For a reaction at 298 K, the activation energy (\(E_a\)) is 21.0 kJ. When the reaction is catalyzed and run at the same temperature, \(E_a\) is 35.9 kJ.

What is the ratio of the rate constant (\(k_{\text{cat}}\)) for the catalyzed reaction to the rate constant (\(k_{\text{uncat}}\)) for the uncatalyzed reaction? Assume the value of the frequency factor (\(A\)) is the same for both reactions.

Question

01-09-2024
Chemistry

High School

Thank you for visiting For a reaction at 298 K the activation energy E a is 21 0 kJ When the reaction is catalyzed and run at the same. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

For a reaction at 298 K, the activation energy (\(E_a\)) is 21.0 kJ. When the reaction is catalyzed and run at the same temperature, \(E_a\) is 35.9 kJ.

What is the ratio of the rate constant (\(k_{\text{cat}}\)) for the catalyzed reaction to the rate constant (\(k_{\text{uncat}}\)) for the uncatalyzed reaction? Assume the value of the frequency factor (\(A\)) is the same for both reactions.

Answer :

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ayushgupta030303 ayushgupta030303 · Answer 1 · 2023-09-08T23:24:50-04:00

Final answer:

In order to answer the question, the Arrhenius equation is used to calculate the rate constants for both catalyzed and uncatalyzed reactions. The ratio of these rate constants is then determined.

Explanation:

The question is asking about comparing the rate constants (k) for the catalyzed and uncatalyzed reactions, using the activation energies given. We can calculate these rate constants using the Arrhenius equation, which is k = Ae^(-Ea/RT), where R is the ideal gas constant, T is temperature on the Kelvin scale, Ea is the activation energy in joules per mole, e is the constant 2.7183, and A is a constant called the frequency factor.

First, calculate the rate constant for the uncatalyzed reaction (kuncat) and the catalyzed reaction (kcat), then take the ratio of kcat to kuncat. This will give the rate constant ratio required. Note that the frequency factor (A), being the same for both reactions, won't affect the ratio.

In this problem, like any other involving rate constants and activation energies, it's essential to utilize the Arrhenius equation properly and understanding the effect of catalyst, which lowers the activation energy and in turn, increases the rate of a chemical reaction.

Learn more about Rate Constants here:

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