menu
bartleby
search
close search
Hit Return to see all results
close solutoin list

Consider a reaction of the type aA ⟶ products, in which the rate law is found to he rate = k [A] 3 (termolecular reactions are improbable but possible). If the first half-tife of the reaction is found to he 40. s, what is the time for the second half-life? Hint: Using your calculus knowledge, derive the integrated rate law from the differential rate law for a tennolecular reaction: Rate = − d [ A ] d t = k [ A ] 3

BuyFindarrow_forward

Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

Solutions

Chapter
Section
BuyFindarrow_forward

Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 11, Problem 102CP
Textbook Problem
25 views

Consider a reaction of the type aA ⟶ products, in which the rate law is found to he rate = k[A]3 (termolecular reactions are improbable but possible). If the first half-tife of the reaction is found to he 40. s, what is the time for the second half-life? Hint: Using your calculus knowledge, derive the integrated rate law from the differential rate law for a tennolecular reaction:

Rate = d [ A ] d t = k [ A ] 3

Interpretation Introduction

Interpretation: The rate law for a reaction and first half-life is given. By using these values, second half-life is to be determined for the reaction.

Concept introduction: Integrated rate law is an expression that combines the rate constant, time and change in concentrations in the form of a mathematical equation. The half-life of the third order reaction can be calculated by using the formula,

t1/2=32k[A]02

To determine: The time for the second half-life of the given reaction.

Explanation of Solution

Given

First half-life of the reaction is 40s.

Rate law for third order reaction is,

Rate=k[A]3 (1)

Differential rate law for third order reaction is,

Rate=d[A]dt (2)

From equation (1) and equation (2),

d[A]dt=k[A]3d[A][A]3=kdt

Integrate the above equation,

k0tdt=[A]0[A]d[A][A]3k(t)0t=(12[A]2)[A]0[A]kt=(12[A]2+12[A]02)kt=(12[A]212[A]02) (3)

