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Chapter 10: Problem 53

Use molecular orbital theory to explain why the \(\mathrm{Be}_{2}\) molecule does not exist.

Short Answer

Expert verified
The molecular orbital theory shows that the bond order of \( \mathrm{Be}_{2} \) will be 0, indicating it is unstable and unlikely to exist.

Step by step solution

01

Electron Configuration

Start by recognizing that Beryllium (Be) has atomic number 4, thus it has 4 electrons. Two electrons occupy the 1s orbital, and the other two occupy the 2s orbital. Consequently, the electron configuration of a Beryllium atom is \(1s^{2} 2s^{2}\).
02

Constructing the Molecular Orbital Diagram

Construct the molecular orbital diagram for \( \mathrm{Be}_{2} \). In molecular orbital theory, individual atomic orbitals (AO) combine to form molecular orbitals. This combination is visualized in a molecular orbital (MO) diagram. For Beryllium, the bonding and anti-bonding orbitals for both the 1s and 2s orbitals will be the same.
03

Filling the Molecular Orbitals

Next, fill up the molecular orbitals with the available electrons. An \( \mathrm{Be}_{2} \) molecule would have a total of 8 electrons (4 from each Beryllium atom). The 1s bonding and anti-bonding orbitals will be filled first (2 electrons each). There are 4 electrons left, which will fill the 2s bonding orbital. The 2s anti-bonding orbital will remain empty.
04

Analyzing the Orbital Filling

The Bond Order, which indicates the stability of a molecule, can be found using the formula: Bond order = (number of electrons in bonding orbitals - number of electrons in anti-bonding orbitals) / 2. For \( \mathrm{Be}_{2} \), this gives a Bond order of 0. This corroborates the experimental fact that \( \mathrm{Be}_{2} \) molecule does not exist. Molecules with a bond order of 0 are generally considered unstable and not prone to exist.

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Most popular questions from this chapter

Draw the Lewis structure of ketene \(\left(\mathrm{C}_{2} \mathrm{H}_{2} \mathrm{O}\right)\) and describe the hybridization states of the \(\mathrm{C}\) atoms. The molecule does not contain \(\mathrm{O}-\mathrm{H}\) bonds. On separate diagrams, sketch the formation of sigma and pi bonds.

Explain why an atom cannot have a permanent dipole moment.

Write the ground-state electron configuration for \(\mathrm{B}_{2}\). Is the molecule diamagnetic or paramagnetic?

What is the relationship between the dipole moment and the bond moment? How is it possible for a molecule to have bond moments and yet be nonpolar?

Compare the Lewis and molecular orbital treatments of the oxygen molecule.
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