Answered: 3. Determine the internal energy of an…

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

3. Determine the internal energy of an HCl molecule having one quantum of vibrational
excitation (v=1) and three quanta (J=3) of rotational excitation. (v = 2990.9 cm³¹ and B =
10.59 cm ¹)

Expert Solution

Step 1: Introduction

To determine the internal energy of an HCl molecule with one quantum of vibrational excitation (v-1) and three quanta (J-3) of rotational excitation, we can use the following formula for the internal energy of a diatomic molecule:

E = (v + 0.5) * h * v + (J * (J + 1)) * B

Where:

E is the internal energy.

v is the vibrational quantum number (v-1 in this case).

h is Planck's constant (6.626 x 10^-34 J·s)

B is the rotational constant (10.59 cm⁻¹ in this case).

J is the rotational quantum number (J-3 in this case).

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