A process uses an exothermic, gas phase reaction to synthesize a compound. The m

Question

A process uses an exothermic, gas phase reaction to synthesize a compound. The manufacturer wants to run the synthesis as quickly as possible so wants to have the reaction go as fast the heat generated can be removed. Let's say our reaction follows the form: A(g) + B(g)--> 2C(g) + D(l). The reaction has an enthalpy of -45 kj/mole of D formed. The reaction occurs in a 50.0L reaction vessel and D is drained out as it is formed. C is a waste product and is flushed out of the system as more A and B are added. The system is filled to a pressure of 5 atmospheres of both A and B at a temperature of 50'c, and then the reaction occurs. Once the vessel is cooled back to the starting temperature by a water cooling system, the vessel is purged of C and refilled with A and B for the next reaction. The reaction vessel has a heat capactiy of 10 kj/'C. The heat is removed by flowing by flowing water over the vessel in a cooling sleeve. The water flows at a rate of 3 Gal/Min. and the water heats up 10'C as it flows over the vessel. How much time does it take for the cooling system to remove the heat generated by the reaction? How many moles of D can be produced in an hour?

Explanation / Answer

moles of A= PV/RT= 50*5/(0.08206*(50+273.15)=9.42 moles = moles of B

D formed (asssuming the reaction to go to completion)= 9.42 moles

Heat produced =45*1000 j/mole*9.42 mole=432900 joules

The entire heat needs to be removed by circulation of cooling water = 3 gal/min*3.78L/gal*1000g/L*4.18*10=474012 joules/min

time taken= 432900/474012 min=0.9 min

in 0.9 min 50 moles of D is produced

60 min D produced =60*50/0.9= 3333.33 mol/hr

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