Chemistry
Chemistry
4th Edition
ISBN: 9780078021527
Author: Julia Burdge
Publisher: McGraw-Hill Education
bartleby

Videos

Textbook Question
Book Icon
Chapter 14, Problem 42QP

The rate constant of a first-order reaction is 4 .60 × 10 -4 s -1 at 350°C . If the activation energy is 104 kJ/mol , calculate the temperature at which its rate constant is 8 .80 × 10 -4 s -1 .

Expert Solution & Answer
Check Mark
Interpretation Introduction

Interpretation:

The final temperature of the given reaction is to be calculated

Concept introduction:

The rate of reaction is the measurement of the concentration change of reactants within a period of time during the course of a reaction. The concentration-versus-time graph of the reaction is used to determine the rate constant of the reaction.

The rate of reaction increases with increase in the temperature of the reaction.

Answer to Problem 42QP

Solution: 371°C

Explanation of Solution

Given information:

Rate constant of the first-order reaction is,

k1=4.60×104s1k2=8.80×104s1

The activation energy of the reaction is 104kJ/mol.

Temperature, T1=350°C

The conversion of activation energy into joules is given as follows:

Ea=104kJ/mol=104000J/mol

The conversion of temperature into kelvin is given as follows:

T1=(350+273.15)K=623.15K

The temperature of the given reaction is calculated by the following expression:

lnk2k1=EaR[1T11T2]T2=EaT1EaT1Rlnk2k1

Here, k1 is the initial rate constant, k2 is the final rate constant, Ea is the activation energy, R is the gas constant, T1 is the initial temperature, and T2 is the final temperature of the reaction.

Substitute the values of k1,k2,Ea,R, and T1 in the above equation,

T2=104000J/mol×623.15K104000J/mol(623.15K)(8.314J/K.mol)ln8.80×104s14.60×104s1=104000J/mol×623.15K104000J/mol(623.15K)(8.314J/K.mol)(ln1.9130)=104000J/mol×623.15K(1040003360.688)J/mol=64807600K(1040003360.688)

Simplify the above equation to obtain the value of temperature.

T2=64807600K100639.31=643.959K644K

The conversion of temperature into °C is given as follows:

T2=(644273.15)°C=370.85°C371°C

The value of temperature at rate constant 8.80×104s1 is 371°C.

Conclusion

The final temperature of the given reaction is 371°C.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 14 Solutions

