For the gas-phase decomposition of compound X to products

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

Problem

For the gas-phase decomposition of compound X to products, a researcher measures the following activation energies: • Uncatalyzed pathway:

E_{a,u}=180\,\text{kJ mol}^{-1}

• Catalyzed pathway:

E_{a,c}=120\,\text{kJ mol}^{-1}

Assume that, for both pathways, the pre-exponential factor A in the Arrhenius expression is the same and that

k\propto e^{-E_a/RT}

. The reaction is carried out isothermally at

T=550\,\text{K}

. (a) Calculate the ratio

\dfrac{k_c}{k_u}

of the rate constant for the catalyzed pathway to that for the uncatalyzed pathway. Express your answer to two significant figures. (b) Determine by what factor the half-life of the reaction changes upon addition of the catalyst, assuming first-order kinetics. (c) State two practical implications of your result for industrial scale-up of this decomposition process.

Related theory

Chemical Kinetics
Arrhenius Equation
Temperature Dependence of Rate

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