Atkins' Physical Chemistry
Atkins' Physical Chemistry
11th Edition
ISBN: 9780198769866
Author: ATKINS, P. W. (peter William), De Paula, Julio, Keeler, JAMES
Publisher: Oxford University Press
Question
Book Icon
Chapter 14, Problem 14B.8P
Interpretation Introduction

Interpretation:

The dependence of the molar potential energy of interaction on the angle θ has to be calculated.

Concept introduction:

Hydrogen bonding occurs when a hydrogen atom is covalently bonded to oxygen, nitrogen or fluorine and it develops some partial charge on both the atom.  Hydrogen bonds can also be formed between the lone pair of an electronegative atom and hydrogen atom attached with an electronegative atom.

Expert Solution & Answer
Check Mark

Answer to Problem 14B.8P

The dependence of the molar potential energy of interaction on the angle θ is shown below.

    Vm=1.386×104Jmol1(1.17×1029+9.562×1039(4.916×10203.828cosθ)1/2)

Explanation of Solution

The arrangement of a system containing an OH group and O group is shown below.

Atkins' Physical Chemistry, Chapter 14, Problem 14B.8P

Figure 1

The expression for the molar potential energy (Vm) of an electrostatic model of hydrogen bonding is shown below.

    Vm=NAe24πε0{δOδHrOH+δOδHrOH+δO2rOO}        (1)

Where,

  • NA is the Avogadro's number. (6.022×1023mol1)
  • ε0 is the vacuum permittivity. (8.854×1012J1C2m1)
  • δ is the charge.
  • r is the distance.
  • e is the charge on an electron. (1.6×1019C)

Equation (1) is solved further as shown below.

    Vm=NAe24πε0{δOδH(1rOH+1rOH)+δO2rOO}        (2)

The value of rOH is calculated by the formula given below.

    rOH=(rOH2+rOO22rOHrOOcosθ)1/2        (3)

The value of rOH is 95.7pm.

The conversion of pm to m is shown below.

    1pm=1012m

Therefore, the conversion of 95.7pm to m is shown below.

    95.7pm=95.7×1012m

The value of rOO is 200pm.

The conversion of pm to m is shown below.

    1pm=1012m

Therefore, the conversion of 200pm to m is shown below.

    200pm=200×1012m

Substitute the value of rOO and rOH in equation (3).

    rOH=((95.7×1012m)2+(200×1012m)2(2×95.7×1012m×200×1012m×cosθ))1/2=(9.16×1021m2+4×1020m2(3.828×1020cosθm2))1/2=(4.916×1020(3.828×1020cosθ))1/2m

The value of δO is 0.83e.

The value of δH is +0.45e.

Substitute the value of NA, ε0, δO, δH, rOO, rOH, and rOH in equation (2).

    Vm=(6.022×1023mol1×e24×31.4×8.854×1012J1C2m1×{(0.83e)(+0.45e)(195.7×1012m+1(4.916×10203.828×1020cosθ)1/2m)+(0.83e)2200×1012m})

Substitute the value of e in the above equation.

    Vm=(6.022×1023mol1×(1.6×1019C)24×3.14×8.854×1012J1C2m1×{(0.83×1.6×1019C)(+0.45×1.6×1019C)(195.7×1012m+1(4.916×10203.828cosθ)1/2m)+(0.83×1.6×1019C)2200×1012m})=1.386×104Jmol1m(9.562×1039m1(1.045×1010+1(4.916×10203.828cosθ)1/2)+8.81792×1029m1)=1.386×104Jmol1(9.99×1029+9.562×1039(4.916×10203.828cosθ)1/2+8.81792×1029)=1.386×104Jmol1(1.17×1029+9.562×1039(4.916×10203.828cosθ)1/2)

Therefore, the dependence of the molar potential energy of interaction on the angle is shown below.

    Vm=1.386×104Jmol1(1.17×1029+9.562×1039(4.916×10203.828cosθ)1/2)

