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Chapter 13: Problem 139

Is the rate constant \((k)\) of a reaction more sensitive to changes in temperature if \(E_{\mathrm{a}}\) is small or large?

Short Answer

Expert verified
The rate constant (\(k\)) of a reaction is more sensitive to changes in temperature if the activation energy (\(E_a\)) is large.

Step by step solution

01

Understanding the Relation

By looking at the formula of the Arrhenius equation, \(k = Ae^{-E_a/RT}\), it's seen that the value of \(k\) (rate constant) decreases when the activation energy (\(E_a\)) increases, and increases when \(E_a\) decreases. This is an inverse relationship.
02

Determining the Sensitivity

The rate constant \(k\) is said to be more sensitive to changes in temperature if a small change in the temperature causes a significant change in the rate constant. From the inverse relationship between \(k\) and \(E_a\), it can be deduced that when \(E_a\) is large, a small change in temperature produces a significant change in \(k\). Thus, the rate constant is more sensitive to changes in temperature if \(E_a\) is large.

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Most popular questions from this chapter

Consider the second-order reaction $$ \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{NOCl}(g)+\mathrm{Cl}(g) $$ Given that the frequency factor and activation energy for the reaction are \(4.0 \times 10^{9} / M \cdot \mathrm{s}\) and \(85 \mathrm{~kJ} / \mathrm{mol}\), respectively, calculate the rate constant at \(500^{\circ} \mathrm{C}\).

A flask contains a mixture of compounds A and B. Both compounds decompose by first-order kinetics. The half-lives are 50.0 min for A and 18.0 min for B. If the concentrations of \(A\) and \(B\) are equal initially, how long will it take for the concentration of A to be four times that of \(\mathrm{B}\) ?

Define activation energy. What role does activation energy play in chemical kinetics?

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A factory that specializes in the refinement of transition metals such as titanium was on fire. The firefighters were advised not to douse the fire with water. Why?
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