Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 11: Problem 99

Which of the following statement(s) is(are) true? a. The half-life for a zero-order reaction increases as the reaction proceeds. b. A catalyst does not change the value of the rate constant. c. The half-life for a reaction, a \(A \longrightarrow\) products, that is first order in A increases with increasing \([\mathrm{A}]_{0}\) d. The half-life for a second-order reaction increases as the reaction proceeds.

Short Answer

Expert verified
The true statement among the given options is statement d: The half-life for a second-order reaction increases as the reaction proceeds.

Step by step solution

01

Statement a: The half-life for a zero-order reaction increases as the reaction proceeds.

To determine the validity of this statement, we recall the expression for half-life for a zero-order reaction. This expression is \(t_{1/2} = \frac{[\mathrm{A}]_0}{2k}\), where \(t_{1/2}\) is the half-life, \(k\) is the rate constant, and \([\mathrm{A}]_0\) is the initial concentration. For a zero-order reaction, as the reaction progresses, the concentration of A decreases, but the half-life remains constant, since it depends only on the initial concentration and the rate constant. Therefore, statement a is false.
02

Statement b: A catalyst does not change the value of the rate constant.

A catalyst is a substance that increases the rate of a chemical reaction without undergoing any permanent change itself. It does this by providing an alternative reaction pathway with a lower activation energy. As a result, a catalyst increases the reaction rate by affecting the rate constant. So, statement b is false.
03

Statement c: The half-life for a reaction, a \(A \longrightarrow\) products, that is first-order in A increases with increasing \([\mathrm{A}]_{0}\).

For a first-order reaction, we have the half-life expression, \(t_{1/2} = \frac{0.693}{k}\), where \(t_{1/2}\) is the half-life and \(k\) is the rate constant. As we can see, the half-life for a first-order reaction is not dependent on the initial concentration of A, thus it does not increase with increasing \([\mathrm{A}]_{0}\). Therefore, statement c is false.
04

Statement d: The half-life for a second-order reaction increases as the reaction proceeds.

For a second-order reaction, the half-life expression is \(t_{1/2} = \frac{1}{k[\mathrm{A}]_0}\), where \(t_{1/2}\) is the half-life, \(k\) is the rate constant, and \([\mathrm{A}]_0\) is the initial concentration. From this expression, we can see that the half-life depends inversely on the initial concentration. As the reaction progresses, the concentration of A decreases, so the half-life increases. Therefore, statement d is true. In conclusion, the true statement(s) among the given options is statement d: The half-life for a second-order reaction increases as the reaction proceeds.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Draw a rough sketch of the energy profile for each of the following cases: a. \(\Delta E=+10 \mathrm{kJ} / \mathrm{mol}, E_{\mathrm{a}}=25 \mathrm{kJ} / \mathrm{mol}\) b. \(\Delta E=-10 \mathrm{kJ} / \mathrm{mol}, E_{\mathrm{a}}=50 \mathrm{kJ} / \mathrm{mol}\) c. \(\Delta E=-50 \mathrm{kJ} / \mathrm{mol}, E_{\mathrm{a}}=50 \mathrm{kJ} / \mathrm{mol}\)

The reaction \(\mathrm{A}(a q)+\mathrm{B}(a q) \longrightarrow\) products \((a q)\) was studied, and the following data were obtained: What is the order of the reaction with respect to A? What is the order of the reaction with respect to B? What is the value of the rate constant for the reaction?

Consider the general reaction $$\mathrm{aA}+\mathrm{bB} \longrightarrow \mathrm{cC}$$ and the following average rate data over some time period \(\Delta t:\) $$-\frac{\Delta \mathrm{A}}{\Delta t}=0.0080 \mathrm{mol} / \mathrm{L} \cdot \mathrm{s}$$ $$-\frac{\Delta \mathrm{B}}{\Delta t}=0.0120 \mathrm{mol} / \mathrm{L} \cdot \mathrm{s}$$ $$\frac{\Delta \mathrm{C}}{\Delta t}=0.0160 \mathrm{mol} / \mathrm{L} \cdot \mathrm{s}$$ Determine a set of possible coefficients to balance this general reaction.

Sulfuryl chloride \(\left(\mathrm{SO}_{2} \mathrm{Cl}_{2}\right)\) decomposes to sulfur dioxide \(\left(\mathrm{SO}_{2}\right)\) and chlorine \(\left(\mathrm{Cl}_{2}\right)\) by reaction in the gas phase. The following pressure data were obtained when a sample containing \(5.00 \times 10^{-2}\) mol sulfury 1 chloride was heated to \(600 . \mathrm{K}\) in a \(5.00 \times 10^{-1}-\mathrm{L}\) container. Defining the rate as $$-\frac{\Delta\left[\mathrm{SO}_{2} \mathrm{Cl}_{2}\right]}{\Delta t}$$ a. determine the value of the rate constant for the decomposition of sulfuryl chloride at \(600 .\) K. b. what is the half-life of the reaction? c. what fraction of the sulfuryl chloride remains after \(20.0 \mathrm{h} ?\)

Would the slope of a \(\ln (k)\) versus \(1 / T\) plot (with temperature in kelvin) for a catalyzed reaction be more or less negative than the slope of the \(\ln (k)\) versus \(1 / T\) plot for the uncatalyzed reaction? Explain. Assume both rate laws are first-order overall.
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Analysis

Read Explanation

Chemical Reactions

Read Explanation

Kinetics

Read Explanation

Inorganic Chemistry

Read Explanation

Organic Chemistry

Read Explanation

Making Measurements

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.

Sign-up for free