(a) Interpretation: The excited-state and the ground-state population ratios for HCI: N ( v = 1 ) / N ( v = 0 ) is to be calculated. Concept introduction: The excited-state of an atom, molecule or electron is a state in which the electrons have sufficient energy to jump in to another orbital. The ground-state is the state of zero energy level. In this state the electron does not have sufficient energy to jump from the orbital. The Boltzmann equation is used to calculate the ratio of the exited-state and ground state. The concept of the energy difference between these states is also used to calculate the required ratio.

Question

The vibrational energy levels for XO molecule can be described by the following formula: E(n) in Joule = 1.88x10-20(n+1/2) – 2.68x10-22(n+1/2)² where n is the vibrational quantum number. What would be the equilibrium dissociation energy (De) of the XO molecule in a kJ mol-1?

Answer 1

Question

Chapter 16, Problem 16.11QAP

Interpretation Introduction

(a)

Interpretation:

The excited-state and the ground-state population ratios for HCI: N(v=1)/N(v=0) is to be calculated.

Concept introduction:

The excited-state of an atom, molecule or electron is a state in which the electrons have sufficient energy to jump in to another orbital. The ground-state is the state of zero energy level. In this state the electron does not have sufficient energy to jump from the orbital.

The Boltzmann equation is used to calculate the ratio of the exited-state and ground state. The concept of the energy difference between these states is also used to calculate the required ratio.

Interpretation Introduction

(b)

Interpretation:

The excited-state and the ground-state population ratios for HCI: N(v=2)/N(v=0) is to be calculated.

Concept introduction:

The excited-state of an atom, molecule or electron is a state in which the electrons have sufficient energy to jump in to another orbital. The ground-state is the state of zero energy level. In this state the electron does not have sufficient energy to jump from the orbital.

The Boltzmann equation is used to calculate the ratio of the exited-state and ground state. The concept of the energy difference between these states is also used to calculate the required ratio.

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The vibrational energy levels for XO molecule can be described by the following formula: E(n) in Joule = 1.88x10-20(n+1/2) – 2.68x10-22(n+1/2)² where n is the vibrational quantum number. What would be the equilibrium dissociation energy (De) of the XO molecule in a kJ mol-1?

The first five vibrational energy levels of ¹H¹27 I are at 1144.83, 3374.90, 5525.51, 7596.66, and 9588.35 cm¹. Treating the molecule as an anharmonic oscillator, estimate the dissociation energy of the molecule in units of reciprocal centimetres (cm-¹). [Note: m(¹H) = 1.0078 u, m(¹271) = 126.9045 u; assume the second order anharmonicity constant, Ye, to be zero.] [Note: Use graph paper in your answer.]

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