Question

The decomposition of Ethylene oxide, (CH2)2 O(g), at 652k is a 1st- order reaction with R=0.012 min^-1 and an activation energy of 218k J/mol (CH2)2 O(g) -----> CH4(g)+ CO (g)

Calculate a) the rate constant of reactin at 525k and b) the temperature at which the rate constant R=0.01min^-1 (universal gas constant R=8.314 J/mol^-1 k^-1)

Answer 1

a ) We know the Arrhenius's law:
K = A*e^(-Ea / RT1)

use Arrhenius's law:

K1 = A*e^(-Ea / RT1)
K2 = A*e^(-Ea / RT2)

now calculate K1/K2 ratio

K1/K2 = e^(-Ea/R*(1/T1 - 1/T2)

= e^{(218,000J. mol-1 / 8.314J.K-1mol-1 * (1 / 652 - 1 / 525)K}

= 1.68*10^4

K2 = K1 / 1.68*10^4

     = 0.0120 / 1.68*10^4

    = 7.15*10^-7 min^-1

b) the temperature at which the rate constant R=0.01min^-1 (universal gas constant R=8.314 J/mol^-1 k^-1)

Given K1 = 0.012min-1   and   T1 = 652K

K2 = 0.01 min-1     and T2 = ?

Ea = 218000 J/mol
R = 8.314 J/mol/K

We know that Arrhenius law:

ln(K1/K2) = -Ea/R [ 1/T1 -1/T2]

ln(0.012min-1/0.01min-1) = -218000J/mol / 8.314 J/mol. K x[ 1/652 - 1/T2]K

0.182 = -26220.8 [1/652 -1/T2]

0.00000694 = 0.00153 - 1/T2

1/T2 = 0.00152306

therefore T2 = 1/0.00152306

                       = 656.6 K