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Ch.9 - Molecular Geometry and Bonding Theories
All textbooksBrown 14th EditionCh.9 - Molecular Geometry and Bonding TheoriesProblem 104
Chapter 9, Problem 104

The highest occupied molecular orbital of a molecule is abbreviated as the HOMO. The lowest unoccupied molecular orbital in a molecule is called the LUMO. Experimentally, one can measure the difference in energy between the HOMO and LUMO by taking the electronic absorption (UV-visible) spectrum of the molecule. Peaks in the electronic absorption spectrum can be labeled as π→π*, σ→σ*, and so on, corresponding to electrons being promoted from one orbital to another. The HOMO-LUMO transition corresponds to molecules going from their ground state to their first excited state. (a) Write out the molecular orbital valence electron configurations for the ground state and first excited state for N₂. (b) Is N₂ paramagnetic or diamagnetic in its first excited state? (d) Calculate the energy of the HOMO-LUMO transition in part (a) in terms of kJ/mol. (e) Is the N≡N bond in the first excited state stronger or weaker compared to that in the ground state?

Verified step by step guidance
1
Step 1: Determine the molecular orbital configuration for N₂ in its ground state. N₂ has 14 electrons. The molecular orbitals are filled in the order: σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², π(2p)⁴, σ(2p)². This configuration corresponds to the ground state.
Step 2: Identify the molecular orbital configuration for N₂ in its first excited state. In the first excited state, an electron is promoted from the HOMO to the LUMO. For N₂, the HOMO is the σ(2p) orbital and the LUMO is the π*(2p) orbital. Thus, the configuration becomes: σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², π(2p)⁴, σ(2p)¹, π*(2p)¹.
Step 3: Determine if N₂ is paramagnetic or diamagnetic in its first excited state. Paramagnetism occurs when there are unpaired electrons. In the first excited state, N₂ has one unpaired electron in the π*(2p) orbital, making it paramagnetic.
Step 4: Calculate the energy of the HOMO-LUMO transition. The energy difference between the HOMO and LUMO can be determined from the UV-visible spectrum. Use the formula: E = hν = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength of the transition. Convert the energy from joules to kJ/mol using Avogadro's number.
Step 5: Compare the bond strength in the first excited state to the ground state. The bond order is related to the number of bonding and antibonding electrons. In the ground state, N₂ has a bond order of 3. In the first excited state, the bond order decreases due to the promotion of an electron to an antibonding orbital, making the bond weaker.

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 rather than being confined to individual atoms. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are crucial for understanding a molecule's electronic properties and reactivity, particularly in transitions that involve electron promotion.
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Electronic Absorption Spectroscopy

Electronic absorption spectroscopy, particularly UV-visible spectroscopy, is a technique used to measure the energy differences between electronic states in a molecule. When a molecule absorbs light, electrons can be promoted from the HOMO to the LUMO, resulting in characteristic peaks in the absorption spectrum. The wavelengths at which these transitions occur provide insight into the energy levels of the molecular orbitals and the electronic structure of the molecule.
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Paramagnetism and Diamagnetism

Paramagnetism and diamagnetism are terms used to describe the magnetic properties of substances based on their electron configurations. Paramagnetic substances have unpaired electrons, which align with external magnetic fields, while diamagnetic substances have all paired electrons and are weakly repelled by magnetic fields. The magnetic behavior of a molecule in its excited state can be determined by examining the occupancy of its molecular orbitals, particularly the HOMO and LUMO.
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Related Practice
Textbook Question

The structure of borazine, B3N3H6, is a six-membered ring of alternating B and N atoms. There is one H atom bonded to each B and to each N atom. The molecule is planar. (a) Write a Lewis structure for borazine in which the formal charge on every atom is zero.

Textbook Question

The structure of borazine, B3N3H6, is a six-membered ring of alternating B and N atoms. There is one H atom bonded to each B and to each N atom. The molecule is planar. (c) What are the formal charges on the atoms in the Lewis structure from part (b)? Given the electronegativities of B and N, do the formal charges seem favorable or unfavorable? What are the formal charges on the atoms in the Lewis structure from part (b)?

Textbook Question

The structure of borazine, B3N3H6, is a six-membered ring of alternating B and N atoms. There is one H atom bonded to each B and to each N atom. The molecule is planar. (e) What are the hybridizations at the B and N atoms in the Lewis structures from parts (a) and (b)? Would you expect the molecule to be planar for both Lewis structures? Would you expect the molecule to be planar for both Lewis structures?

Textbook Question

The highest occupied molecular orbital of a molecule is abbreviated as the HOMO. The lowest unoccupied molecular orbital in a molecule is called the LUMO. Experimentally, one can measure the difference in energy between the HOMO and LUMO by taking the electronic absorption (UV-visible) spectrum of the molecule. Peaks in the electronic absorption spectrum can be labeled as π2p-π2p*, σs-σ2s*, and so on, corresponding to electrons being promoted from one orbital to another. The HOMO-LUMO transition corresponds to molecules going from their ground state to their first excited state. (c) The electronic absorption spectrum of the N2 molecule has the lowest energy peak at 170 nm. To what orbital transition does this correspond?

Textbook Question

One of the molecular orbitals of the H2- ion is sketched below:

(a) Is the molecular orbital a s or p MO? Is it bonding or antibonding?

Textbook Question

One of the molecular orbitals of the H2- ion is sketched below: (d) Compared to the H¬H bond in H2, the H¬H bond in H2- is expected to be which of the following: (i) Shorter and stronger, (ii) longer and stronger, (iii) shorter and weaker, (iv) longer and weaker, or (v) the same length and strength?