Chapter 7, Problem 7.61QP

Which of the following pairs of atomic orbitals of adjacent nuclei can overlap to form a sigma bond? Which overlap to form a pi bond? Which cannot overlap (no bond)? Consider the x axis to be the internuclear axis, that is, the line joining the nuclei of the two atoms, (a) 1s and 1s, (b) 1s and 2p_x. (c) 2p_x and 2p_y, (d) 3p_y and 3p_y, (e) 2p_x and 2p_x. (f) 1s and 2s.

Interpretation Introduction

Interpretation:

From the given set of orbitals, the ones that forms sigma bond, the ones that forms pi bond and the ones that doesn’t form any bond have to be identified.

${\text{(a) 1s and 1s (b) 1s and 2p}}_{\text{x}}{\text{ (c) 2p}}_{\text{x}}{\text{ and 2p}}_{\text{y}}{\text{ (d) 3p}}_y{\text{ and 3p}}_y{\text{ (e) 2p}}_x{\text{ and 2p}}_x\text{ (f) 1s and 2s}\text{.}$

Concept Introduction:

There are two different types of chemical bond – sigma bond and pi bond.  A bond between two atoms is known as sigma bond if the atomic orbitals of the atoms overlap end to end – it is also called head on overlapping.  A bond is said to pi bond if it is formed by sideways overlapping of atomic orbitals of the atoms. This is also known as lateral overlapping.

Answer to Problem 7.61QP

Solution:

S.No	Set of atomic orbitals	Type of bond formation
(a)	$\text{1s and 1s}$	Sigma bond

Explanation of Solution

Two $\text{1s}$ orbitals overlap end to end and form sigma bond.  This can be represented as follows –

End to end overlapping of two $1s$ orbitals

Figure 1

For example, the sigma bond between two Hydrogen atoms formed by end to end overlapping of $\text{1s}$ orbitals of the two Hydrogen atoms.

Interpretation Introduction

Interpretation:

From the given set of orbitals, the ones that forms sigma bond, the ones that forms pi bond and the ones that doesn’t form any bond have to be identified.

${\text{(a) 1s and 1s (b) 1s and 2p}}_{\text{x}}{\text{ (c) 2p}}_{\text{x}}{\text{ and 2p}}_{\text{y}}{\text{ (d) 3p}}_y{\text{ and 3p}}_y{\text{ (e) 2p}}_x{\text{ and 2p}}_x\text{ (f) 1s and 2s}\text{.}$

Concept Introduction:

There are two different types of chemical bond – sigma bond and pi bond.  A bond between two atoms is known as sigma bond if the atomic orbitals of the atoms overlap end to end – it is also called head on overlapping.  A bond is said to pi bond if it is formed by sideways overlapping of atomic orbitals of the atoms. This is also known as lateral overlapping.

Answer to Problem 7.61QP

Solution:

S.No	Set of atomic orbitals	Type of bond formation
(b)	${\text{1s and 2p}}_{\text{x}}$	Sigma bond

Explanation of Solution

${\text{1s and 2p}}_{\text{x}}$ orbitals overlap end to end and form sigma bond.  This can be represented as follows –

End to end overlapping of $1sand2p_x$ orbitals

Figure 2

Interpretation Introduction

Interpretation:

From the given set of orbitals, the ones that forms sigma bond, the ones that forms pi bond and the ones that doesn’t form any bond have to be identified.

${\text{(a) 1s and 1s (b) 1s and 2p}}_{\text{x}}{\text{ (c) 2p}}_{\text{x}}{\text{ and 2p}}_{\text{y}}{\text{ (d) 3p}}_y{\text{ and 3p}}_y{\text{ (e) 2p}}_x{\text{ and 2p}}_x\text{ (f) 1s and 2s}\text{.}$

Concept Introduction:

There are two different types of chemical bond – sigma bond and pi bond.  A bond between two atoms is known as sigma bond if the atomic orbitals of the atoms overlap end to end – it is also called head on overlapping.  A bond is said to pi bond if it is formed by sideways overlapping of atomic orbitals of the atoms. This is also known as lateral overlapping.

