Chapter 1, Problem 1.47AP

Interpretation Introduction

(a)

Interpretation:

The bonding and anti-bonding combinations $\left(2s\sigma \text{and}2s{\sigma }^{\ast },\text{respectively}\right)$ that formed if the $2s$ atomic orbitals interact are to be drawn. The nodes of the bonding and anti-bonding combinations are to be shown.

Concept introduction:

The linear combination of atomic orbital (LCAO) states that two atomic orbitals combine together to form a new orbital which is known as bonding molecular orbital.

The molecular orbital theory also states that two atoms combines together to form a molecule. During the formation of a molecule, the electrons are shared between two atoms to form a chemical bond.

Answer to Problem 1.47AP

The bonding and anti-bonding combinations $\left(2s\sigma \text{and}2s{\sigma }^{\ast },\text{respectively}\right)$ with their nodes that formed if the $2s$ atomic orbitals interact are represented below.

Explanation of Solution

The bond electrons which on addition form a molecular orbital are known as bonding electrons.

The bond electrons which on subtraction form a molecular orbital are known as anti-bonding electrons.

The bonding and anti-bonding combinations for the interaction of two $2s$$\left(2s\sigma \text{and}2s{\sigma }^{\ast },\text{respectively}\right)$ orbital of two oxygen atoms are shown as,

Figure 1

The bonding and anti-bonding molecular orbital are obtained by the overlapping of two $2s$ orbital of two oxygen atoms. The above shown diagram shows the shape of anti-bonding molecular orbital with one node and the shape of bonding molecular orbital with zero nodes.

Conclusion

The bonding and anti-bonding combinations $\left(2s\sigma \text{and}2s{\sigma }^{\ast },\text{respectively}\right)$ with their nodes that formed if the $2s$ atomic orbitals interact are shown Figure 1.

Interpretation Introduction

(b)

Interpretation:

The bonding and anti-bonding combinations $\left(2p\sigma \text{and}2p{\sigma }^{\ast },\text{respectively}\right)$ that result if the $2p_x$ atomic orbitals overlap are to be drawn. The nodes of the bonding and anti-bonding combinations are to be shown.

Concept introduction:

The linear combination of atomic orbital (LCAO) states that two atomic orbitals combine together to form a new orbital which is known as bonding molecular orbital.

The molecular orbital theory also states that two atoms combines together to form a molecule. During the formation of a molecule, the electrons are shared between two atoms to form a chemical bond.

Answer to Problem 1.47AP

The bonding and anti-bonding combinations $\left(2p\sigma \text{and}2p{\sigma }^{\ast },\text{respectively}\right)$ with their nodes that result if the $2p_x$ atomic orbitals overlap are represented below.

Explanation of Solution

The bond electrons which on addition form a molecular orbital are known as bonding electrons.

The bond electrons which on subtraction form a molecular orbital are known as anti-bonding electrons.

The bonding and anti-bonding combinations for the interaction of two $2p_x$$\left(2p\sigma \text{and}2p{\sigma }^{\ast },\text{respectively}\right)$ orbital of two oxygen atoms are shown as,

Figure 2

The bonding and anti-bonding molecular orbital are obtained by the overlapping of two $2p_x$ orbital of two oxygen atoms. The above shown diagram shows the shape of anti-bonding molecular orbital with one node and the shape of bonding molecular orbital with two nodes.

Conclusion

The bonding and anti-bonding combinations $\left(2p\sigma \text{and}2p{\sigma }^{\ast },\text{respectively}\right)$ with their nodes that result if the $2p_x$ atomic orbitals overlap are shown Figure 2.

Interpretation Introduction

(c)

Interpretation:

The bonding and anti-bonding combinations $\left(2p{\pi }_y\text{and}2p{\pi }_y^{\ast },\text{respectively}\right)$ that result when the $2p_y$ atomic orbitals overlap are to be drawn. The nodes of the bonding and anti-bonding combinations are to be shown.

Concept introduction:

The linear combination of atomic orbital (LCAO) states that two atomic orbitals combine together to form a new orbital which is known as bonding molecular orbital.

