A decomposition reaction follows the stoichiometry and obeys the rate law At the rate…

CHEMISTRY · Multi-part · A Level · Chemistry · Rate equations · Rate equations

Problem

A decomposition reaction follows the stoichiometry 2 A→products2\,\text{A} \rightarrow \text{products} and obeys the rate law rate=k[A]2\text{rate} = k[A]^{2} At 298 K298\,\text{K} the rate constant kk is 0.120 L mol−1 s−10.120\,\text{L}\,\text{mol}^{-1}\,\text{s}^{-1}, and the activation energy for the reaction is 75 kJ mol−175\,\text{kJ}\,\text{mol}^{-1}. A laboratory currently carries out the reaction with an initial concentration [A]0=0.50 mol L−1[A]_0 = 0.50\,\text{mol}\,\text{L}^{-1}. For a subsequent experiment the chemist wishes to triple the initial rate, but the concentration of A may not be increased by more than 40%40\% because of solubility limits. (a) Calculate the initial rate under the current conditions. (b) If [A]0[A]_0 is increased by the maximum allowable 40%40\%, calculate the new initial rate. (c) Determine the additional factor by which the rate must be increased beyond the value in part (b) to reach the overall three-fold target. Then calculate the temperature, in kelvins, required to achieve this remaining increase (assume the Arrhenius equation applies and that the pre-exponential factor is independent of temperature). (d) Discuss briefly whether the temperature you found in part (c) is feasible for a typical laboratory setup, citing at least one practical consideration.

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