The activation energy for a particular reaction is 102 kJ/mol. If the rate constant is 1.35 × 10⁻⁴ s⁻¹ at 314 K, what is the rate constant at 273 K?

Question

this question has to do with integrated rate law.

Answer 1

I don't think that problem is related to integrated rate laws, but rather it seems to be an example of using the Arrhenius equation:

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

k1 = 1.35x10^-4 s^-1

k2 = ?

T1 = 314K

T2 = 273K

Ea = 102 kJ/mol

R = 8.314 J/Kmol = 0.008314 kJ/Kmol (note to change units of R to agree with units of Ea)

Solving for k2, we have ...

ln(k2/1.35x10^-4) = -(102/0.008314) (1/273 - 1/314)

ln(k2/1.35x10^-4) = -12268(0.00366 - 0.00318)

ln(k2/1.35x10^-4) = -12268 * 4.8x10^-4

ln(k2/1.35x10^-4) = -5.89

k2/1.35x10^-4 = 2.77x10^-3

k2 = 3.74x10^-7 s^-1