
(i)
Interpretation: The proportions of gas, according to the Maxwell-Boltzmann distribution have speeds more than the root mean square speed has to be calculated.
Concept introduction: Root mean square speed is the average of squares of speed in the square root. This speed is represented as,
Where,
(i)

Answer to Problem 1B.4P
The proportion of molecules that have speed more than the mean square speed,
Explanation of Solution
The expression for the Maxwell-Boltzmann distribution is,
The proportion of molecules that have speed less than the mean square speed,
Let
Define
The identity used in the above expression is,
Substitute the equations (2) and (3) in equation (1).
The value of
Substitute the above values in equation (4).
Hence, the proportion of molecules that have speed more than the mean square speed,
(ii)
Interpretation: The proportions of gas, according to the Maxwell-Boltzmann distribution have speeds less than the root mean square speed has to be calculated.
Concept introduction: The compression factor is defined as the ratio of molar volume of a gas to the molar volume of a perfect gas. This is represented by the formula given below as,
(ii)

Answer to Problem 1B.4P
The proportion of molecules that have speed less than the mean square speed,
Explanation of Solution
The expression for the Maxwell-Boltzmann distribution is,
The proportion of molecules that have speed less than the mean square speed,
Let
Define
The identity used in the above expression is,
Substitute the equations (2) and (3) in equation (1).
The value of
Substitute the above values in equation (4).
Hence, the proportion of molecules that have speed less than the mean square speed,
(iii)
Interpretation: The proportions of gas, according to the Maxwell-Boltzmann distribution have greater and less speeds than the mean speed has to be calculated.
Concept introduction: The expression for the mean speed is derived from Maxwell Boltzmann distribution. The mean speed for the gas particles is represented as,
(iii)

Answer to Problem 1B.4P
The proportion of molecules that have speed less than the mean speed,
Explanation of Solution
The expression for the Maxwell-Boltzmann distribution is,
The proportion of molecules that have speed less than the mean square speed,
Let
Define
The identity used in the above expression is,
To calculate the proportion of molecules that have speed less than the mean speed,
Therefore,
Hence,
Hence, the proportion of molecules that have speed less than the mean speed,
Want to see more full solutions like this?
Chapter 1 Solutions
Atkins' Physical Chemistry
- How many chiral carbons are in the molecule? OH F CI Brarrow_forwardA mixture of three compounds Phen-A, Acet-B and Rin-C was analyzed using TLC with 1:9 ethanol: hexane as the mobile phase. The TLC plate showed three spots of R, 0.1 and 0.2 and 0.3. Which of the three compounds (Phen-A; Acet-B or Rin-C) would have the highest (Blank 1), middle (Blank 2) and lowest (Blank 3) spot respectively? 0 CH: 0 CH, 0 H.C OH H.CN OH Acet-B Rin-C phen-A A A <arrow_forwardHow many chiral carbons are in the molecule? Farrow_forward
- ChemistryChemistryISBN:9781305957404Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCostePublisher:Cengage LearningChemistryChemistryISBN:9781259911156Author:Raymond Chang Dr., Jason Overby ProfessorPublisher:McGraw-Hill EducationPrinciples of Instrumental AnalysisChemistryISBN:9781305577213Author:Douglas A. Skoog, F. James Holler, Stanley R. CrouchPublisher:Cengage Learning
- Organic ChemistryChemistryISBN:9780078021558Author:Janice Gorzynski Smith Dr.Publisher:McGraw-Hill EducationChemistry: Principles and ReactionsChemistryISBN:9781305079373Author:William L. Masterton, Cecile N. HurleyPublisher:Cengage LearningElementary Principles of Chemical Processes, Bind...ChemistryISBN:9781118431221Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. BullardPublisher:WILEY





