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Chapter 11: Problem 30

The paramagnetism of gaseous \(\mathrm{B}_{2}\) has been established. Explain how this observation confirms that the \(\pi_{2 p}\) orbitals are at a lower energy than the \(\sigma_{2 p}\) orbital for \(\mathrm{B}_{2}\)

Short Answer

Expert verified
The paramagnetism of \(\mathrm{B}_{2}\) confirms that the \(\pi_{2 p}\) orbitals are at a lower energy level than the \(\sigma_{2 p}\) orbital because the unpaired electrons indicate that the \(\pi_{2 p}\) orbital filled before the \(\sigma_{2 p}\) orbital. If the \(\sigma_{2 p}\) had a lower energy level, it would fill before the \(\pi_{2 p}\), resulting in paired electrons and a diamagnetic molecule.

Step by step solution

01

Understanding the Electron Filling Order

The filling order of electron orbitals typically goes from lower energy levels to higher ones. Paired electrons in a specific orbital must have opposite spins because of a quantum mechanical principle called the Pauli Exclusion Principle.
02

Constructing the Electron Orbital Diagram for the Molecule

For \(\mathrm{B}_{2}\) molecule, the electrons fill the lower energy \(\pi_{2 p\}}\) orbitals first. As a result, there are two unpaired electrons, one in each \(\pi_{2 p}\) orbital, which makes \(\mathrm{B}_{2}\) paramagnetic.
03

Analyzing the Observation

The fact that \(\mathrm{B}_{2}\) is paramagnetic confirms that the \(\pi_{2 p}\) orbitals are at a lower energy than the \(\sigma_{2 p}\) orbital. If the \(\sigma_{2 p}\) orbital had a lower energy level, it would fill up before the \(\pi_{2 p}\) orbitals, resulting in paired electrons and a diamagnetic molecule.

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Most popular questions from this chapter

Write Lewis structures for the following molecules, and then label each \(\sigma\) and \(\pi\) bond. (a) \(\mathrm{HCN} ;\) (b) \(\mathrm{C}_{2} \mathrm{N}_{2}\) (c) \(\mathrm{CH}_{3} \mathrm{CHCHCCl}_{3} ;\) (d) HONO.

Furan, \(\mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O},\) is a substance derivable from oat hulls, corn cobs, and other cellulosic waste. It is a starting material for the synthesis of other chemicals used as pharmaceuticals and herbicides. The furan molecule is planar and the \(\mathrm{C}\) and \(\mathrm{O}\) atoms are bonded into a fivemembered pentagonal ring. The H atoms are attached to the C atoms. The chemical behavior of the molecule suggests that it is a resonance hybrid of several contributing structures. These structures show that the double bond character is associated with the entire ring in the form of a \(\pi\) electron cloud. (a) Draw Lewis structures for the several contributing structures to the resonance hybrid mentioned above. (b) Draw orbital diagrams to show the orbitals that are involved in the \(\sigma\) and \(\pi\) bonding in furan. [Hint: You need use only one of the contributing structures, such as the one with no formal charges.] (c) How many \(\pi\) electrons are there in the furan molecule? Show that this number of \(\pi\) electrons is the same, regardless of the contributing structure you use for this assessment.

Indicate several ways in which the valence-bond method is superior to Lewis structures in describing covalent bonds.

Construct a molecular orbital diagram for \(\mathrm{HF}\), and label the molecular orbitals as bonding, antibonding, or nonbonding.

Why does the hybridization \(s p^{3} d\) not account for bonding in the molecule BrF \(_{5} ?\) What hybridization scheme does work? Explain.
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