Question

The pyrolysis of ethane is 2000 times faster at 650?C than at 500?C. By what factor will the activation energy have to be changed for the rate-ratio to be quartered (i.e. 500 times instead of 2000). Try to answer this question without evaluating either activation energy.

Answer 1

By Arrhenius law,

k = k₀ e^-E/RT

k = Rate constant

k₀ = frequency factor

T =Absolute temperature in K

At T = T1,

k1 = k₀ e^-E/RT1

Similarly, at T = T2

On subtracting these equations, we get

T1 = 650 C = 650 + 273 = 923 K

T2 = 500 C = 773 K

(-r_A) k

Therefore,

Case 1: (-r_A)₁ = 2000 x (-r_A)₂ for E = E1

Case 2:  (-r_A)₁ = 500 x (-r_A)₂ for E = E2

Dividing these equations, we get

.: E1 = 1.223 E2

or E2 = 0.8176 E1 ....................................................Answer