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

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

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).

We first need to convert the activation energy from kJ/mol to J/mol:

1 kJ = 10^{3} J

${\mathbf{E}}_{\mathbf{a}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{50}\mathbf{\times}{\mathbf{10}}^{\mathbf{2}}\frac{\overline{)\mathbf{kJ}}}{\mathbf{mol}}\mathbf{\times}\frac{{\mathbf{10}}^{\mathbf{3}}\mathbf{}\mathbf{J}}{\mathbf{1}\mathbf{}\overline{)\mathbf{kJ}}}\mathbf{=}$$\mathbf{150}\mathbf{,}\mathbf{000}\mathbf{}\frac{\mathbf{J}}{\mathbf{mol}}$

The reaction between nitrogen dioxide and carbon monoxide is NO_{2}(g) + CO(g) NO(g) + CO_{2}(g). The rate constant at 701 K is measured as 2.57 M^{-1}s^{-1} and that at 895 K is measured as 567 M^{-1}s^{-1}.

Use the value of the activation energy (E_{a }= 1.50 x 10^{2} kJ/mol) and the given rate constant of the reaction at either of the two temperatures to predict the rate constant at 551 K.

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