Chapter 9, Problem 9C.4BE

Interpretation Introduction

Interpretation:

The bond orders of cations and anions for elements of period $2$ have to be stated.

Concept introduction:

Electronic configuration tells about the arrangement of the electrons in each subshell and each orbital of an atom.  The distribution of the electrons in the molecules is described by the molecular orbital theory.  The bond order of a molecule is given by the expression as shown below.

  $b=\frac{N-N^{*}}{2}$

Answer to Problem 9C.4BE

The bond orders of cations, ${\text{Li}}_2^{+}\text{,}{\text{Be}}_2^{+}\text{,}{\text{B}}_2^{+}\text{,}{\text{C}}_2^{+}\text{,}{\text{N}}_2^{+}\text{,}{\text{O}}_2^{+}\text{,}{\text{F}}_2^{+}$ and ${\text{Ne}}_2^{+}$ are $\underset{\_}{0.5},\underset{\_}{0.5},\underset{\_}{0.5},\underset{\_}{1.5},\underset{\_}{2.5},\underset{\_}{2.5},\underset{\_}{1.5}$ and $\underset{\_}{0.5}$ respectively.

The bond orders of anions, ${\text{Li}}_2^{-}\text{,}{\text{Be}}_2^{-}\text{,}{\text{B}}_2^{-}\text{,}{\text{C}}_2^{-}\text{,}{\text{N}}_2^{-}\text{,}{\text{O}}_2^{-}\text{,}{\text{F}}_2^{-}$ and ${\text{Ne}}_2^{-}$ are $\underset{\_}{0.5},\underset{\_}{0.5},\underset{\_}{1.5},\underset{\_}{2.5},\underset{\_}{2.5},\underset{\_}{1.5},\underset{\_}{0.5}$ and $\underset{\_}{0.5}$ respectively.

Explanation of Solution

The diatomic molecules of elements that belong to period $2$ are ${\text{Li}}_2\text{,}{\text{Be}}_2\text{,}{\text{B}}_{\text{2}}\text{,}{\text{C}}_{\text{2}}\text{,}{\text{N}}_{\text{2}}\text{,}{\text{O}}_{\text{2}}\text{,}{\text{F}}_{\text{2}}$ and ${\text{Ne}}_{\text{2}}$.

The total number of electrons possessed by ${\text{Li}}_2\text{,}{\text{Be}}_2\text{,}{\text{B}}_{\text{2}}\text{,}{\text{C}}_{\text{2}}\text{,}{\text{N}}_{\text{2}}\text{,}{\text{O}}_{\text{2}}\text{,}{\text{F}}_{\text{2}}$ and ${\text{Ne}}_{\text{2}}$ molecules is $6,8,10,12,14,16,18$ and $20$ respectively.

Therefore, the number of electrons possesssed by cations ${\text{Li}}_2^{+}\text{,}{\text{Be}}_2^{+}\text{,}{\text{B}}_2^{+}\text{,}{\text{C}}_2^{+}\text{,}{\text{N}}_2^{+}\text{,}{\text{O}}_2^{+}\text{,}{\text{F}}_2^{+}$ and ${\text{Ne}}_2^{+}$ is $5,7,9,11,13,15,17$ and $19$ respectively.

The electronic configuration of ${\text{Li}}_2^{+}$ molecule for outer shell is $1{\sigma }_{\text{g}}^1$.

The bond order of a molecule ($b$) is given by the expression as shown below.

  $b=\frac{N-N^{*}}{2}$        (1)

Where,

• $N$ is the number of electrons in the bonding orbital.
• $N^{*}$ is the number of electrons in the anti-bonding orbital.

Substitute the value of $N$ and $N^{*}$ in the equation (1).

  $\begin{array}{c}b=\frac{1-0}{2}\\ =\underset{\_}{0.5}\end{array}$

The bond order of ${\text{Li}}_2^{+}$ is $\underset{\_}{0.5}$.

The electronic configuration of ${\text{Be}}_2^{+}$ molecule for outer shell is $1{\sigma }_{\text{g}}^{2}1{\sigma }_{\text{u}}^{\ast 1}$.

Substitute the value of $N$ and $N^{*}$ for ${\text{Be}}_2^{+}$ in the equation (1) as shown below.

  $\begin{array}{c}b=\frac{2-1}{2}\\ =\underset{\_}{0.5}\end{array}$

The bond order of ${\text{Be}}_2^{+}$ is $\underset{\_}{0.5}$.

The electronic configuration of ${\text{B}}_2^{+}$ molecule for outer shell is $1{\sigma }_{\text{g}}^{2}1{\sigma }_{\text{u}}^{\ast 2}1{\text{π}}_{\text{u}}^1$.