Chemistry

Ch. 14.2 - Answer questions 14.2.1 through 14.2.4 using the...Ch. 14.2 - Answer questions 14.2.1 through 14.2.4 using the...Ch. 14.2 - 14.2.5 The diagrams represent three experiments in...Ch. 14.3 - Prob. 1PPACh. 14.3 - Practice Problem BUILD For the following general...Ch. 14.3 - Practice Problem CONCEPTUALIZE Three initial-rate...Ch. 14.3 - The first-order decomposition of dinitrogen...Ch. 14.3 - The first-order decomposition of dinitrogen...Ch. 14.3 - 14.3.3 Consider the first-order reaction in which...Ch. 14.3 - Which figure below represents the numbers of...Ch. 14.3 - 14.3.5 Of the plots shown here, ___________...Ch. 14.4 - Practice Problem ATTEMPT The rate constant for the...Ch. 14.4 - Practice Problem BUILD Refer again to the reaction...Ch. 14.4 - Practice Problem CONCEPTUALIZE The diagrams on...Ch. 14.4 - Use the table of data collected for a first-order...Ch. 14.4 - Prob. 2CPCh. 14.4 - Prob. 3CPCh. 14.5 - Practice Problem ATTEMPT Ethyl iodide ( C 2 H 5 I)...Ch. 14.5 - Practice Problem BUILD Use the calculated k from...Ch. 14.5 - Practice Problem CONCEPTUALIZE Use the graph in...Ch. 14.5 - Use the following information to answer questions...Ch. 14.5 - Use the following information to answer questions...Ch. 14.5 - Use the following information to answer questions...Ch. 14.5 - 14.5.4 A plausible mechanism for the reaction: Ch. 14.6 - Practice ProblemATTEMPT Calculate the half-life of...Ch. 14.6 - Practice ProblemBUILD Calculate the rate constant...Ch. 14.6 - Practice Problem CONCEPTUALIZE The diagrams show a...Ch. 14.7 - Practice Problem ATTEMPT The reaction is second...Ch. 14.7 - Practice Problem BUILD Determine the initial...Ch. 14.7 - Practice ProblemCONCEPTUALIZE The diagrams below...Ch. 14.8 - Practice ProblemATTEMPT The second-order rate...Ch. 14.8 - Practice Problem BUILD Use the graph to determine...Ch. 14.8 - Prob. 1PPCCh. 14.9 - Practice ProblemATTEMPT Use the data in the...Ch. 14.9 - Practice ProblemBUILD Based on the data shown in...Ch. 14.9 - Practice Problem CONCEPTUALIZE According to the...Ch. 14.10 - Practice ProblemATTEMPT Calculate the rate...Ch. 14.10 - Practice ProblemBUILD Calculate the rate constant...Ch. 14.10 - Practice ProblemCONCEPTUALIZE According to the...Ch. 14.11 - Practice Problem ATTEMPT The reaction between and...Ch. 14.11 - Practice ProblemBUILD Propose a plausible...Ch. 14.11 - Practice Problem CONCEPTUALIZE How many steps are...Ch. 14.12 - Practice Problem ATTEMPT Show that the following...Ch. 14.12 - Practice Problem BUILD The reaction proceeds via...Ch. 14.12 - Practice Problem CONCEPTUALIZE The reaction of is...Ch. 14 - Prob. 1KSPCh. 14 - Prob. 2KSPCh. 14 - Prob. 3KSPCh. 14 - Prob. 4KSPCh. 14 - 14.1 What is meant by the rate of a chemical...Ch. 14 - Distinguish between average rate and instantaneous...Ch. 14 - What are the advantages of measuring the initial...Ch. 14 - Identify two reactions that are very slow (take...Ch. 14 - Write the reaction rate expressions for the...Ch. 14 - Write the reaction rate expressions for the...Ch. 14 - Consider the reaction: 2NO ( g ) + O 2 ( g ) → 2NO...Ch. 14 - 14.8 Consider the reaction: Suppose that at a...Ch. 14 - 14.9 Explain what is meant by the rate law of a...Ch. 14 - Prob. 10QPCh. 14 - What are the units for the rate constants of...Ch. 14 - 14.12 Consider the zeroth-order reaction: a ...Ch. 14 - 14.13 The rate constant of a first-order reaction...Ch. 14 - Identify two reactions that are very slow (take...Ch. 14 - The rate law for the reaction: N H 4 + ( a q )+N O...Ch. 14 - Use the data in Table 14.2 to calculate the rate...Ch. 14 - 14.17 Consider the reaction: From the following...Ch. 14 - Consider the reaction: X + Y → Z From the...Ch. 14 - Determine the overall orders