A reaction has rate constant of 0.27 min^{-1} at 45 C and 0.90 min^{-1} at 55 C. What is the activation energy for the reaction (in kJ/mol)?

A. -10.4

B. 10.4

C. 104

D. 10,400

E. 104,000

We’re being asked to **determine the activation energy** of the reaction when the rate increases from 0.27 min^{-1} to 0.90 min^{-1} at 45 to 55°C

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

$\overline{){\mathbf{ln}}\left(\frac{{\mathbf{k}}_{\mathbf{2}}}{{\mathbf{k}}_{\mathbf{1}}}\right){\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{-}}\frac{\mathbf{Ea}}{\mathbf{R}}\left[\frac{\mathbf{1}}{{\mathbf{T}}_{\mathbf{2}}}\mathbf{-}\frac{\mathbf{1}}{{\mathbf{T}}_{\mathbf{1}}}\right]}$

where:

**k _{1}** = rate constant at T

**k _{2}** = rate constant at T

**E _{a}** = activation energy (in J/mol)

**R** = gas constant (8.314 J/mol•K)

**T _{1} and T_{2}** = temperature (in K).

Arrhenius Equation

Arrhenius Equation

Arrhenius Equation

Arrhenius Equation