Substitute the value of $N$ and $N^{*}$ for ${\text{B}}_2^{+}$ in the equation (1) as shown below.

  $\begin{array}{c}b=\frac{3-1}{2}\\ =\underset{\_}{0.5}\end{array}$

The bond order of ${\text{B}}_2^{+}$ is $\underset{\_}{0.5}$.

The electronic configuration of ${\text{C}}_2^{+}$ molecule for outer shell is $1{\sigma }_{\text{g}}^{2}1{\sigma }_{\text{u}}^{\ast 2}1{\text{π}}_{\text{u}}^3$.

Substitute the value of $N$ and $N^{*}$ for ${\text{C}}_2^{+}$ in the equation (1) as shown below.

  $\begin{array}{c}b=\frac{5-2}{2}\\ =\underset{\_}{1.5}\end{array}$

The bond order of ${\text{C}}_2^{+}$ is $\underset{\_}{1.5}$.

The electronic configuration of ${\text{N}}_2^{+}$ molecule for outer shell is $1{\sigma }_{\text{g}}^{2}1{\sigma }_{\text{u}}^{\ast 2}1{\text{π}}_{\text{u}}^{4}2{\sigma }_{\text{g}}^1$.

Substitute the value of $N$ and $N^{*}$ for ${\text{N}}_2^{+}$ in the equation (1) as shown below.

  $\begin{array}{c}b=\frac{7-2}{2}\\ =\underset{\_}{2.5}\end{array}$

The bond order of ${\text{N}}_2^{+}$ is $\underset{\_}{2.5}$.

The electronic configuration of ${\text{O}}_2^{+}$ molecule for outer shell is $1{\sigma }_{\text{g}}^{2}1{\sigma }_{\text{u}}^{\ast 2}2{\sigma }_{\text{g}}^{2}1{\text{π}}_{\text{u}}^{4}1{\text{π}}_{\text{g}}^{*1}$.

Substitute the value of $N$ and $N^{*}$ for ${\text{O}}_2^{+}$ in the equation (1) as shown below.

  $\begin{array}{c}b=\frac{8-3}{2}\\ =\underset{\_}{2.5}\end{array}$

The bond order of ${\text{O}}_2^{+}$ is $\underset{\_}{2.5}$.

The electronic configuration of ${\text{F}}_2^{+}$ molecule for outer shell is $1{\sigma }_{\text{g}}^{2}1{\sigma }_{\text{u}}^{\ast 2}2{\sigma }_{\text{g}}^{2}1{\text{π}}_{\text{u}}^{4}1{\text{π}}_{\text{g}}^{*3}$.

Substitute the value of $N$ and $N^{*}$ for ${\text{F}}_2^{+}$ in the equation (1) as shown below.

  $\begin{array}{c}b=\frac{8-5}{2}\\ =\underset{\_}{1.5}\end{array}$

The bond order of ${\text{F}}_2^{+}$ is $\underset{\_}{1.5}$.

The electronic configuration of ${\text{Ne}}_2^{+}$ molecule for outer shell is $1{\sigma }_{\text{g}}^{2}1{\sigma }_{\text{u}}^{\ast 2}2{\sigma }_{\text{g}}^{2}1{\text{π}}_{\text{u}}^{4}1{\text{π}}_{\text{g}}^{*4}2{\sigma }_{\text{u}}^{\ast 1}$.

Substitute the value of $N$ and $N^{*}$ for ${\text{Ne}}_2^{+}$ in the equation (1) as shown below.

  $\begin{array}{c}b=\frac{8-7}{2}\\ =\underset{\_}{0.5}\end{array}$

The bond order of ${\text{Ne}}_2^{+}$ is $\underset{\_}{0.5}$.

The number of electrons possesssed by anions ${\text{Li}}_2^{-}\text{,}{\text{Be}}_2^{-}\text{,}{\text{B}}_2^{-}\text{,}{\text{C}}_2^{-}\text{,}{\text{N}}_2^{-}\text{,}{\text{O}}_2^{-}\text{,}{\text{F}}_2^{-}$ and ${\text{Ne}}_2^{-}$ is $7,9,11,13,15,17,19$ and $21$ respectively.

The electronic configuration of ${\text{Li}}_2^{-}$ molecule for outer shell is $1{\sigma }_{\text{g}}^{2}1{\sigma }_{\text{u}}^{\ast 1}$.

Substitute the value of $N$ and $N^{*}$ for ${\text{Li}}_2^{-}$ in the equation (1).

  $\begin{array}{c}b=\frac{2-1}{2}\\ =\underset{\_}{0.5}\end{array}$

The bond order of ${\text{Li}}_2^{-}$ is $\underset{\_}{0.5}$.

