Textbook Question
Draw a picture that shows all three 2p orbitals on one atom and all three 2p orbitals on another atom. (c) How many antibonding orbitals, and of what type can be made from the two sets of 2p orbitals?
Ch.9 - Molecular Geometry and Bonding Theories
Chapter 9, Problem 76
a. Based on its molecular-orbital diagram, what is the bond order of the O2 molecule?
b. What is the expected bond order for the peroxide ion, O22−?
c. What is the expected bond order for the superoxide ion, O2−?
d. From shortest to longest, predict the ordering of the bond lengths for O2, O22−, and O2−.
e. From weakest to strongest, predict the ordering of the bond strengths for O2, O22−, and O2−.
Verified step by step guidance1
Step 1: Understand the concept of bond order. Bond order is calculated using the formula: \( \text{Bond Order} = \frac{\text{Number of bonding electrons} - \text{Number of antibonding electrons}}{2} \).
Step 2: Determine the bond order for \( \text{O}_2 \). The molecular orbital configuration for \( \text{O}_2 \) is \( \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi^*_{2p_x}^1 \pi^*_{2p_y}^1 \). Calculate the bond order using the formula.
Step 3: Calculate the bond order for the peroxide ion \( \text{O}_2^{2-} \). Add two electrons to the antibonding orbitals of \( \text{O}_2 \) and recalculate the bond order.
Step 4: Calculate the bond order for the superoxide ion \( \text{O}_2^- \). Add one electron to the antibonding orbitals of \( \text{O}_2 \) and recalculate the bond order.
Step 5: Compare the bond orders to predict the bond lengths and strengths. Higher bond order generally means shorter bond length and stronger bond. Arrange \( \text{O}_2 \), \( \text{O}_2^{2-} \), and \( \text{O}_2^- \) in order of bond length and strength based on their bond orders.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Molecular Orbital Theory
Molecular Orbital Theory describes how atomic orbitals combine to form molecular orbitals, which can be occupied by electrons. In this theory, electrons are delocalized over the entire molecule, and the bond order can be calculated as the difference between the number of bonding and antibonding electrons divided by two. This concept is crucial for understanding the stability and properties of molecules like O2 and its ions.
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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. It is calculated using the formula: Bond Order = (Number of bonding electrons - Number of antibonding electrons) / 2. A higher bond order indicates a stronger bond and typically correlates with shorter bond lengths, making it essential for predicting the stability and reactivity of molecules and ions.
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Bond Length and Bond Strength
Bond length refers to the distance between the nuclei of two bonded atoms, while bond strength indicates the energy required to break that bond. Generally, shorter bonds are stronger due to the increased overlap of atomic orbitals. Understanding the relationship between bond order, bond length, and bond strength is vital for predicting the physical properties of molecules like O2, O2−, and O22−.
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Related Practice
Textbook Question
Indicate whether each statement is true or false. c. Antibonding orbitals are higher in energy than bonding orbitals (if all orbitals are created from the same atomic orbitals).
Textbook Question
Indicate whether each statement is true or false. (d) Electrons cannot occupy a nonbonding orbital.
Textbook Question
Determine whether each of the following statements about diamagnetism and paramagnetism is true or false:
a. A diamagnetic substance is weakly repelled from a magnetic field.
b. A substance with unpaired electrons will be diamagnetic.
c. A paramagnetic substance is attracted to a magnetic field.
d. The O2 molecule is paramagnetic.
Textbook Question
a. Which of the following is expected to be paramagnetic: Ne, Li2, Li2+, N2, N2+, N22−? b. For each of the substances in part (a) that is paramagnetic, determine the number of unpaired electrons it has.
Textbook Question
Using Figures 9.39 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.