Chapter 9, Problem 9.112QP

Interpretation Introduction

Interpretation: The bond length of $\text{-1}\text{and}\text{-2}$ anions of homonuclear diatomic molecules of $\text{B,}\text{C,}\text{N,}\text{O}\text{and}\text{F}$  is to be compared with their corresponding neutral molecules.

Concept introduction: The bond length is the distance between the nuclei of two bonded atoms. The bond length is in inverse proportion with the number of bonded electrons higher the number of bonded electrons shorter would be the bond length.

To determine: The bond lengths of $\text{-1}\text{and}\text{-2}$ anions of homonuclear diatomic molecules of $\text{B,}\text{C,}\text{N,}\text{O}\text{and}\text{F}$ with respect to their corresponding neutral molecules.

Answer to Problem 9.112QP

If the bond order of an anion is higher than its corresponding neutral molecule then, the anion has shorter bond length then its corresponding molecule.

Explanation of Solution

Explanation

Whenever the bond order of the molecular anion is greater than its corresponding species, the bong lengths of their species is reduced. The electronic configuration and bond order of anions and their corresponding neutral species is given in table below.

Molecular species	Electronic configuration	Bond order
${\text{B}}_{\text{2}}$	${\left({\text{σ}}_{\text{2s}}\right)}^{\text{2}}{\left({\text{σ}}_{\text{2s}}^{\text{*}}\right)}^{\text{2}}{\left({\text{π}}_{\text{2p}}\right)}^{\text{2}}$	$1.0$
${\text{B}}_{\text{2}}^{\text{1-}}$	${\left({\text{σ}}_{\text{2s}}\right)}^{\text{2}}{\left({\text{σ}}_{\text{2s}}^{\text{*}}\right)}^{\text{2}}{\left({\text{π}}_{\text{2p}}\right)}^3$	$1.5$
${\text{B}}_{\text{2}}^{\text{2-}}$	${\left({\text{σ}}_{\text{2s}}\right)}^{\text{2}}{\left({\text{σ}}_{\text{2s}}^{\text{*}}\right)}^{\text{2}}{\left({\text{π}}_{\text{2p}}\right)}^4$	$2.0$
${\text{C}}_{\text{2}}$	${\left({\text{σ}}_{\text{2s}}\right)}^{\text{2}}{\left({\text{σ}}_{\text{2s}}^{\text{*}}\right)}^{\text{2}}{\left({\text{π}}_{\text{2p}}\right)}^4$	$2.0$
${\text{C}}_{\text{2}}^{\text{1-}}$	${\left({\text{σ}}_{\text{2s}}\right)}^{\text{2}}{\left({\text{σ}}_{\text{2s}}^{\text{*}}\right)}^{\text{2}}{\left({\text{π}}_{\text{2p}}\right)}^4{\left({\text{σ}}_{\text{2p}}\right)}^1$	$2.5$
${\text{C}}_{\text{2}}^{\text{2-}}$	${\left({\text{σ}}_{\text{2s}}\right)}^{\text{2}}{\left({\text{σ}}_{\text{2s}}^{\text{*}}\right)}^{\text{2}}{\left({\text{π}}_{\text{2p}}\right)}^4{\left({\text{σ}}_{\text{2p}}\right)}^2$	$3.0$
${\text{N}}_{\text{2}}$	${\left({\text{σ}}_{\text{2s}}\right)}^{\text{2}}{\left({\text{σ}}_{\text{2s}}^{\text{*}}\right)}^{\text{2}}{\left({\text{π}}_{\text{2p}}\right)}^4{\left({\text{σ}}_{\text{2p}}\right)}^2$	$3.0$