Answer to Problem 7.61QP

Solution:

S.No	Set of atomic orbitals	Type of bond formation
(c)	${\text{2p}}_{\text{x}}{\text{ and 2p}}_{\text{y}}$	No bond formation

Explanation of Solution

${\text{2p}}_{\text{x}}{\text{ and 2p}}_{\text{y}}$ orbitals cannot overlap and so doesn’t form bond.  ${\text{2p}}_{\text{x}}$ orbital lies on X-axis whereas ${\text{2p}}_{\text{y}}$ orbital lies on Y-axis.  They cannot overlap with each other because the electron density at the origin is zero.

Shape of $2p_{x}and2p_y$orbitals

Figure 3

Interpretation Introduction

Interpretation:

From the given set of orbitals, the ones that forms sigma bond, the ones that forms pi bond and the ones that doesn’t form any bond have to be identified.

${\text{(a) 1s and 1s (b) 1s and 2p}}_{\text{x}}{\text{ (c) 2p}}_{\text{x}}{\text{ and 2p}}_{\text{y}}{\text{ (d) 3p}}_y{\text{ and 3p}}_y{\text{ (e) 2p}}_x{\text{ and 2p}}_x\text{ (f) 1s and 2s}\text{.}$

Concept Introduction:

There are two different types of chemical bond – sigma bond and pi bond.  A bond between two atoms is known as sigma bond if the atomic orbitals of the atoms overlap end to end – it is also called head on overlapping.  A bond is said to pi bond if it is formed by sideways overlapping of atomic orbitals of the atoms. This is also known as lateral overlapping.

Answer to Problem 7.61QP

Solution:

S.No	Set of atomic orbitals	Type of bond formation
(d)	${\text{3p}}_y{\text{ and 3p}}_y$	Pi bond

Explanation of Solution

The ${\text{p}}_y$ orbital lies on Y-axis. Two ${\text{p}}_y$ orbitals lie on the same plane.  They overlap sideways and form pi bond as follows –

Sideways overlapping of two $3p_y$orbitals

Figure 4

Interpretation Introduction

Interpretation:

From the given set of orbitals, the ones that forms sigma bond, the ones that forms pi bond and the ones that doesn’t form any bond have to be identified.

${\text{(a) 1s and 1s (b) 1s and 2p}}_{\text{x}}{\text{ (c) 2p}}_{\text{x}}{\text{ and 2p}}_{\text{y}}{\text{ (d) 3p}}_y{\text{ and 3p}}_y{\text{ (e) 2p}}_x{\text{ and 2p}}_x\text{ (f) 1s and 2s}\text{.}$

Concept Introduction:

There are two different types of chemical bond – sigma bond and pi bond.  A bond between two atoms is known as sigma bond if the atomic orbitals of the atoms overlap end to end – it is also called head on overlapping.  A bond is said to pi bond if it is formed by sideways overlapping of atomic orbitals of the atoms. This is also known as lateral overlapping.

Answer to Problem 7.61QP

Solution:

S.No	Set of atomic orbitals	Type of bond formation
(e)	${\text{2p}}_x{\text{ and 2p}}_x$	Pi bond

Explanation of Solution

The ${\text{p}}_x$ orbital lies on X-axis. Two ${\text{p}}_x$ orbitals lie on the same plane.  They overlap laterally and form pi bond as follows –

Lateral overlapping of two $2p_x$ orbitals

Figure 5

Interpretation Introduction

Interpretation:

From the given set of orbitals, the ones that forms sigma bond, the ones that forms pi bond and the ones that doesn’t form any bond have to be identified.

${\text{(a) 1s and 1s (b) 1s and 2p}}_{\text{x}}{\text{ (c) 2p}}_{\text{x}}{\text{ and 2p}}_{\text{y}}{\text{ (d) 3p}}_y{\text{ and 3p}}_y{\text{ (e) 2p}}_x{\text{ and 2p}}_x\text{ (f) 1s and 2s}\text{.}$

Concept Introduction:

There are two different types of chemical bond – sigma bond and pi bond.  A bond between two atoms is known as sigma bond if the atomic orbitals of the atoms overlap end to end – it is also called head on overlapping.  A bond is said to pi bond if it is formed by sideways overlapping of atomic orbitals of the atoms. This is also known as lateral overlapping.

Answer to Problem 7.61QP

Solution:

S.No	Set of atomic orbitals	Type of bond formation
(f)	$\text{1s and 2s}$	Sigma bond

Explanation of Solution

Overlapping of two s-orbitals always result in sigma bond formation as two s-orbitals overlap head to head as follows –

End to end overlapping of $1sand2s$ orbitals

Figure 6