Concise Physical Chemistry

c18 JWBS043-Rogers September 13, 2010 11:29 Printer Name: Yet to Come

302 EXPERIMENTAL DETERMINATION OF MOLECULAR STRUCTURE

2100.5 cm-1 2185.5 cm-1

FIGURE 18.11 The vibration–rotation spectrum of CO. Only one vibrational absorption and

the accompanying rotational absorptions are depicted.

the levels in the parabolic Hooke’s law energy well? (The superscripted 1 and 35 are

the isotopic numbers. The mass of each isotope can be taken as an integer.)

Problem 18.2

What is the force constant for the diatomic molecule^1 H^35 Cl? Take advantage of the

fact that it absorbs light atλ= 2. 991 × 10 −^4 cm= 2. 991 × 10 −^6 m. Assume that

the molecule is a harmonic oscillator.

Problem 18.3

It is reasonable to suppose that the force constant governing a stretch has units of

force (newtons) per unit displacement (how long the stretch is). Show that the units

ofkfare Nm−^1.

Problem 18.4

In early experiments on HCl, line separation in the rotational part of its spectrum was

found to be 2B ̃=20.794 cm−^1. What is the length of the H Cl bond?

Problem 18.5

A somewhat idealized microwave spectral band of carbon monoxide CO is shown

in Fig. 18.11. The actual band would show some anharmonic distortion. Find the

vibrational frequency. Locate the transition from the 0 to the 1 rotational states.

Calculate the force constant of the CO bond.

Comment: Notice that the speed of light (electromagnetic radiation) is used in units

of cm s−^1 because the frequency is given in cm−^1. The reduced mass is in kg because

the force constant is in Nm−^1.

Problem 18.6

From the information is Problem 18.5, estimate the CO bond length.