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

Atkins' Physical Chemistry

Ch. 14 - Prob. 14A.3DQCh. 14 - Prob. 14A.1AECh. 14 - Prob. 14A.1BECh. 14 - Prob. 14A.2AECh. 14 - Prob. 14A.2BECh. 14 - Prob. 14A.3AECh. 14 - Prob. 14A.3BECh. 14 - Prob. 14A.4AECh. 14 - Prob. 14A.4BECh. 14 - Prob. 14A.5AECh. 14 - Prob. 14A.5BECh. 14 - Prob. 14A.6AECh. 14 - Prob. 14A.6BECh. 14 - Prob. 14A.7AECh. 14 - Prob. 14A.7BECh. 14 - Prob. 14A.8AECh. 14 - Prob. 14A.8BECh. 14 - Prob. 14A.9AECh. 14 - Prob. 14A.9BECh. 14 - Prob. 14A.1PCh. 14 - Prob. 14A.2PCh. 14 - Prob. 14A.3PCh. 14 - Prob. 14A.4PCh. 14 - Prob. 14A.5PCh. 14 - Prob. 14A.6PCh. 14 - Prob. 14A.7PCh. 14 - Prob. 14A.8PCh. 14 - Prob. 14A.10PCh. 14 - Prob. 14A.12PCh. 14 - Prob. 14A.13PCh. 14 - Prob. 14B.1DQCh. 14 - Prob. 14B.2DQCh. 14 - Prob. 14B.3DQCh. 14 - Prob. 14B.4DQCh. 14 - Prob. 14B.5DQCh. 14 - Prob. 14B.1AECh. 14 - Prob. 14B.1BECh. 14 - Prob. 14B.2AECh. 14 - Prob. 14B.2BECh. 14 - Prob. 14B.3AECh. 14 - Prob. 14B.3BECh. 14 - Prob. 14B.4AECh. 14 - Prob. 14B.4BECh. 14 - Prob. 14B.5AECh. 14 - Prob. 14B.5BECh. 14 - Prob. 14B.6AECh. 14 - Prob. 14B.6BECh. 14 - Prob. 14B.1PCh. 14 - Prob. 14B.2PCh. 14 - Prob. 14B.3PCh. 14 - Prob. 14B.4PCh. 14 - Prob. 14B.5PCh. 14 - Prob. 14B.6PCh. 14 - Prob. 14B.7PCh. 14 - Prob. 14B.8PCh. 14 - Prob. 14B.10PCh. 14 - Prob. 14C.1DQCh. 14 - Prob. 14C.2DQCh. 14 - Prob. 14C.1AECh. 14 - Prob. 14C.1BECh. 14 - Prob. 14C.2AECh. 14 - Prob. 14C.2BECh. 14 - Prob. 14C.3AECh. 14 - Prob. 14C.3BECh. 14 - Prob. 14C.4AECh. 14 - Prob. 14C.4BECh. 14 - Prob. 14C.1PCh. 14 - Prob. 14C.2PCh. 14 - Prob. 14D.1DQCh. 14 - Prob. 14D.2DQCh. 14 - Prob. 14D.3DQCh. 14 - Prob. 14D.4DQCh. 14 - Prob. 14D.5DQCh. 14 - Prob. 14D.1AECh. 14 - Prob. 14D.1BECh. 14 - Prob. 14D.2AECh. 14 - Prob. 14D.2BECh. 14 - Prob. 14D.3AECh. 14 - Prob. 14D.3BECh. 14 - Prob. 14D.4AECh. 14 - Prob. 14D.4BECh. 14 - Prob. 14D.5AECh. 14 - Prob. 14D.5BECh. 14 - Prob. 14D.6AECh. 14 - Prob. 14D.6BECh. 14 - Prob. 14D.8AECh. 14 - Prob. 14D.8BECh. 14 - Prob. 14D.9AECh. 14 - Prob. 14D.9BECh. 14 - Prob. 14D.2PCh. 14 - Prob. 14D.3PCh. 14 - Prob. 14D.4PCh. 14 - Prob. 14D.6PCh. 14 - Prob. 14D.7PCh. 14 - Prob. 14D.8PCh. 14 - Prob. 14D.9PCh. 14 - Prob. 14D.10PCh. 14 - Prob. 14E.1DQCh. 14 - Prob. 14E.2DQCh. 14 - Prob. 14E.3DQCh. 14 - Prob. 14E.4DQCh. 14 - Prob. 14E.5DQCh. 14 - Prob. 14E.1AECh. 14 - Prob. 14E.1BECh. 14 - Prob. 14E.1PCh. 14 - Prob. 14E.3PCh. 14 - Prob. 14.1IACh. 14 - Prob. 14.2IACh. 14 - Prob. 14.6IACh. 14 - Prob. 14.8IA
Knowledge Booster
Background pattern image
Recommended textbooks for you
Text book image
Chemistry
Chemistry
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Cengage Learning
Text book image
Chemistry
Chemistry
ISBN:9781259911156
Author:Raymond Chang Dr., Jason Overby Professor
Publisher:McGraw-Hill Education
Text book image
Principles of Instrumental Analysis
Chemistry
ISBN:9781305577213
Author:Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:Cengage Learning
Text book image
Organic Chemistry
Chemistry
ISBN:9780078021558
Author:Janice Gorzynski Smith Dr.
Publisher:McGraw-Hill Education
Text book image
Chemistry: Principles and Reactions
Chemistry
ISBN:9781305079373
Author:William L. Masterton, Cecile N. Hurley
Publisher:Cengage Learning
Text book image
Elementary Principles of Chemical Processes, Bind...
Chemistry
ISBN:9781118431221
Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:WILEY