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Chapter 10: Problem 54

Which of these species has a longer bond, \(\mathrm{B}_{2}\) or \(\mathrm{B}_{2}^{+} ?\) Explain in terms of molecular orbital theory.

Short Answer

Expert verified
\(\mathrm{B}_{2}\) has a shorter bond length than \(\mathrm{B}_{2}^{+}\) due to more filled bonding \(\pi_{2p}\) orbitals.

Step by step solution

01

Identify Electron Configurations

The electron configuration of \(\mathrm{B}_{2}\) is \(\sigma_{1s}^2 \sigma_{1s*}^2 \sigma_{2s}^2 \sigma_{2s*}^2 \pi_{2p}^4\). The electron configuration of \(\mathrm{B}_{2}^{+}\) is \(\sigma_{1s}^2 \sigma_{1s*}^2 \sigma_{2s}^2 \sigma_{2s*}^2 \pi_{2p}^3\) because it has one fewer electron.
02

Compare the Filled Orbitals

Both \(\mathrm{B}_{2}\) and \(\mathrm{B}_{2}^{+}\) have the same filled \(\sigma_{2s}\) and \(\sigma_{2s*}\) orbitals, but \(\mathrm{B}_{2}\) has both \(\pi_{2p}\) orbitals filled whereas \(\mathrm{B}_{2}^{+}\) has only three electrons in those orbitals.
03

Determine Bond Length

Since \(\mathrm{B}_{2}\) has more electrons in its bonding \(\pi_{2p}\) orbitals, its bonds are stronger and therefore shorter. Hence, \(\mathrm{B}_{2}\) has a shorter bond length than \(\mathrm{B}_{2}^{+}\).

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Most popular questions from this chapter

Explain why an atom cannot have a permanent dipole moment.

Predict the geometry of the following molecules using the VSEPR method: (a) \(\mathrm{HgBr}_{2}\), (b) \(\mathrm{N}_{2} \mathrm{O}(\mathrm{ar}-\) rangement of atoms is \(\mathrm{NNO}\) ), (c) \(\mathrm{SCN}^{-}\) (arrangement of atoms is \(\mathrm{SCN}\) ).

How would you distinguish between a sigma bond and a pi bond?

The compound 1,2 -dichloroethane \(\left(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}\right)\) is nonpolar, while \(c i s\) -dichloroethylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2} \mathrm{Cl}_{2}\right)\) has a dipole moment: The reason for the difference is that groups connected by a single bond can rotate with respect to each other, but no rotation occurs when a double bond connects the groups. On the basis of bonding considerations, explain why rotation occurs in 1,2 -dichloroethane but not in \(c i s\) -dichloroethylene.

Sketch the shapes of the following molecular orbitals: \(\sigma_{1 s}, \sigma_{1 s}^{\star}, \pi_{2 p},\) and \(\pi_{2 p}^{\star} .\) How do their energies compare?
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