# Problem: One mechanism for the destruction of ozone in the upper atmosphere isc. Ea for the uncatalyzed reactionO3 (g) + O (g) → 2O2 (g)is 14.0 kJ. Ea for the same reaction when catalyzed is 11.9 kJ. What is the ratio of the rate constant for the catalyzed reaction to that for the uncatalyzed reaction at 25°C? Assume that the frequency factor A is the same for each reaction.

###### FREE Expert Solution

Arrhenius Equation:

Ratio of rate constant for catalyzed to uncatalyzed:

$\frac{{\mathbf{k}}_{\mathbf{catalyzed}}}{{\mathbf{k}}_{\mathbf{uncatalyzed}}}\mathbf{=}\frac{\overline{)\mathbf{A}}{\mathbf{e}}^{\mathbf{-}\frac{{\mathbf{E}}_{\mathbf{a}\mathbf{,}\mathbf{cat}\mathbf{.}}}{\mathbf{RT}}}}{\overline{)\mathbf{A}}{\mathbf{e}}^{\mathbf{-}\frac{{\mathbf{E}}_{\mathbf{a}\mathbf{,}\mathbf{uncat}\mathbf{.}}}{\mathbf{RT}}}}$

T = 25°C + 273 = 298 K

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###### Problem Details

One mechanism for the destruction of ozone in the upper atmosphere is

c. Ea for the uncatalyzed reaction

O3 (g) + O (g) → 2O2 (g)

is 14.0 kJ. Ea for the same reaction when catalyzed is 11.9 kJ. What is the ratio of the rate constant for the catalyzed reaction to that for the uncatalyzed reaction at 25°C? Assume that the frequency factor A is the same for each reaction.