What is the value of the rate constant at 820.0 K?

Question

C4H8(g)⟶2C2H4(g)has an activation energy of 262 kJ/mol.

At 600.0 K, the rate constant, 𝑘, is 6.1×10−8 s−1. What is the value of the rate constant at 820.0 K?

Answer 1

C4H8(g)⟶2C2H4(g) has an activation energy of 262 kJ/mol.

Given:

T₁ = 600.0 K

k₁ = 6.1 x 10^-8 s^-1

T₂ = 820.0 K

R = 8.314 JK^-1mol^-1

Activation Energy, E_a = 262 KJ / mol = 2.62 x 10⁵ J/mol

Using the Arrhenius equation,

ln (k₂ / k₁) = - E_a/R (1/T₂ - 1/T₁)

substituting the values we have in the above equation, we get

ln (k₂ / 6.1 x 10^-8 s^-1) = - 2.62 x 10⁵ J/mol / 8.314 JK^-1mol^-1 (1/820.0K - 1/600.0K)

k₂ = 8.036 x 10^-2 = 0.08036 s^-1

The value of the rate constant at 820.0 K is 0.08036 s^-1