${\text{N}}_{\text{2}}^{\text{1-}}$	${\left({\text{σ}}_{\text{2s}}\right)}^{\text{2}}{\left({\text{σ}}_{\text{2s}}^{\text{*}}\right)}^{\text{2}}{\left({\text{π}}_{\text{2p}}\right)}^4{\left({\text{σ}}_{\text{2p}}\right)}^2{\left({\text{π}}_{\text{2p}}^{\text{*}}\right)}^1$	$2.5$
${\text{N}}_{\text{2}}^{\text{2-}}$	${\left({\text{σ}}_{\text{2s}}\right)}^{\text{2}}{\left({\text{σ}}_{\text{2s}}^{\text{*}}\right)}^{\text{2}}{\left({\text{π}}_{\text{2p}}\right)}^4{\left({\text{σ}}_{\text{2p}}\right)}^2{\left({\text{π}}_{\text{2p}}^{\text{*}}\right)}^2$	$2.0$
${\text{O}}_{\text{2}}$	${\left({\text{σ}}_{\text{2s}}\right)}^{\text{2}}{\left({\text{σ}}_{\text{2s}}^{\text{*}}\right)}^{\text{2}}{\left({\text{π}}_{\text{2p}}\right)}^4{\left({\text{σ}}_{\text{2p}}\right)}^2{\left({\text{π}}_{\text{2p}}^{\text{*}}\right)}^2$	$2.0$
${\text{O}}_{\text{2}}^{\text{1-}}$	${\left({\text{σ}}_{\text{2s}}\right)}^{\text{2}}{\left({\text{σ}}_{\text{2s}}^{\text{*}}\right)}^{\text{2}}{\left({\text{π}}_{\text{2p}}\right)}^4{\left({\text{σ}}_{\text{2p}}\right)}^2{\left({\text{π}}_{\text{2p}}^{\text{*}}\right)}^3$	$1.5$
${\text{O}}_{\text{2}}^{\text{2-}}$	${\left({\text{σ}}_{\text{2s}}\right)}^{\text{2}}{\left({\text{σ}}_{\text{2s}}^{\text{*}}\right)}^{\text{2}}{\left({\text{π}}_{\text{2p}}\right)}^4{\left({\text{σ}}_{\text{2p}}\right)}^2{\left({\text{π}}_{\text{2p}}^{\text{*}}\right)}^4$	$1.0$
${\text{F}}_{\text{2}}$	${\left({\text{σ}}_{\text{2s}}\right)}^{\text{2}}{\left({\text{σ}}_{\text{2s}}^{\text{*}}\right)}^{\text{2}}{\left({\text{π}}_{\text{2p}}\right)}^4{\left({\text{σ}}_{\text{2p}}\right)}^2{\left({\text{π}}_{\text{2p}}^{\text{*}}\right)}^4$	$1.0$
${\text{F}}_{\text{2}}^{\text{1-}}$	${\left({\text{σ}}_{\text{2s}}\right)}^{\text{2}}{\left({\text{σ}}_{\text{2s}}^{\text{*}}\right)}^{\text{2}}{\left({\text{π}}_{\text{2p}}\right)}^4{\left({\text{σ}}_{\text{2p}}\right)}^2{\left({\text{π}}_{\text{2p}}^{\text{*}}\right)}^4{\left({\text{σ}}_{\text{2p}}^{\text{*}}\right)}^1$	$0.5$
${\text{O}}_{\text{2}}^{\text{2-}}$	${\left({\text{σ}}_{\text{2s}}\right)}^{\text{2}}{\left({\text{σ}}_{\text{2s}}^{\text{*}}\right)}^{\text{2}}{\left({\text{π}}_{\text{2p}}\right)}^4{\left({\text{σ}}_{\text{2p}}\right)}^2{\left({\text{π}}_{\text{2p}}^{\text{*}}\right)}^4{\left({\text{σ}}_{\text{2p}}^{\text{*}}\right)}^2$	$0$

Hence, from the table the bond orders of anions of carbon and boron molecule is higher than their corresponding molecules. Therefore their anions will have shorter bond length then the neutral species.

The anions of oxygen, nitrogen and fluorine molecules have bond orders lower than their corresponding neutral molecules. So their bond lengths are not shorter than their neutral molecules.

Conclusion

The $\text{-1}\text{and}\text{-2}$ anions of homonuclear diatomic molecules of $\text{B}\text{and}\text{C}$ have shorter bond lengths than their corresponding neutral molecules.