The molecular orbital theory also states that two atoms combines together to form a molecule. During the formation of a molecule, the electrons are shared between two atoms to form a chemical bond.

Answer to Problem 1.47AP

The bonding and anti-bonding combinations $\left(2p{\pi }_y\text{and}2p{\pi }_y^{\ast },\text{respectively}\right)$ with their nodes that result if the $2p_y$ atomic orbitals overlap are represented below.

Explanation of Solution

The bond electrons which on addition form a molecular orbital are known as bonding electrons.

The bond electrons which on subtraction form a molecular orbital are known as anti-bonding electrons.

The bonding and anti-bonding combinations for the interaction of two $2p_y$$\left(2p{\pi }_y\text{and}2p{\pi }_y^{\ast },\text{respectively}\right)$ orbital of two oxygen atoms are shown as,

Figure 3

The bonding and anti-bonding molecular orbital are obtained by the overlapping of two $2p_y$ orbital of two oxygen atoms. The above shown diagram shows the shape of anti-bonding molecular orbital with one node and the shape of bonding molecular orbital with zero nodes.

Conclusion

The bonding and anti-bonding combinations $\left(2p{\pi }_y\text{and}2p{\pi }_y^{\ast },\text{respectively}\right)$ with their nodes that result if the $2p_y$ atomic orbitals overlap are shown Figure 3.

Interpretation Introduction

(d)

Interpretation:

The bonding and anti-bonding combinations $\left(2p{\pi }_z\text{and}2p{\pi }_z^{\ast },\text{respectively}\right)$ that result if the $2p_z$ atomic orbitals overlap are identical to the $2p{\pi }_y\text{and}2p{\pi }_y^{\ast }$ MOs but oriented at $90°$ are to be drawn.

Concept introduction:

The linear combination of atomic orbital (LCAO) states that two atomic orbitals combine together to form a new orbital which is known as bonding molecular orbital.

The molecular orbital theory also states that two atoms combines together to form a molecule. During the formation of a molecule, the electrons are shared between two atoms to form a chemical bond.

Answer to Problem 1.47AP

The bonding and anti-bonding combinations $\left(2p{\pi }_z\text{and}2p{\pi }_z^{\ast },\text{respectively}\right)$ that result if the $2p_z$ atomic orbitals overlap are identical to the $2p{\pi }_y\text{and}2p{\pi }_y^{\ast }$ MOs but oriented at $90°$ are represented below.

Explanation of Solution

The bond electrons which on addition form a molecular orbital are known as bonding electrons.

The bond electrons which on subtraction form a molecular orbital are known as anti-bonding electrons.

The bonding and anti-bonding combinations for the interaction of two $2p_z$$\left(2p{\pi }_z\text{and}2p{\pi }_z^{\ast },\text{respectively}\right)$ orbital of two oxygen atoms are shown as,

Figure 4

The bonding and anti-bonding molecular orbital are obtained by the overlapping of two $2p_z$ orbital of two oxygen atoms.

Conclusion

The bonding and anti-bonding combinations $\left(2p{\pi }_y\text{and}2p{\pi }_y^{\ast },\text{respectively}\right)$ with their nodes that result if the $2p_y$ atomic orbitals overlap are shown Figure 4.

Interpretation Introduction

(e)

Interpretation:

The orbital interaction energy diagram showing the energy levels of the atomic orbitals along with the energies of the given MOs is to be drawn.

Concept introduction:

The linear combination of atomic orbital (LCAO) states that two atomic orbitals combine together to form a new orbital which is known as bonding molecular orbital.

The molecular orbital theory also states that two atoms combines together to form a molecule. During the formation of a molecule, the electrons are shared between two atoms to form a chemical bond.

Answer to Problem 1.47AP

The orbital interaction energy diagram showing the energy levels of the atomic orbitals along with the energies of the given MOs is represented below.

Explanation of Solution

According to the rules for filling the electrons in the molecular orbital, first of all the lower energy molecular orbital is filled followed by the filling of increasing energy order of the molecular orbital.

Thus, the orbital interaction energy diagram showing the energy levels of the atomic orbitals along with the energies of the given MOs of oxygen atom is shown as,

Figure 5

The energy of sigma, $\sigma$, bond is lower than the pi bond. Thus, the filling of electron is done according to the rule from $\sigma$ to $\pi$ bond.

