction with no volume change.  What is the Damkohler number for an n^th order irreversible reaction with no volume change where r=kC_Aⁿ?