Question

The follow second order, irreversible gas phase reaction AB --> A + B, where k=2.0X10^4 cm^3/mol.min is allowed to decompose isothermally in a constant pressure batch reactor. The reactor initially contains pure AB with a volume of 2.0 m^3 at 2.5 atm and 500 C. Assume ideal behavior, determine the time for the reaction to reach 70% conversion (Given R = 82.05 atm cm^3/mol.K) Answer= 4.39 min.

Answer 1

Given that k = 2.0 x 10^4   cm^3/mol.min = 2x 10^2 L/mol.min

We have to calculate moles of reactant.

moles n = PV/RT = 2.5 atm x 2.0 x 10^6 cm^3 / 82.05 atm cm^3/mol.K x 773 K

                           = 78.83 mol

[A]o = 78.83 mol

[A]t = 70% conversion = 30 % of [A]o = 30 % of 78.83 mol = 23.65 mol

t = ?

For 2nd order reaction

     kt = 1/[A]t - 1/[A]o

t = (1/k) { 1/[A]t - 1/[A]o}

= (1/ 2.0 x 10^2) [ (1/23.65) - (1/78.83) ]