Explanation Given information: Diameter of methyl radical is 308 pm . Temperature is given as 298 K . In case of radical recombination, experimentally it is found that the activation energy is approximately zero. The maximum rate of recombination of radical is when the steric factor is 1 or more. Therefore, Arrhenius factor can be given by the equation according to collision theory as shown below, k 2 = A = N A σ * ( 8 k T π μ ) − − − − − − − − − − − ( 1 ) Where, μ is reduced mass σ * is collision cross section area N A is Avogadro number k is the Boltzmann constant Reduced mass of methyl radical can be calculated as shown below, μ = 1 2 m (CH 3 ) = 1 2 ( 15.03 u ) ( 1 .6605 x 10 -27 kg 1 u ) = 7.515 u ( 1 .6605 x 10 -27 kg 1 u ) = 1 .25 x 10 -26 kg Reactive cross section can be calculated using the formula as shown below, σ * = π d 2 Where d is the diameter. σ * = 3.14 × ( 308 × 10 − 12 m) 2 = 3.14 × 94864 × 10 − 14 m 2 = 297872.96 × 10 − 14 m 2 = 3.0 × 10 − 19 m 2 Substituting the obtained values in equation (1), the rate of the recombination reaction can be obtained as shown below, k 2 = N A σ * ( 8 k T π μ ) 1 / 2 = 6.022 × 10 23 mol -1 × 3.0 × 10 − 19 m 2 × ( 8 × 1.381 × 10 -23 JK -1 × 298 K 3.14 × 1 .25 x 10 -26 kg ) 1 / 2 = 18.066 × 10 4 mol -1 m 2 × ( 3292.304 J × 10 3 3.925 kg ) 1 / 2 = 1.7 × 10 8 mol -1 m 3 s -1 = 1.7 × 10 11 M − 1 s -1 Rate constant for the rate law is given as, ν = k 2 [ CH 3 ] 2 ∴ d [ CH 3 ] / d t = 2 k 2 [ CH 3 ] 2 Solving the above equation, 1 [CH 3 ] − 1 [CH 3 ] 0 = 2 k 2 t In case of 90 percent recombination [CH 3 ] = 0

11th Edition

ISBN: 9780198769866

Author: ATKINS, P. W. (peter William), De Paula, Julio, Keeler, JAMES

Publisher: Oxford University Press

See similar textbooks

Concept explainers

Photochemistry

Photochemistry is the part of chemistry that studies the various mechanisms of reactions that are triggered by the presence of light energy. It also helps to study the changes involved in a molecule that can undergo the absorption of radiation.

Videos

Question

Chapter 18, Problem 18A.3P

Interpretation Introduction

Interpretation:

The maximum rate constant for second order recombination of radicals and minimum time that is required for 90 percent recombination of methyl radicals to form ethane has to be calculated.

Expert Solution & Answer

Chapter 18 Solutions

Atkins' Physical Chemistry

Ch. 18 - Prob. 18A.1ST Ch. 18 - Prob. 18C.2ST Ch. 18 - Prob. 18A.1DQ Ch. 18 - Prob. 18A.2DQ Ch. 18 - Prob. 18A.3DQ Ch. 18 - Prob. 18A.4DQ Ch. 18 - Prob. 18A.1AE Ch. 18 - Prob. 18A.1BE Ch. 18 - Prob. 18A.2AE Ch. 18 - Prob. 18A.2BE

Knowledge Booster

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.

Recommended textbooks for you

Chemistry
Chemistry
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Cengage Learning
Chemistry
Chemistry
ISBN:9781259911156
Author:Raymond Chang Dr., Jason Overby Professor
Publisher:McGraw-Hill Education
Principles of Instrumental Analysis
Chemistry
ISBN:9781305577213
Author:Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:Cengage Learning
Organic Chemistry
Chemistry
ISBN:9780078021558
Author:Janice Gorzynski Smith Dr.
Publisher:McGraw-Hill Education
Chemistry: Principles and Reactions
Chemistry
ISBN:9781305079373
Author:William L. Masterton, Cecile N. Hurley
Publisher:Cengage Learning
Elementary Principles of Chemical Processes, Bind...
Chemistry
ISBN:9781118431221
Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:WILEY

Chemistry

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Cengage Learning

Chemistry

ISBN:9781259911156

Author:Raymond Chang Dr., Jason Overby Professor

Publisher:McGraw-Hill Education

Principles of Instrumental Analysis

Chemistry

ISBN:9781305577213

Author:Douglas A. Skoog, F. James Holler, Stanley R. Crouch

Publisher:Cengage Learning

Organic Chemistry

Chemistry

ISBN:9780078021558

Author:Janice Gorzynski Smith Dr.

Publisher:McGraw-Hill Education

Chemistry: Principles and Reactions

Chemistry

ISBN:9781305079373

Author:William L. Masterton, Cecile N. Hurley

Publisher:Cengage Learning

Elementary Principles of Chemical Processes, Bind...

Chemistry

ISBN:9781118431221

Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard

Publisher:WILEY

SEE MORE TEXTBOOKS

Photochemistry : Introduction to Basic Theory of Photochemical Process [Part 1]; Author: Dr. Vikrant Palekar;https://www.youtube.com/watch?v=2NDOL11d6no;License: Standard YouTube License, CC-BY

Photochemistry-1; Author: CH-08:ARYABHATT [Mathematics, Physics, Chemistry];https://www.youtube.com/watch?v=DC4J0t1z3e8;License: Standard Youtube License

The maximum rate constant for second order recombination of radicals and minimum time that is required for 90 percent recombination of methyl radicals to form ethane has to be calculated.

Concept explainers

Videos

Interpretation: The maximum rate constant for second order recombination of radicals and minimum time that is required for 90 percent recombination of methyl radicals to form ethane has to be calculated.

Chapter 18 Solutions

Interpretation:

The maximum rate constant for second order recombination of radicals and minimum time that is required for 90 percent recombination of methyl radicals to form ethane has to be calculated.