Chapter 8, Problem 76A

(a)

Interpretation Introduction

Interpretation: The angles between the $s{p}^3$ hybrids orbitals need to be determined.

Concept Introduction: VSEPR theory is used to predict the molecular shape with the help of electron pairs around the central atoms of the molecule. It is based on the assumption that the shape of the molecule is such that there is minimum electronic repulsion between the valence shell and the atom.

Explanation of Solution

According to VSEPR theory, the following table shows the relation between the total number of bonding and non-bonding pair of electrons and the geometry of a molecule.

Total number of bonding and non-bonding pairs	Hybridization	Electron pair geometry	Shape
			No lone pairs	1	2	3	4
6	$s{p}^3{d}^2$	Octahedral	Octahedral	Square pyramidal	Square planar	T-shaped	Linear
5	$s{p}^{3}d$	Trigonal pyramidal	Trigonal pyramidal	Sawhorse	T-shared	Linear
4	$s{p}^3$	Tetrahedral	Tetrahedral	Trigonal planar	Bent
3	$s{p}^2$	Trigonal planar	Trigonal planar	Bent
2	$sp$	Linear	Linear

Now, the bond angle corresponding to the shape of the molecule is as follows:

Octahedral	${90}^o$ and   ${180}^o$
Trigonal pyramidal	${90}^o$ and   ${109.5}^o$
Tetrahedral	${109.5}^o$
Trigonal planar	${120}^{\text{o}}$
Linear	${180}^o$

Therefore, the angle between the $s{p}^3$ hybrids orbitals is ${109.5}^o$ because it has tetrahedral geometry.

(b)

Interpretation Introduction

Interpretation: The angles between the $s{p}^2$ hybrids orbitals need to be determined.

Concept Introduction: VSEPR theory is used to predict the molecular shape with the help of electron pairs around the central atoms of the molecule. It is based on the assumption that the shape of the molecule is such that there is minimum electronic repulsion between the valence shell and the atom.

Explanation of Solution

According to VSEPR theory, the following table shows the relation between the total number of bonding and non-bonding pair of electrons and the geometry of a molecule.

Total number of bonding and non-bonding pairs	Hybridization	Electron pair geometry	Shape
			No lone pairs	1	2	3	4
6	$s{p}^3{d}^2$	Octahedral	Octahedral	Square pyramidal	Square planar	T-shaped	Linear
5	$s{p}^{3}d$	Trigonal pyramidal	Trigonal pyramidal	Sawhorse	T-shared	Linear
4	$s{p}^3$	Tetrahedral	Tetrahedral	Trigonal planar	Bent
3	$s{p}^2$	Trigonal planar	Trigonal planar	Bent
2	$sp$	Linear	Linear

Now, the bond angle corresponding to the shape of the molecule is as follows:

Octahedral	${90}^o$ and   ${180}^o$
Trigonal pyramidal	${90}^o$ and   ${109.5}^o$
Tetrahedral	${109.5}^o$
Trigonal planar	${120}^{\text{o}}$
Linear	${180}^o$

Therefore, the angle between the $s{p}^2$ hybrids orbitals is ${120}^{\text{o}}$ because it has trigonal planar.

(c)

Interpretation Introduction

Interpretation: The angles between the $sp$ hybrids orbitals need to be determined.

Concept Introduction: VSEPR theory is used to predict the molecular shape with the help of electron pairs around the central atoms of the molecule. It is based on the assumption that the shape of the molecule is such that there is minimum electronic repulsion between the valence shell and the atom.

Explanation of Solution

According to VSEPR theory, the following table shows the relation between the total number of bonding and non-bonding pair of electrons and the geometry of a molecule.

Total number of bonding and non-bonding pairs	Hybridization	Electron pair geometry	Shape
			No lone pairs	1	2	3	4
6	$s{p}^3{d}^2$	Octahedral	Octahedral	Square pyramidal	Square planar	T-shaped	Linear
5	$s{p}^{3}d$	Trigonal pyramidal	Trigonal pyramidal	Sawhorse	T-shared	Linear
4	$s{p}^3$	Tetrahedral	Tetrahedral	Trigonal planar	Bent
3	$s{p}^2$	Trigonal planar	Trigonal planar	Bent
2	$sp$	Linear	Linear

Now, the bond angle corresponding to the shape of the molecule is as follows:

Octahedral	${90}^o$ and   ${180}^o$
Trigonal pyramidal	${90}^o$ and   ${109.5}^o$
Tetrahedral	${109.5}^o$
Trigonal planar	${120}^{\text{o}}$
Linear	${180}^o$

Therefore, the angle between the $sp$ hybrids orbitals is ${180}^o$ because it has linear geometry.