of the reactions to...Ch. 14 - 14.20 Consider the reaction: The rate of the...Ch. 14 - Cyclobutane decomposes to ethylene according to...Ch. 14 - The following gas-phase reaction was studied at...Ch. 14 - Write an equation relating the concentration of a...Ch. 14 - 14.24 Define half-life. Write the equation...Ch. 14 - Prob. 25QPCh. 14 - 14.26 For a first-order reaction, how long will it...Ch. 14 - What is the half-life of a compound if 75 percent...Ch. 14 - 14.28 The thermal decomposition of phosphine into...Ch. 14 - The rate constant for the second-order reaction:...Ch. 14 - The rate constant for the second-order reaction:...Ch. 14 - 14.31 The second-order rate constant for the...Ch. 14 - Prob. 32QPCh. 14 - 14.33 The reaction shown here follows first-order...Ch. 14 - 14 34 Define activation energy. What role does...Ch. 14 - Prob. 35QPCh. 14 - Prob. 36QPCh. 14 - The burning of methane in oxygen is a highly...Ch. 14 - Sketch a potential-energy versus reaction progress...Ch. 14 - The reaction H+H 2 → H 2 +H has been studied for...Ch. 14 - Over the range of about ±3°C from normal body...Ch. 14 - For the reaction: NO ( g ) + O 3 ( g ) → NO 2 ( g...Ch. 14 - The rate constant of a first-order reaction is 4...Ch. 14 - The rate constants of some reactions double with...Ch. 14 - 14.44 The rate at which tree crickets chirp is ...Ch. 14 - The rate of bacterial hydrolysis of fish muscle is...Ch. 14 - Prob. 46QPCh. 14 - Given the same reactant concentrations, the...Ch. 14 - 14.48 Variation of the rate constant with...Ch. 14 - 14.49 Diagram A describes the initial state of...Ch. 14 - 14 50 What do we mean by the mechanism of a...Ch. 14 - 14.51 What is an elementary step? What is the...Ch. 14 - 14.52 Classify the following elementary reactions...Ch. 14 - Reactions can be classified as unimolecular,...Ch. 14 - Determine the molecularity, and write the rate law...Ch. 14 - 14.55 What is the rate-determining step of a...Ch. 14 - 14.56 The equation for the combustion of ethane ...Ch. 14 - Specify which of the following species cannot be...Ch. 14 - Classify each of the following elementary steps as...Ch. 14 - 14.59 The rate law for the reaction: is given by...Ch. 14 - For the reaction x 2 + y + z → x y + x z , it is...Ch. 14 - The rate law for the reaction: 2H 2 ( g ) + 2NO (...Ch. 14 - 14.62 The rate law for the decomposition of ozone...Ch. 14 - 14.63 How does a catalyst increase the rate of a...Ch. 14 - 14.64 What are the characteristics of a...Ch. 14 - A certain reaction is known to proceed slowly at...Ch. 14 - Most reactions, including enzyme-catalyzed...Ch. 14 - 14.67 Are enzyme-catalyzed reactions examples of...Ch. 14 - The concentrations of enzymes in cells are usually...Ch. 14 - When fruits such as apples and pears are cut. the...Ch. 14 - The first-order rate constant for the dehydration...Ch. 14 - Which two potential-energy profiles represent the...Ch. 14 - Consider the following mechanism for the...Ch. 14 - List four factors that influence the rate of a...Ch. 14 - 14.71 Suggest experimental means by which the...Ch. 14 - 14.75 “The rate constant for the reaction: is .”...Ch. 14 - Prob. 76APCh. 14 - The following diagrams represent the progress of...Ch. 14 - The following diagrams show the progress of the...Ch. 14 - Prob. 79APCh. 14 - Prob. 80APCh. 14 - 14.81 When methyl phosphate is heated in acid...Ch. 14 - The rate of the reaction: CH 3 COOC 2 H 5 ( a q )...Ch. 14 - Explain why most metals used in catalysis are...Ch. 14 - Prob. 84APCh. 14 - The bromination of acetone is acid-catalyzed: CH 3...Ch. 14 - The decomposition of N 2 O to N 2 and O 2 is a...Ch. 14 - 14.87 The reaction proceeds slowly in aqueous...Ch. 14 - Prob. 88APCh. 14 - The integrated rate law for the zeroth-order...Ch. 