/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 57 Indicate whether each statement ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

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

Expert verified
(a) False: Reactions with larger activation energy generally take longer to occur, making them slower, not faster. (b) False: Having a small rate constant does not necessarily mean having a small frequency factor. (c) True: Higher temperatures result in higher kinetic energy, boosting the probability of successful collisions between molecules and increasing the overall reaction rate.

Step by step solution

01

Statement (a) Analysis

To determine whether the statement is true or false, we need to understand the relationship between activation energy and the rate of a reaction. Activation energy is the minimum energy required for a chemical reaction to take place. Reactions with lower activation energy generally proceed faster, whereas reactions with higher activation energy proceed slower. Now, let's examine the statement.
02

Statement (a) Solution

The statement says, "If you compare two reactions with similar collision factors, the one with the larger activation energy will be faster." This statement is \(\textbf{false}\) since reactions with larger activation energy generally take longer to occur, making them slower, not faster.
03

Statement (b) Analysis

We need to understand the role of the rate constant (k) and the frequency factor (A) in a reaction's rate. The rate constant is a proportionality constant that relates the rate of a reaction to the concentration of the reactants, while the frequency factor is a measure of the number of collisions between molecules per unit time. The Arrhenius equation relates the rate constant, activation energy, and temperature, as follows: \(k = Ae^{\frac{-E_a}{RT}}\) In the equation, k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. Let's analyze the statement.
04

Statement (b) Solution

The statement says, "A reaction that has a small rate constant must have a small frequency factor." According to the Arrhenius equation, a small rate constant (k) could result from either a small frequency factor (A), high activation energy (Ea), or low temperature (T). Therefore, the statement is \(\textbf{false}\) because having a small rate constant does not necessarily mean having a small frequency factor.
05

Statement (c) Analysis

Let's analyze the relationship between reaction temperature and the fraction of successful collisions between reactants. The number of successful collisions depends on the kinetic energy of the molecules. As the temperature increases, the molecules have more kinetic energy, which in turn leads to an increased likelihood of successful collisions. Let's examine the statement.
06

Statement (c) Solution

The statement says, "Increasing the reaction temperature increases the fraction of successful collisions between reactants." This statement is \(\textbf{true}\) as higher temperatures result in higher kinetic energy, boosting the probability of successful collisions between molecules and increasing the overall reaction rate.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

(a) Most commercial heterogeneous catalysts are extremely finely divided solid materials. Why is particle size important? (b) What role does adsorption play in the action of a heterogeneous catalyst?

Ozone in the upper atmosphere can be destroyed by the following two-step mechanism: $$ \begin{aligned} \mathrm{Cl}(g)+\mathrm{O}_{3}(g) & \longrightarrow \mathrm{ClO}(g)+\mathrm{O}_{2}(g) \\ \mathrm{ClO}(g)+\mathrm{O}(g) & \longrightarrow \mathrm{Cl}(g)+\mathrm{O}_{2}(g) \end{aligned} $$ (a) What is the overall equation for this process? (b) What is the catalyst in the reaction? (c) What is the intermediate in the reaction?

Understanding the high-temperature behavior of nitrogen oxides is essential for controlling pollution generated in automobile engines. The decomposition of nitric oxide \((\mathrm{NO})\) to \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) is second order with a rate constant of \(0.0796 \mathrm{M}^{-1} \mathrm{~s}^{-1}\) at \(737^{\circ} \mathrm{C}\) and \(0.0815 \mathrm{M}^{-1} \mathrm{~s}^{-1}\) at \(947{ }^{\circ} \mathrm{C}\). Calculate the activation energy for the reaction.

The gas-phase decomposition of $\mathrm{NO}_{2}, 2 \mathrm{NO}_{2}(g) \longrightarrow\( \)2 \mathrm{NO}(g)+\mathrm{O}_{2}(g),$ is studied at \(383^{\circ} \mathrm{C}\), giving the following data: $$ \begin{array}{cc} \hline \text { Time (s) } & {\left[\mathrm{NO}_{2}\right](M)} \\ \hline 0.0 & 0.100 \\ 5.0 & 0.017 \\ 10.0 & 0.0090 \\ 15.0 & 0.0062 \\ 20.0 & 0.0047 \\ \hline \end{array} $$ (a) Is the reaction first order or second order with respect to the concentration of \(\mathrm{NO}_{2} ?(\mathbf{b})\) What is the rate constant? (c) Predict the reaction rates at the beginning of the reaction for initial concentrations of \(0.200 \mathrm{M}, 0.100 \mathrm{M},\) and $0.050 \mathrm{M} \mathrm{NO}_{2}$.

Based on their activation energies and energy changes and assuming that all collision factors are the same, which of the following reactions would be fastest and which would be slowest? (a) \(E_{a}=45 \mathrm{~kJ} / \mathrm{mol} ; \Delta E=-25 \mathrm{~kJ} / \mathrm{mol}\) (b) \(E_{a}=35 \mathrm{~kJ} / \mathrm{mol} ; \Delta E=-10 \mathrm{~kJ} / \mathrm{mol}\) (c) \(E_{a}=55 \mathrm{~kJ} / \mathrm{mol} ; \Delta E=10 \mathrm{~kJ} / \mathrm{mol}\)
See all solutions

Recommended explanations on Chemistry Textbooks

Kinetics

Read Explanation

Nuclear Chemistry

Read Explanation

Organic Chemistry

Read Explanation

Chemical Analysis

Read Explanation

Inorganic Chemistry

Read Explanation

Chemistry Branches

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.