The liquid phase thermal decomposition of 1,3,5-TriisopropyIcyclohexane has been

Question

The liquid phase thermal decomposition of 1,3,5-TriisopropyIcyclohexane has been studied recently. This compound is a surrogate in simulated diesel fuels. The reaction is simply represented as A products. The rate -rA is first order in the concentration of A. The Arrhenius parameters reported (Gough ct al, I&EC; Research, 2013) are given below. You will test these results by running the reaction in a small, heated flow tube approximating a PFR. A furnace keeps the PFR at 400degree C. The feed is A in an inert solvent. Feed and product compositions will be measured by gas chromatography. What is the rate constant k? What is the space-time t (seconds) ? What is the outlet concentration Ca (molcs/litcr) ? What arc the molar flow rates Fao and exit FA (moles/min) ? What is the steady-state conversion X_A?

Explanation / Answer

1)K=Af*e-Ea/RT

Af= 5.67*1016/sec

Ea= 279*1000 j/mole RT= 8.314*(400+273.15)=5.67*1016*2.2364*10-22 =1.27*10-5/sec

2) T= V/VO = 2*10-3/1*10-6=2000 min

3) For first order reaction in PFR, KT= -ln(1-XA), where XA= 1-CA/CAO

1.27*10-5*2000 =-ln(1-XA), 1-XA=0.975

XA=10-0.975= 0.025

1-CA/CAO= 0.025

CA/CAO= 1-0.025= 0.975

CA=0.975*CAO= 0.975*0.5=0.4875

Vo= FAO/CAO , FAO = V0*CAO= 1*10-6L/min*0.5 Moles/L=0.000002 moles/min

FA= FAO*(1-XA)= 0.000002*(1-0.025)= 0.00000195 moles/min

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