Textbook Question
Indicate whether each statement is true or false. (b) The probability is always 0% for finding an electron in an antibonding orbital.
Ch.9 - Molecular Geometry and Bonding Theories
Chapter 9, Problem 75
According to molecular orbital theory, would Be2 be expected to exist? Explain. Would Be2+ be expected to exist? Explain. What are the relationships among bond order, bond length, and bond energy?
Verified step by step guidance1
Step 1: Begin by understanding the molecular orbital (MO) theory, which describes the distribution of electrons in molecules in terms of molecular orbitals that can extend over the entire molecule.
Step 2: Construct the molecular orbital diagram for Be2. Beryllium (Be) has an atomic number of 4, so each Be atom has 4 electrons. In Be2, there are a total of 8 electrons to place in molecular orbitals.
Step 3: Fill the molecular orbitals for Be2 starting from the lowest energy level. The order is: \( \sigma_{1s} \), \( \sigma_{1s}^* \), \( \sigma_{2s} \), \( \sigma_{2s}^* \). Place the 8 electrons accordingly.
Step 4: Calculate the bond order for Be2 using the formula: \( \text{Bond Order} = \frac{(\text{Number of electrons in bonding MOs} - \text{Number of electrons in antibonding MOs})}{2} \). Determine if the bond order is greater than zero to predict the existence of Be2.
Step 5: For Be2+, remove one electron from the highest occupied molecular orbital (HOMO) of Be2 and recalculate the bond order. Discuss the relationships among bond order, bond length, and bond energy: higher bond order generally means shorter bond length and higher bond energy.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Molecular Orbital Theory
Molecular Orbital Theory (MOT) describes the behavior of electrons in molecules by considering atomic orbitals that combine to form molecular orbitals. These orbitals can be bonding, antibonding, or non-bonding, and the distribution of electrons among them determines the stability and existence of a molecule. For example, in diatomic molecules like Be2, the filling of molecular orbitals can indicate whether the molecule is stable or not.
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Molecular Orbital Theory
Bond Order
Bond order is a measure of the number of chemical bonds between a pair of atoms, calculated as the difference between the number of bonding and antibonding electrons divided by two. A higher bond order indicates a stronger bond and greater stability of the molecule. For instance, a bond order of zero suggests that the molecule is unlikely to exist, as seen in the case of Be2, which has a bond order of zero due to its electron configuration.
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Bond Length and Bond Energy
Bond length is the distance between the nuclei of two bonded atoms, while bond energy is the amount of energy required to break a bond. Generally, shorter bonds (lower bond lengths) correspond to higher bond energies, indicating stronger bonds. This relationship is crucial in understanding molecular stability; for example, as bond order increases, bond length decreases and bond energy increases, leading to more stable molecules.
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Related Practice
Textbook Question
Indicate whether each statement is true or false. (c) Molecules containing electrons that occupy antibonding orbitals must be unstable.
Textbook Question
Indicate whether each statement is true or false. (d) Electrons cannot occupy a nonbonding orbital.
Textbook Question
Explain the following: (c) The O22 + ion has a stronger O—O bond than O2 itself.
Textbook Question
How would we describe a substance that contains only paired electrons and is weakly repelled by a magnetic field? Which of the following ions would you expect to possess similar characteristics: H2-, Ne2+, F2, O22 +?
Textbook Question
Using Figures 9.35 and 9.43 as guides, draw the molecular orbital electron configuration for (d) Ne22 +. In each case indicate whether the addition of an electron to the ion would increase or decrease the bond order of the species.