Where,

  • [A]0 is the initial concentration of reactant A

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Chapter 11 Solutions

Chemistry: An Atoms First Approach
Show all chapter solutions
add
Ch. 11 - Why does a catalyst increase the rate of a...Ch. 11 - Define stability from both a kinetic and...Ch. 11 - Describe at least two experiments you could...Ch. 11 - Make a graph of [A] versus time for zero-, first-,...Ch. 11 - How does temperature affect k. the rate constant?...Ch. 11 - Consider the following statements: In general, the...Ch. 11 - For the reaction A + B C, explain at least two...Ch. 11 - A friend of yours states, A balanced equation...Ch. 11 - Provide a conceptual rationale for the differences...Ch. 11 - The rate constant (k) depends on which of the...Ch. 11 - Each of the statements given below is false....Ch. 11 - Define what is meant by unimolecular and...Ch. 11 - The plot below shows the number of collisions with...Ch. 11 - For the reaction O2(g)+2NO(g)2NO2(g) the observed...Ch. 11 - The rate law for a reaction can be determined only...Ch. 11 - Table 11-2 illustrates how the average rate of a...Ch. 11 - The type of rate law for a reaction, either the...Ch. 11 - The initial rate of a reaction doubles as the...Ch. 11 - Hydrogen reacts explosively with oxygen. However,...Ch. 11 - The central idea of the collision model is that...Ch. 11 - Consider the following energy plots for a chemical...Ch. 11 - Enzymes are kinetically important for many of the...Ch. 11 - Would the slope of a ln(k) versus 1/T plot (with...Ch. 11 - Consider the reaction 4PH3(g)P4(g)+6H2(g) If, in a...Ch. 11 - In the Haber process for the production of...Ch. 11 - At 40C, H2O2 (aq) will decompose according to the...Ch. 11 - Consider the general reaction aA+bBcC and the...Ch. 11 - What are the units for each of the following if...Ch. 11 - The rate law for the reaction...Ch. 11 - The reaction 2NO(g)+Cl2(g)2NOCl(g) was studied at...Ch. 11 - The reaction 2I-(aq)+S2O82-(aq)I2(aq)+2SO42-(aq)...Ch. 11 - The decomposition of nitrosyl chloride was...Ch. 11 - The following data were obtained for the gas-phase...Ch. 11 - The reaction I(aq)+OCl(aq)IO(aq)+Cl(aq) was...Ch. 11 - The reaction 2NO(g)+O2(g)2NO2(g) was studied. and...Ch. 11 - The rote of the reaction between hemoglobin (Hb)...Ch. 11 - The following data were obtained for the reaction...Ch. 11 - The decomposition of hydrogen peroxide was...Ch. 11 - A certain reaction has the following general form:...Ch. 11 - The rate of the reaction NO2(g)+CO(g)NO(g)+CO2(g)...Ch. 11 - A certain reaction has the following general form:...Ch. 11 - The decomposition of ethanol (C2H5OH) on an...Ch. 11 - At 500 K in the presence of a copper surface,...Ch. 11 - The dimerization of butadiene 2C4H6(g)C8H12(g) was...Ch. 11 - The rate of the reaction O(g)+NO2(g)NO(g)+O2(g)...Ch. 11 - Experimental data for the reaction A2B+C have been...Ch. 11 - Consider the data plotted in Exercise 45 when...Ch. 11 - The reaction AB+C is known to be zero order in A...Ch. 11 - The decomposition of hydrogen iodide on finely...Ch. 11 - A certain first-order reaction is 45.0% complete...Ch. 11 - A first-order reaction is 75.0% complete in 320....Ch. 11 - The rate law for the decomposition of phosphine...Ch. 11 - DDT (molar mass = 354.49 g/mol) was a widely used...Ch. 11 - Consider the following initial rate data for the...Ch. 11 - The rate law for the reaction...Ch. 11 - For the reaction A products, successive...Ch. 11 - Theophylline is a pharmaceutical drug that is...Ch. 11 - You and a coworker have developed a molecule...Ch. 11 - Consider the hypothetical reaction A+B+2C2D+3E...Ch. 11 - Write the rate laws for the following elementary...Ch. 11 - A possible mechanism for the decomposition of...Ch. 11 - A proposed mechanism for a reaction is...Ch. 11 - The mechanism for the gas-phase reaction of...Ch. 11 - For the following reaction profile, indicate a....Ch. 11 - Draw a rough sketch of the energy profile for each...Ch. 11 - The activation energy for the reaction...Ch. 11 - The activation energy for some reaction...Ch. 11 - The rate constant for the gas-phase decomposition...Ch. 11 - The reaction (CH3)3CBr+OH(CH3)3COH+Br in a certain...Ch. 11 - The activation energy for the decomposition of...Ch. 11 - A first-order reaction has rate constants of 4.6 ...Ch. 11 - A certain reaction has an activation energy of...Ch. 11 - Chemists commonly use a rule of thumb that an...Ch. 11 - Which of the following reactions would you expect...Ch. 11 - One reason suggested for the instability of long...Ch. 11 - One mechanism for the destruction of ozone in the...Ch. 11 - One of the concerns about the use of Freons is...Ch. 11 - Assuming that the mechanism for the hydrogenation...Ch. 11 - The decomposition of NH3 to N2 and H2 was studied...Ch. 11 - The decomposition of many substances on the...Ch. 11 - For enzyme-catalyzed reactions that follow the...Ch. 11 - A popular chemical demonstration is the magic...Ch. 11 - The activation energy for a reaction is changed...Ch. 11 - Consider the following representation of the...Ch. 11 - The reaction H2SeO3(aq) + 6I-(aq) + 4H+(aq) Se(s)...Ch. 11 - Consider two reaction vessels, one containing A...Ch. 11 - Sulfuryl chloride (SO2Cl2) decomposes to sulfur...Ch. 11 - For the reaction 2N2O5(g)4NO2(g)+O2(g) the...Ch. 11 - Experimental values for the temperature dependence...Ch. 11 - Cobra venom helps the snake secure food by binding...Ch. 11 - Iodomethane (CH3I) is a commonly used reagent in...Ch. 11 - Experiments during a recent summer on a number of...Ch. 11 - The activation energy of a certain uncatalyzed...Ch. 11 - Consider the reaction 3A+B+CD+E where the rate law...Ch. 11 - The thiosulfate ion (S2O32) is oxidized by iodine...Ch. 11 - The reaction A(aq)+B(aq)products(aq) was studied,...Ch. 11 - A certain substance, initially present at 0.0800...Ch. 11 - A reaction of the form aAProducts gives a plot of...Ch. 11 - A certain reaction has the form aAProducts At a...Ch. 11 - Which of the following statement(s) is( are) true?...Ch. 11 - Consider the hypothetical reaction A2(g) + B2(g) ...Ch. 11 - Experiments have shown that the average frequency...Ch. 11 - Consider a reaction of the type aA products, in...Ch. 11 - A study was made of the effect of the hydroxide...Ch. 11 - Two isomers (A and B) of a given compound dimerize...Ch. 11 - The reaction NO(g)+O3NO2(g)+O2(g) was studied by...Ch. 11 - Most reactions occur by a series of steps. The...Ch. 11 - You are studying the kinetics of the reaction...Ch. 11 - The decomposition of NO2(g) occurs by the...Ch. 11 - The following data were collected in two studies...Ch. 11 - Consider the following hypothetical data collected...Ch. 11 - Consider the hypothetical reaction A+B+2C2D+3E In...Ch. 11 - Hydrogen peroxide and the iodide ion react in...Ch. 11 - Sulfuryl chloride undergoes first-order...Ch. 11 - Upon dissolving InCl(s) in HCl, In+(aq) undergoes...Ch. 11 - The decomposition of iodoethane in the gas phase...Ch. 11 - Consider the following reaction: CH3X+YCH3Y+X At...

Additional Science Textbook Solutions

Find more solutions based on key concepts
Show solutions add
What are the moral implications of using alcohol during pregnancy?

Understanding Nutrition (MindTap Course List)

Two tablespoons of peanut butter offer about the same amount of protein as a hot dog. T F

Nutrition: Concepts and Controversies - Standalone book (MindTap Course List)

What are the two major divisions of natural science?

An Introduction to Physical Science

What are the chemical differences between DNA and RNA?

Biology: The Dynamic Science (MindTap Course List)

How many autosomes are present in a body cell of a human being? In a gamete?

Human Heredity: Principles and Issues (MindTap Course List)

A nonconducting ring of radius 10.0 cm is uniformly charged with a total positive charge 10.0 C. The ring rotat...

Physics for Scientists and Engineers, Technology Update (No access codes included)

What are submarine canyons? Where are they found, and how are they thought to have been formed?

Oceanography: An Invitation To Marine Science, Loose-leaf Versin