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Chapter 11: Problem 102

102\. Which of the following species are paramagnetic? (a) \(\mathrm{B}_{2} ;\) (b) \(\mathrm{B}_{2}^{-} ;\) (c) \(\mathrm{B}_{2}^{+}\). Which species has the strongest bond?

Short Answer

Expert verified
\(\mathrm{B}_{2}^{-}\) and \(\mathrm{B}_{2}^{+}\) are paramagnetic while \(\mathrm{B}_{2}\) is diamagnetic. \(\mathrm{B}_{2}\) has the strongest bond.

Step by step solution

01

Understand the Molecules

Identify the particles under review, here \(\mathrm{B}_{2}, \mathrm{B}_{2}^{-},\) and \(\mathrm{B}_{2}^{+}\). All three are variations of a diatomic boron molecule, which differ in their electron number due to charge.
02

Apply the Molecular Orbital Theory

Use the rules of molecular orbital theory to fill up the molecular orbitals. For boron molecules, the energy order of molecular orbitals is \(\sigma_{1s}<\sigma_{1s}^*<\sigma_{2s}<\sigma_{2s}^*<\pi_{2p}\). As each boron atom contributes 3 valence electrons, \(\mathrm{B}_{2}\) has a total of 6, \(\mathrm{B}_{2}^{-}\) has 7, and \(\mathrm{B}_{2}^{+}\) has 5 electrons to distributed in the molecular orbitals.
03

Identify the Paramagnetic Species

A paramagnetic species has unpaired electrons. Hence, distribute the electrons in the molecular orbitals. For \(\mathrm{B}_{2},\) the six electrons can be paired in the molecular orbitals, so it is diamagnetic. For \(\mathrm{B}_{2}^{-},\) with seven electrons, one electron will remain unpaired, so it is paramagnetic. For \(\mathrm{B}_{2}^{+}\) with five electrons, one electron will also remain unpaired, so it is paramagnetic.
04

Determine the Strongest Bond

For \(\mathrm{B}_{2}, \mathrm{B}_{2}^{-},\) and \(\mathrm{B}_{2}^{+}\), the bond order can be calculated as \([Number\:of\:bonding\:electrons - Number\:of\:antibonding\:electrons] / 2\). The \(\mathrm{B}_{2}\) molecule has the highest bond order, indicating the strongest bond among the three.

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Most popular questions from this chapter

In which of the following ions would you expect to find delocalized molecular orbitals: (a) \(\mathrm{HCO}_{2}^{-} ;\) (b) \(\mathrm{CO}_{3}^{2-}\) (c) \(\mathrm{CH}_{3}^{+} ?\) Explain.

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