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Chapter 14: Problem 57

Indicate whether each statement is true or false. (a) If you compare two reactions with similar collision factors, the one with the larger activation energy will be faster. (b) A reaction that has a small rate constant must have a small frequency factor. (c) Increasing the reaction temperature increases the fraction of successful collisions between reactants.

Short Answer

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(a) False (b) False (c) True

Step by step solution

01

Statement (a) Analysis and Verification

Let's analyze the statement: If you compare two reactions with similar collision factors, the one with the larger activation energy will be faster. Activation energy is the energy barrier that must be overcome for a reaction to occur. The higher the activation energy, the slower the reaction rate as fewer molecules possess the necessary energy to overcome the barrier. Collision factors help determine the probability of successful collisions. Given that the collision factors are similar, the difference in reaction rates will depend only on the activation energy. Therefore, the statement is False.
02

Statement (b) Analysis and Verification

Let's analyze the statement: A reaction that has a small rate constant must have a small frequency factor. The rate constant (k) is related to the frequency factor (A) and the activation energy (Ea) by the Arrhenius equation: \( k = Ae^{(-Ea/RT)} \) A small rate constant does not necessarily mean a small frequency factor, as it could also be due to a high activation energy or a low temperature. The statement does not mention either of these factors. Therefore, the statement is False.
03

Statement (c) Analysis and Verification

Let's analyze the statement: Increasing the reaction temperature increases the fraction of successful collisions between reactants. Increasing the temperature provides more energy to the reactant molecules, which increases the number of molecules with enough energy to overcome the activation energy barrier. The higher the temperature, the greater the fraction of molecules possessing sufficient energy to react. Therefore, increasing the temperature increases the probability of successful collisions between reactants. Therefore, the statement is True.

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Most popular questions from this chapter

Consider the following hypothetical aqueous reaction: $\mathrm{A}(a q) \rightarrow \mathrm{B}(a q)\(. A flask is charged with \)0.065 \mathrm{~mol}$ of \(\mathrm{A}\) in a total volume of \(100.0 \mathrm{~mL}\). The following data are collected: $$ \begin{array}{lccccc} \hline \text { Time (min) } & 0 & 10 & 20 & 30 & 40 \\ \hline \text { Moles of A } & 0.065 & 0.051 & 0.042 & 0.036 & 0.031 \\ \hline \end{array} $$ (a) Calculate the number of moles of \(\mathrm{B}\) at each time in the table, assuming that there are no molecules of \(\mathrm{B}\) at time zero and that A cleanly converts to B with no intermediates. (b) Calculate the average rate of disappearance of A for each 10 -min interval in units of \(M /\) s. (c) Between \(t=0 \mathrm{~min}\) and \(t=30 \mathrm{~min},\) what is the average rate of appearance of \(\mathrm{B}\) in units of \(\mathrm{M} / \mathrm{s}\) ? Assume that the volume of the solution is constant.

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