14 - 14.90 A flask contains a mixture of compounds A...Ch. 14 - Prob. 91APCh. 14 - 14.92 The rate law for the reaction . Which of the...Ch. 14 - 14.93 The reaction of to form 2EG is exothermic,...Ch. 14 - 14.94 The activation energy for the decomposition...Ch. 14 - Prob. 95APCh. 14 - 14.96 When 6 g of granulated Zn is added to a...Ch. 14 - Prob. 97APCh. 14 - 14.98 A certain first-order reaction is 35.5...Ch. 14 - 14.99 The decomposition of dinitrogen pentoxide...Ch. 14 - 14.100 The thermal decomposition of obeys...Ch. 14 - 14.101 When a mixture of methane and bromine is...Ch. 14 - 14.102 The rate of the reaction between to form...Ch. 14 - The rate constant for the gaseous reaction: H 2 (...Ch. 14 - A gas mixture containing CH 3 fragments. C 2 H 6...Ch. 14 - Consider the following elementary step: X + 2Y →...Ch. 14 - 14.106 The following scheme in which A is...Ch. 14 - 14.107 (a) Consider two reactions, A and B. If the...Ch. 14 - The rate law for the following reaction: CO ( g )...Ch. 14 - Consider the following elementary steps for a...Ch. 14 - Prob. 110APCh. 14 - Consider the following potential-energy profile...Ch. 14 - The rate of a reaction was followed by the...Ch. 14 - 14.113 The first-order rate constant for the...Ch. 14 - 14.114 Many reactions involving heterogeneous...Ch. 14 - Thallium(I) is oxidized by cerium(IV) as follows:...Ch. 14 - The activation energy for the reaction: N 2 O ( g...Ch. 14 - Δ H ° for the reaction in Problem 14.116 is -164...Ch. 14 - 14.118 At a certain elevated temperature, ammonia...Ch. 14 - 14.119 The following expression shows the...Ch. 14 - In a certain industrial process involving a...Ch. 14 - Strontium-90, a radioactive isotope, is a major...Ch. 14 - Prob. 122APCh. 14 - Prob. 123APCh. 14 - A factory that specializes in the refinement of...Ch. 14 - 14.125 When the concentration of A in the reaction...Ch. 14 - 14.126 The activity of a radioactive sample is the...Ch. 14 - Prob. 127APCh. 14 - Prob. 128APCh. 14 - Prob. 129APCh. 14 - Prob. 130APCh. 14 - Prob. 131APCh. 14 - Prob. 132APCh. 14 - Prob. 133APCh. 14 - 14.134 At a certain elevated temperature, ammonia...Ch. 14 - Polyethylene is used in many items, including...Ch. 14 - In recent years, ozone in the stratosphere has...Ch. 14 - Metastron, an aqueous solution of 89 SrCl 2 , is a...Ch. 14 - Metastron, an aqueous solution of 89 SrCl 2 , is a...Ch. 14 - Metastron, an aqueous solution of 89 SrCl 2 , is a...Ch. 14 - Metastron, an aqueous solution of 89 SrCl 2 , is a...
Knowledge Booster
Background pattern image
Chemistry
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Chemistry: The Molecular Science
Chemistry
ISBN:9781285199047
Author:John W. Moore, Conrad L. Stanitski
Publisher:Cengage Learning
Text book image
Chemistry & Chemical Reactivity
Chemistry
ISBN:9781337399074
Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher:Cengage Learning
Text book image
Chemistry & Chemical Reactivity
Chemistry
ISBN:9781133949640
Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher:Cengage Learning
Text book image
Chemistry: Matter and Change
Chemistry
ISBN:9780078746376
Author:Dinah Zike, Laurel Dingrando, Nicholas Hainen, Cheryl Wistrom
Publisher:Glencoe/McGraw-Hill School Pub Co
Text book image
Chemistry for Engineering Students
Chemistry
ISBN:9781337398909
Author:Lawrence S. Brown, Tom Holme
Publisher:Cengage Learning
Text book image
General Chemistry - Standalone book (MindTap Cour...
Chemistry
ISBN:9781305580343
Author:Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; Darrell
Publisher:Cengage Learning
Kinetics: Initial Rates and Integrated Rate Laws; Author: Professor Dave Explains;https://www.youtube.com/watch?v=wYqQCojggyM;License: Standard YouTube License, CC-BY