Problem: The following reaction has an activation energy of 262 kJ/mol. C4H8 (g) → 2 C2H4 (g)At 600.0 K the rate constant is 6.1x 10-8 s-1. What is the value of the rate constant at 795.0 K?

We’re being asked to determine the rate constant at 795.0 K. We are asked for rates at two different temperatures.

This means we need to use the two-point form of the Arrhenius Equation:

$\boxed{\mathbf{ln}\mathbf{ }\frac{{\mathbf{k}}_{\mathbf{2}}}{{\mathbf{k}}_{\mathbf{1}}}\mathbf{=}\mathbf{-}\frac{{\mathbf{E}}_{\mathbf{a}}}{\mathbf{R}}\mathbf{[}\frac{\mathbf{1}}{{\mathbf{T}}_{\mathbf{2}}}\mathbf{-}\frac{\mathbf{1}}{{\mathbf{T}}_{\mathbf{1}}}\mathbf{]}}$

where k₁ = rate constant at T₁

k₂ = rate constant at T₂

E_a = activation energy (in J/mol)

R = gas constant (8.314 J/mol•K)

T₁ and T₂ = temperature (in K)