The first-order isomerization reaction: cyclopropane → propene, has a rate constant of 1.1 × 10-4 s-1 at 470°C and an activation energy of 264 kJ/mol.

Question

What is the temperature of the reaction when the rate constant is equal to 4.36 × 10-3 s-1?

Answer 1

Use the Arrhenius equation (or a form of the Arrhenius equation):

ln (k1/k2) = -Ea/R(1/T1 - 1/T2)

k1 = 1.1x10-4 s-1

k2 = 4.36x10-3 s-1

Ea = 264 kJ/mol

R = gas constant = 8.314 J/Kmol = 0.008314 J/Kmol (note changed units to agree with units of Ea)

T1 = 470C +273 = 743K

T2 = ?

ln(1.1x10-4/4.36x10-3) = -(264/0.008314) (0.001345 - 1/T2)

-5.98 = -42.71 - 31753/T2

T2 = 864K = 591ºC