The gas-phase oxidation of nitric oxide is represented by the equation 2 , NO(g) + O…

CHEMISTRY · Multi-part · A Level · Chemistry · Kinetics · Kinetics

Problem

The gas-phase oxidation of nitric oxide is represented by the equation

2\,\text{NO(g)} + \text{O}_2(\text{g}) \rightarrow 2\,\text{NO}_2(\text{g})

(Reaction 1) An industrial chemist discovers a heterogeneous catalyst that lowers the activation energy of Reaction 1. Laboratory measurements at

298\,\text{K}

give the following activation energies: • Uncatalyzed reaction:

E_a = 95\,\text{kJ\,mol}^{-1}

• Catalyzed reaction:

E_a = 60\,\text{kJ\,mol}^{-1}

Assume that the pre-exponential factor

A

in the Arrhenius equation is the same for both pathways. (a) Derive an expression for the ratio

k_{\text{cat}}/k_{\text{uncat}}

in terms of the activation energies, the universal gas constant

R

, and the absolute temperature

T

. (b) Using

R = 8.314\,\text{J\,mol}^{-1}\,\text{K}^{-1}

and

T = 298\,\text{K}

, calculate the numerical value of

k_{\text{cat}}/k_{\text{uncat}}

for Reaction 1. (c) Interpret the magnitude of the ratio you obtained in part (b) in the context of industrial process design, citing one potential benefit and one possible safety concern.

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