We’re being asked to **determine the activation energy (E _{a})** when nitrogen tetraoxide, N

We’re given the rates at two different temperatures.

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

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

where **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)

Dinitrogen tetraoxide, N_{2}O_{4}, decomposes to nitrogen dioxide, NO_{2}, in a first-order process. If k = 1.5 x 10^{3} s^{-1} at 10 °C and k = 4.0 x 10^{3} s^{-1} at 30 °C, what is the activation energy for the decomposition?

a. 34998 kJ/mol

b. -35.0 kJ/mol

c. 34998 kJ/mol

d. 35.0 kJ/mol

e. 14.7 kJ/mol

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Arrhenius Equation concept. You can view video lessons to learn Arrhenius Equation. Or if you need more Arrhenius Equation practice, you can also practice Arrhenius Equation practice problems.