Question

Use MO diagrams to place${{\mathbf{B}}_{\mathbf{2}}}^{\mathbf{+}\mathbf{}}\mathbf{,}{\mathbf{B}}_{\mathbf{2}}\mathbf{,}$and ${{\mathbf{B}}_{\mathbf{2}}}^{\mathbf{-}}$in order of

a. Decreasing bond energy

b. Decreasing bond length

Short answer

Electrons in bonding orbitals stabilize they are between the nuclei.

1. Decreasing bond energy: ${{\mathbf{B}}_{\mathbf{2}}}^{+}\mathbf{<}{\mathbf{B}}_{\mathbf{2}\mathbf{}}\mathbf{<}{{\mathbf{B}}_{\mathbf{2}}}^{-}$
2. Decreasing bond length:${{\mathbf{B}}_{\mathbf{2}}}^{\mathbf{-}}\mathbf{<}{\mathbf{B}}_{\mathbf{2}\mathbf{}}\mathbf{<}{{\mathbf{B}}_{\mathbf{2}}}^{\mathbf{+}}$

Step-by-step solution

Bonding

Bonding may be defined as the force of attraction between two or more atoms to form a compound. The molecule can have the same atom and a different atom.

Bondenergy is the energy that is released or required during the formation of a bond.

The bond length is the length between the two atoms in a molecule, which can be the same or different atoms, showing the force of attraction from the bond.

Bond Energy

Bond order of the following molecule:

$$\begin{gathered} {{\mathbf{BondOrderofB}}_{\mathbf{2}}}^{\mathbf{-}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\left[\left(\mathrm{ElectroninBMO}\right)-\left(\mathrm{ElectroninABMO}\right)\right] \\ \mathbf{BondOrder}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\left[(5-2)\right] \\ \mathbf{BondOrder}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{5} \\ {\mathbf{BondOrderofB}}_{\mathbf{2}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\left[\left(\mathrm{ElectroninBMO}\right)-\left(\mathrm{ElectroninABMO}\right)\right] \\ \mathbf{BondOrder}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\left[(4-2)\right] \\ \mathbf{BondOrder}\mathbf{=}\mathbf{1} \\ {{\mathbf{BondOrderofB}}_{\mathbf{2}}}^{\mathbf{+}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\left[\left(\mathrm{ElectroninBMO}\right)-\left(\mathrm{ElectroninABMO}\right)\right] \\ \mathbf{BondOrder}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\left[(3-2)\right] \\ \mathbf{BondOrder}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{5} \end{gathered}$$

BMO = Bonding Molecular Orbital

ABMO = Anti-Bonding Molecular Orbital

The bond energy depends upon the bond order. The bond energy is proportional to the bond order, as the bond order increases, the bond energy tends to increase.

${{\mathbf{B}}_{\mathbf{2}}}^{+}\mathbf{<}{\mathbf{B}}_{\mathbf{2}\mathbf{}}\mathbf{<}{{\mathbf{B}}_{\mathbf{2}}}^{-}$

Bond length

The bond order is inversely proportional to the bond length. The bond length of the molecule depends upon the bond order, lower the bond order then higher is the bond length.

Increasing order of the Bond length:

${{\mathbf{B}}_{\mathbf{2}}}^{\mathbf{-}}\mathbf{<}{\mathbf{B}}_{\mathbf{2}\mathbf{}}\mathbf{<}{{\mathbf{B}}_{\mathbf{2}}}^{\mathbf{+}}$