   Chapter 14, Problem 14.51E

Chapter
Section
Textbook Problem

# Use the data in Example 14.12 to determine the force constant k in the 1 H 35 Cl molecule.

Interpretation Introduction

Interpretation:

The force constant k for the molecule 1H35Cl is to be calculated.

Concept introduction:

The vibrational frequency for any molecule is related to its force constant and reduced mass of molecule. The vibrational frequency is directly proportional to the force constant of the molecule and inversely proportional to the reduced mass of the molecule.

Explanation

The relationship of frequency of vibration and reduced mass of the molecule is represented as follows.

ν=1kμ…(1)

Where,

ν is the vibrational frequency.

k is the force constant of the molecule.

μ is the reduced mass of the molecule.

The formula to calculate the reduced mass is shown below.

μ=mambma+mb

Where,

ma is the mass of one element

mb is the mass of another element.

The ma here is the mass of H element and is equals to 1 amu.

The mb here is the mass of Cl element and is equals to 35 amu.

Substitute the values of ma and mb in the formula.

μ=mambma+mb=35amu×1amu35amu+1amu=3536amu=0.9722amu

Convert this reduced mass into kg by multiplying it with 1.66×1027amu1kg.

μ=0.9722amu×1.66×1027amu1kg=1

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