Conclusion

The orbital interaction energy diagram showing the energy level of the atomic orbitals along with the energies of the given MOs is shown Figure 5.

Interpretation Introduction

(f)

Interpretation:

The reason corresponding to the fact that liquid ${\text{O}}_{\text{2}}$ can be trapped between the poles of a magnet is to be explained.

Concept introduction:

The atoms which contain no unpaired electron in their orbital and have total spin equals to zero are known as diamagnetic atoms. The atoms which contain one or more unpaired electron in their orbital are known as paramagnetic atoms.

Answer to Problem 1.47AP

The liquid ${\text{O}}_{\text{2}}$ can be trapped between the poles of a magnet due to slow movement of its molecules as compared to oxygen gas molecules.

Explanation of Solution

In oxygen molecule, two unpaired electrons are present in the anti-bonding molecular orbital. Thus, oxygen molecule is paramagnetic in nature due to which it gets attracted towards the magnetic field.

In comparison to liquid oxygen, the movement of the oxygen gas molecules is faster. Therefore, liquid oxygen molecules are not attracted by the magnetic field.

Hence, liquid ${\text{O}}_{\text{2}}$ can be trapped between the poles of a magnet instead of attracted towards it.

Conclusion

The reason corresponding to the fact that liquid ${\text{O}}_{\text{2}}$ can be trapped between the poles of a magnet is stated above.

Interpretation Introduction

(g)

Interpretation:

The Lewis structure that best describes the covalent bond(s) in ${\text{O}}_{\text{2}}$ is to be identified.

Concept introduction:

The Lewis structure shows the connectivity between atoms by identifying the lone pairs of electrons in a compound. Lewis structures are also called Lewis dot structures. The valence electrons around an atom are shown by dots. Bonds between atoms are shown by lines and the lone pair of electrons is shown by a pair of dots.

Answer to Problem 1.47AP

The Lewis structure that best describes the covalent bond(s) in ${\text{O}}_{\text{2}}$ is given in option A as shown below.

Explanation of Solution

The given Lewis structures of ${\text{O}}_{\text{2}}$ are shown as,

The reason corresponding to the fact that liquid ${\text{O}}_{\text{2}}$ can be trapped between the poles of a magnet is stated above.

Figure 6

The total number of bonding electrons in ${\text{O}}_{\text{2}}$ is $6$.

The total number of anti-bonding electrons in ${\text{O}}_{\text{2}}$ is $2$.

The bond order of ${\text{O}}_{\text{2}}$ molecules is calculated by the formula,

$\text{Bond}\text{order}=\frac{\text{Electrons}\text{of}\text{BMO}-\text{Electrons}\text{of}\text{ABMO}}{2}$

Substitute the number of bonding molecular orbital and anti-bonding molecular orbital electrons in the above expression.

$\begin{array}{rll}\text{Bond}\text{order}& =& \frac{\text{6}-\text{2}}{2}\\ & =& 2\end{array}$

Thus, the bond order of oxygen molecule is $2$. As, the bond order of oxygen molecule is $2$, thus, two bonds are present between the two oxygen atoms.

Therefore, the Lewis structures of ${\text{O}}_{\text{2}}$ given in options B, C and E do not describes the covalent bond(s) in ${\text{O}}_{\text{2}}$.

In option D, the Lewis structures of ${\text{O}}_{\text{2}}$ possesses the total of nine electrons. Thus, this option does not satisfy the octet rule. Hence, the option D does not describes the covalent bond(s) in ${\text{O}}_{\text{2}}$.

In option A, the Lewis structures of ${\text{O}}_{\text{2}}$ possesses the total of $8$ electrons. Thus, this option satisfies the octet rule as well as it has two bonds between the atoms of oxygen. Hence, the option A best describes the covalent bond(s) in ${\text{O}}_{\text{2}}$ as shown below.

Figure 7

Conclusion

The Lewis structure that best describes the covalent bond(s) in ${\text{O}}_{\text{2}}$ is shown in Figure 7.