The electronic configuration of ${\text{Be}}_2^{-}$ molecule for outer shell is $1{\sigma }_{\text{g}}^{2}1{\sigma }_{\text{u}}^{\ast 2}1{\text{π}}_{\text{u}}^1$.

Substitute the value of $N$ and $N^{*}$ for ${\text{Be}}_2^{-}$ in the equation (1) as shown below.

  $\begin{array}{c}b=\frac{3-2}{2}\\ =\underset{\_}{0.5}\end{array}$

The bond order of ${\text{Be}}_2^{-}$ is $\underset{\_}{0.5}$.

The electronic configuration of ${\text{B}}_2^{-}$ molecule for outer shell is $1{\sigma }_{\text{g}}^{2}1{\sigma }_{\text{u}}^{\ast 2}1{\text{π}}_{\text{u}}^3$.

Substitute the value of $N$ and $N^{*}$ for ${\text{B}}_2^{-}$ in the equation (1) as shown below.

  $\begin{array}{c}b=\frac{5-2}{2}\\ =\underset{\_}{1.5}\end{array}$

The bond order of ${\text{B}}_2^{-}$ is $\underset{\_}{1.5}$.

The electronic configuration of ${\text{C}}_2^{-}$ molecule for outer shell is $1{\sigma }_{\text{g}}^{2}1{\sigma }_{\text{u}}^{\ast 2}1{\text{π}}_{\text{u}}^{4}2{\sigma }_{\text{g}}^1$.

Substitute the value of $N$ and $N^{*}$ for ${\text{C}}_2^{-}$ in the equation (1) as shown below.

  $\begin{array}{c}b=\frac{7-2}{2}\\ =\underset{\_}{2.5}\end{array}$

The bond order of ${\text{C}}_2^{-}$ is $\underset{\_}{2.5}$.

The electronic configuration of ${\text{N}}_2^{-}$ molecule for outer shell is $1{\sigma }_{\text{g}}^{2}1{\sigma }_{\text{u}}^{\ast 2}1{\text{π}}_{\text{u}}^{4}2{\sigma }_{\text{g}}^{2}1{\text{π}}_{\text{g}}^{*1}$.

Substitute the value of $N$ and $N^{*}$ for ${\text{N}}_2^{-}$ in the equation (1) as shown below.

  $\begin{array}{c}b=\frac{8-3}{2}\\ =\underset{\_}{2.5}\end{array}$

The bond order of ${\text{N}}_2^{-}$ is $\underset{\_}{2.5}$.

The electronic configuration of ${\text{O}}_2^{-}$ molecule for outer shell is $1{\sigma }_{\text{g}}^{2}1{\sigma }_{\text{u}}^{\ast 2}2{\sigma }_{\text{g}}^{2}1{\text{π}}_{\text{u}}^{4}1{\text{π}}_{\text{g}}^{*3}$.

Substitute the value of $N$ and $N^{*}$ for ${\text{O}}_2^{-}$ in the equation (1) as shown below.

  $\begin{array}{c}b=\frac{8-5}{2}\\ =\underset{\_}{1.5}\end{array}$

The bond order of ${\text{O}}_2^{-}$ is $\underset{\_}{1.5}$.

The electronic configuration of ${\text{F}}_2^{-}$ molecule for outer shell is $1{\sigma }_{\text{g}}^{2}1{\sigma }_{\text{u}}^{\ast 2}2{\sigma }_{\text{g}}^{2}1{\text{π}}_{\text{u}}^{4}1{\text{π}}_{\text{g}}^{*4}2{\sigma }_{\text{u}}^{*1}$.

Substitute the value of $N$ and $N^{*}$ for ${\text{F}}_2^{-}$ in the equation (1) as shown below.

  $\begin{array}{c}b=\frac{8-7}{2}\\ =\underset{\_}{0.5}\end{array}$

The bond order of ${\text{F}}_2^{-}$ is $\underset{\_}{0.5}$.

The electronic configuration of ${\text{Ne}}_2^{-}$ molecule for outer shell is $1{\sigma }_{\text{g}}^{2}1{\sigma }_{\text{u}}^{\ast 2}2{\sigma }_{\text{g}}^{2}1{\text{π}}_{\text{u}}^{4}1{\text{π}}_{\text{g}}^{*4}2{\sigma }_{\text{u}}^{\ast 2}3{\sigma }_{\text{g}}^1$.

Substitute the value of $N$ and $N^{*}$ for ${\text{Ne}}_2^{-}$ in the equation (1) as shown below.

  $\begin{array}{c}b=\frac{9-8}{2}\\ =\underset{\_}{0.5}\end{array}$

The bond order of ${\text{Ne}}_2^{-}$ is $\underset{\_}{0.5}$.