Question

Give the correct order of bond length for $\mathrm{CO}$, ${\mathrm{CO}}_2$, ${\mathrm{CO}}_3^{2-}$ (carbonate) and why?

Answer 1

Bond length:

• Average distance between nuclei of two bonded atoms in a molecule, is called bond length.
• Bond length and bond order are inversely proportional to each other that is if bond order is increased, the bond length will decrease.

Bond order:

• The Bond Order is half of the difference between the number of electrons in bonding (Orbitals formed by the additive effect of atomic orbitals) and antibonding orbitals (Orbitals formed by the subtractive effect of atomic orbitals).
• It can also be defined as the ratio between the total number of bonds associated between two atoms in all structures and a total number of canonical forms (the resonating structures of a molecule that are formed by the delocalization of charge).
• If the compound has only one structure then the bond order will be the ratio of the total number of bonds to the total number of bonding molecules.

Bond order of Carbon monoxide $\left(\mathrm{CO}\right)$:

• The bond between the atoms Carbon and Oxygen is a triple bond in Carbon monoxide.

• Carbon monoxide has only one structure, that is bond order will be the ratio of a total number of bonds to the total number of bonding molecules.
• Here the number of bonds is 3 and the number of bonding molecules is 1 (since the carbon is bonded to one Oxygen).
• Therefore here the bond order will be the ratio of the total number of bonds to the total

$$\begin{gathered} \mathrm{Bond}\mathrm{order}=\frac{\mathrm{Number}\mathrm{of}\mathrm{bonds}}{\mathrm{Number}\mathrm{of}\mathrm{bonding}\mathrm{molecules}} \\ =\frac{3}{1} \\ =3 \end{gathered}$$.

• Hence the bond order of $\mathrm{CO}$ is 3.

Bond order of Carbon dioxide $\left({\mathrm{CO}}_2\right)$:

• In Carbon dioxide, the bond between the Carbon atom and two Oxygen atoms is a double bond

• Carbon dioxide has only one structure, that is the bond order will be the ratio of the total number of bonds to the total number of bonding molecules.
• Here the number of bonds is 4 and the number of bonding molecules is 2 (since the Carbon is bonded to two Oxygen).
• Hence the bond order is the ratio of the total number of bonds to the total.

$$\begin{gathered} \mathrm{Bond}\mathrm{order}=\frac{\mathrm{Number}\mathrm{of}\mathrm{bonds}}{\mathrm{Number}\mathrm{of}\mathrm{bonding}\mathrm{molecules}} \\ =\frac{4}{2} \\ =2 \end{gathered}$$

• Hence the bond order of ${\mathrm{CO}}_2$ is 2.

Bond order of Carbonate ${\mathrm{CO}}_3^{2-}$:

• There is resonance in this structure for Carbonate ions and the charge on Oxygen atoms will keep on moving.

• Here the number of bonds is 4 and the number of the canonical structures is 3.
• Here the Bond order is the ratio between the total number of bonds associated between two atoms in all structures and the total number of canonical forms.

$$\begin{gathered} \mathrm{Bond}\mathrm{order}=\frac{\mathrm{Number}\mathrm{of}\mathrm{bonds}}{\mathrm{Number}\mathrm{of}\mathrm{Canonical}\mathrm{structures}} \\ =\frac{4}{3} \\ =1.3 \end{gathered}$$

• Hence the bond order of ${\mathrm{CO}}_3^{2-}$ is 1.3

Correct order for bond length:

• Bond length and bond order are inversely proportional.
• That is, the increasing order of bond length is$\mathrm{CO}<{\mathrm{CO}}_2<{\mathrm{CO}}_3^{2-}$

Therefore, the increasing order of bond length of $\mathrm{CO}$, ${\mathrm{CO}}_2$ and ${\mathrm{CO}}_3^{2-}$is $\mathrm{CO}<{\mathrm{CO}}_2<{\mathrm{CO}}_3^{2-}$.