Chapter 9.3, Problem B9.2P

(a)

Interpretation Introduction

Interpretation:

The wavelengths that correspond to the vibrations of a ${\text{CO}}_2$ molecule is to be determined.

Concept introduction:

A covalent bond is formed by the interaction of two nonmetals. Covalent compounds are formed by the sharing of electrons between two or more atoms. A covalent bond is the strong forces of attraction between the shared pairs of electrons and the nuclei of the combining atoms.

In the covalent bond, bond energy is the energy needed to overcome the attractive forces between the nuclei of atoms and the shared pair of electrons. Bond energy is the enthalpy change associated with breaking of bond of $1\text{mol}$ of gaseous molecule. The enthalpy associated with equation (1) is $\Delta H_{\text{bond}\text{breaking}}$ or ${\text{BE}}_{\text{AB}}$.

$\text{AB}\left(g\right)\to \text{A}\left(g\right)+\text{B}\left(g\right)$ (1)

The bond energy of a bond is directly related to the bond strength of a bond. Greater the bond strength of the bond more will be the bond energy of the bond and vice-versa.

Bond order is the number of electron pairs that are shared between the pair of atoms. The bond order of a pair of an atom is directly proportional to the strength of the bonds.

The expression to relate frequency, speed of light and wavelength is as follows:

$\lambda =\frac{c}{v}$ (2)

Here,

$c$ is the speed of light in vacuum.

$\lambda$ is the wavelength of the photon.

$v$ is the frequency of the photon.

Energy is directly proportional to the frequency and the expression to relate energy and frequency are as follows:

$E=hv$ (3)

Here,

$E$ is the energy of the photon.

$h$ is the Planck’s constant.

(b)

Interpretation Introduction

Interpretation:

The energy in $\text{J}$ of each vibration is to be calculated. Also, the vibration that requires the least amount of energy is to be determined.

Concept introduction:

A covalent bond is formed by the interaction of two nonmetals. Covalent compounds are formed by the sharing of electrons between two or more atoms. A covalent bond is the strong forces of attraction between the shared pairs of electrons and the nuclei of the combining atoms.

In the covalent bond, bond energy is the energy needed to overcome the attractive forces between the nuclei of atoms and the shared pair of electrons. Bond energy is the enthalpy change associated with breaking of bond of $1\text{mol}$ of gaseous molecule. The enthalpy associated with equation (1) is $\Delta H_{\text{bond}\text{breaking}}$ or ${\text{BE}}_{\text{AB}}$.

$\text{AB}\left(g\right)\to \text{A}\left(g\right)+\text{B}\left(g\right)$ (1)

The bond energy of a bond is directly related to the bond strength of a bond. Greater the bond strength of the bond more will be the bond energy of the bond and vice-versa.

Bond order is the number of electron pairs that are shared between the pair of atoms. The bond order of a pair of an atom is directly proportional to the strength of the bonds.

The expression to relate frequency, speed of light and wavelength is as follows:

$\lambda =\frac{c}{v}$ (2)

Here,

$c$ is the speed of light in vacuum.

$\lambda$ is the wavelength of the photon.

$v$ is the frequency of the photon.

Energy is directly proportional to the frequency and the expression to relate energy and frequency are as follows:

$E=hv$ (3)

Here,

$E$ is the energy of the photon.

$h$ is the Planck’s constant.