# Problem: The reaction between nitrogen dioxide and carbon monoxide is NO2(g) + CO(g) NO(g) + CO2(g). The rate constant at 701 K is measured as 2.57 M-1s-1 and that at 895 K is measured as 567 M-1s-1.Use the value of the activation energy (Ea = 1.50 x 102 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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###### FREE Expert Solution

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:

k1 = rate constant at T1

k2 = rate constant at T

Ea = activation energy (in J/mol)

R = gas constant (8.314 J/mol∙K)

T1 and T2 = temperature (in K).

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

1 kJ = 103 J ###### Problem Details

The reaction between nitrogen dioxide and carbon monoxide is NO2(g) + CO(g) NO(g) + CO2(g). The rate constant at 701 K is measured as 2.57 M-1s-1 and that at 895 K is measured as 567 M-1s-1.

Use the value of the activation energy (E= 1.50 x 102 kJ/mol) and the given rate constant of the reaction at either of the two temperatures to predict the rate constant at 551 K.