Di-tert-butyl peroxide is a stable organic peroxide compound. At elevated temper

Question

Di-tert-butyl peroxide is a stable organic peroxide compound. At elevated temperature it will decompose to yield ethane and di-methyl ketone (acetone). (CH_3)_3C00C(CH_3)_3 rightarrow C_2H_6 + 2CH_3COCH_3 The kinetics of this reaction are typically considered to be first order. The pure peroxide is fed to a tubular reactor at 10 atm and 400 K with a molar flow rate of 2.5 mol/min. Calculate the reactor volume required for 90 % conversion assuming plug flow behavior. Assume that T and P are constant. At 400 K the rate constant has a value of 0.0443/min. If this reaction was reversible with a K_c (based on concentration units) Of 0.025 mole^2/liter^2 what would be the equilibrium conversion?

Explanation / Answer

The equation for first orer kinetics is

[A] = [A]e^-kt

k = rate constant ; time in minutes

here 90% conversion assumed so;

0.9 [Ao] = [Ao] e^-kt

substituting k value ;

we get t = 2.378 minutes

given 2.5 per minute

for 2.378 minutes =====> 5.944 moles

using PV= nRT

we have R= 0.0821 and other values are given in the question

V = 19.5 litres.

At equilibrium: rateforward=ratereverse

The equilibrium constant of concentration gives the ratio of concentrations of products over reactants for a reaction that is at equilibrium.

since here Kc<1 the equilibrium favours the reactants. [As products is in excess it tries to convert to reactants to maintain equilibrium ]

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