Elements Of Physical Chemistry
Elements Of Physical Chemistry
7th Edition
ISBN: 9780198727873
Author: ATKINS, P. W. (peter William), De Paula, Julio
Publisher: Oxford University Press
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Chapter 11, Problem 11B.5E

(a)

Interpretation Introduction

Interpretation:

Rotational constants for SO3 molecule have to be calculated.

Concept Introduction:

Rotational constant B can be calculated using the following formula.

B=h8π2cI

Where,

    B=rotationalconstanth=plank'sconstantc=velocityoflightI=momentofinertia

The total moment of inertia can be calculated by following equation.

I=Σmiri2

Where,

    I=momentofinertiami=massofithatomri=distancefromtherotatingaxis

(a)

Expert Solution
Check Mark

Answer to Problem 11B.5E

The rotational constant A and B are 17.8 and 26.92 respectively.

Explanation of Solution

The SO3 molecule is planar.  So it has two axes of rotation.  Along each axes it has different moment of inertias.  One rotating axis is perpendicular to the plane of molecule and the other two degenerate axis lies in the plane of molecule.  Let the moment of inertia along the axis perpendicular to the plane of the molecule be IA and the moment of inertia along the axes that lie in the plane of the molecule be IB.

IA can be calculated through following steps,

IA=m1r12+m2r22+m3r32

Since mass of all oxygen atoms and their distance from the sulfur atom is same, moment of inertia can be written as follows,

Given,

    m=massofoxygenatom=16×1.6×1027kgr=distanceofoxygenfromsulfur=143×1012m

IA=mr2+mr2+mr2=3mr2=3×(16×1.6×1027kg)×(143×1012m)2=1.57×10-45kgm2

Let the rotational constant corresponds to IA be A and it can be calculated as follows,

Given,

    h=6.626 × 10-34 m2 kg/sc=3×108m/sIA=1.57×10-45kgm2

A=h8π2cIA=6.626 × 10-34 m2 kg/s(3.14)2×(3×108m/s)(1.57×10-45kgm2)=17.8

IB can be calculated through following steps,

IB=m1r12+m2r22

Since mass of all oxygen atoms and their distance from the sulfur atom is same, moment of inertia can be written as follows,

Given,

    m=massofoxygenatom=16×1.6×1027kgr=distanceofoxygenfromsulfur=143×1012m

IB=mr2+mr2=2mr2=2×(16×1.6×1027kg)×(143×1012m)2=1.04×10-45kgm2

Let the rotational constant corresponds to IA be A and it can be calculated as follows,

Given,

    h=6.626 × 10-34 m2 kg/sc=3×108m/sIB=1.04×10-45kgm2

B=h8π2cIB=6.626 × 10-34 m2 kg/s(3.14)2×(3×108m/s)(1.04×10-45kgm2)=26.92

The rotational constant A and B are 17.8 and 26.92 respectively.

(b)

Interpretation Introduction

Interpretation:

The use of microwave spectroscopy for distinguishing the relative abundance of S32O163andS33O163 has to be explained.

Concept Introduction:

Rotational constant B can be calculated using the following formula.

B=h8π2cI

Where,

    B=rotationalconstanth=plank'sconstantc=velocityoflightI=momentofinertia

The total moment of inertia can be calculated by following equation.

I=Σmiri2

Where,

    I=momentofinertiami=massofithatomri=distancefromtherotatingaxis

(b)

Expert Solution
Check Mark

Explanation of Solution

Microwave spectroscopy cannot be used to distinguish the relative abundance of S32O163andS33O163.  Because the center of mass lies on sulfur atom so the axis pass through sulfur atom.  Hence the rotational constant obtained for both the molecule will be same.  But the isotopes of oxygen in the same compound can be distinguished due to their contribution in moment of inertia.

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Chapter 11 Solutions

Elements Of Physical Chemistry

Ch. 11 - Prob. 11C.3STCh. 11 - Prob. 11C.4STCh. 11 - Prob. 11C.5STCh. 11 - Prob. 11C.6STCh. 11 - Prob. 11C.7STCh. 11 - Prob. 11D.1STCh. 11 - Prob. 11D.2STCh. 11 - Prob. 11D.3STCh. 11 - Prob. 11E.1STCh. 11 - Prob. 11E.2STCh. 11 - Prob. 11E.3STCh. 11 - Prob. 11E.4STCh. 11 - Prob. 11A.1ECh. 11 - Prob. 11A.2ECh. 11 - Prob. 11A.3ECh. 11 - Prob. 11A.4ECh. 11 - Prob. 11A.5ECh. 11 - Prob. 11A.6ECh. 11 - Prob. 11A.7ECh. 11 - Prob. 11A.8ECh. 11 - Prob. 11B.1ECh. 11 - Prob. 11B.2ECh. 11 - Prob. 11B.3ECh. 11 - Prob. 11B.4ECh. 11 - Prob. 11B.5ECh. 11 - Prob. 11B.6ECh. 11 - Prob. 11B.7ECh. 11 - Prob. 11B.8ECh. 11 - Prob. 11B.9ECh. 11 - Prob. 11B.10ECh. 11 - Prob. 11B.11ECh. 11 - Prob. 11B.12ECh. 11 - Prob. 11B.13ECh. 11 - Prob. 11B.14ECh. 11 - Prob. 11B.15ECh. 11 - Prob. 11B.16ECh. 11 - Prob. 11C.1ECh. 11 - Prob. 11C.2ECh. 11 - Prob. 11C.3ECh. 11 - Prob. 11C.4ECh. 11 - Prob. 11C.5ECh. 11 - Prob. 11C.6ECh. 11 - Prob. 11C.7ECh. 11 - Prob. 11C.8ECh. 11 - Prob. 11C.9ECh. 11 - Prob. 11D.1ECh. 11 - Prob. 11D.2ECh. 11 - Prob. 11D.3ECh. 11 - Prob. 11D.4ECh. 11 - Prob. 11D.5ECh. 11 - Prob. 11D.6ECh. 11 - Prob. 11E.1ECh. 11 - Prob. 11E.2ECh. 11 - Prob. 11E.3ECh. 11 - Prob. 11.1DQCh. 11 - Prob. 11.2DQCh. 11 - Prob. 11.3DQCh. 11 - Prob. 11.4DQCh. 11 - Prob. 11.5DQCh. 11 - Prob. 11.6DQCh. 11 - Prob. 11.7DQCh. 11 - Prob. 11.8DQCh. 11 - Prob. 11.9DQCh. 11 - Prob. 11.10DQCh. 11 - Prob. 11.11DQCh. 11 - Prob. 11.12DQCh. 11 - Prob. 11.13DQCh. 11 - Prob. 11.1PCh. 11 - Prob. 11.2PCh. 11 - Prob. 11.4PCh. 11 - Prob. 11.5PCh. 11 - Prob. 11.6PCh. 11 - Prob. 11.7PCh. 11 - Prob. 11.8PCh. 11 - Prob. 11.9PCh. 11 - Prob. 11.11PCh. 11 - Prob. 11.12PCh. 11 - Prob. 11.13PCh. 11 - Prob. 11.14PCh. 11 - Prob. 11.15PCh. 11 - Prob. 11.1PRCh. 11 - Prob. 11.2PRCh. 11 - Prob. 11.3PRCh. 11 - Prob. 11.5PR
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