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Chapter 9: Problem 80

Describe the bonding in the first excited state of \(\mathrm{N}_{2}\) (the one closest in energy to the ground state) using the molecular orbital model. What differences do you expect in the properties of the molecule in the ground state as compared to the first excited state? (An excited state of a molecule corresponds to an electron arrangement other than that giving the lowest possible energy.)

Short Answer

Expert verified
In the first excited state of N₂, the electron configuration is (σ₁s)²(σ*₁s)²(σ₂s)²(σ*₂s)²(π₂p)³(σ*₂p)¹, with one electron moving from the π₂p orbital to the σ*₂p orbital. Consequently, the bond order reduces from 2 in the ground state to 1, indicating less stability in the N-N bond. In this excited state, the molecule would be more reactive, susceptible to reactions, and more likely to absorb energy from light or heat due to the higher energy orbitals occupied by the excited electrons.

Step by step solution

01

Molecular Orbitals in N₂

In N₂, both nitrogen atoms contribute a total of 10 valence electrons. The molecular orbitals involved in this case are: σ₁s, σ*₁s, σ₂s, σ*₂s, π₂p, π*₂p, σ₂p, and σ*₂p. These orbitals are in increasing order of energy levels. Using the aufbau principle, electrons will occupy the lower energy orbitals first, up to a total of 10 electrons.
02

Ground State Electron Configuration

In the ground state, N₂ has the electron configuration: (σ₁s)²(σ*₁s)²(σ₂s)²(σ*₂s)²(π₂p)⁴. In this configuration, there are 8 electrons in bonding orbitals (σ₁s, σ₂s, π₂p) and 4 electrons in antibonding orbitals (σ*₁s, σ*₂s). The bond order of N₂ in the ground state is (8-4)/2 = 2.
03

First Excited State Electron Configuration

In the first excited state, one of the electrons in the highest occupied molecular orbital (HOMO), which is π₂p, moves to the lowest unoccupied molecular orbital (LUMO), which is σ*₂p. The new electron configuration in the first excited state would be: (σ₁s)²(σ*₁s)²(σ₂s)²(σ*₂s)²(π₂p)³(σ*₂p)¹.
04

Bond Order in the First Excited State

In this excited state configuration, there are now 7 electrons in bonding orbitals (σ₁s, σ₂s, π₂p) and 5 electrons in antibonding orbitals (σ*₁s, σ*₂s, σ*₂p). The bond order of N₂ in the first excited state is (7-5)/2 = 1.
05

Comparison of Ground State vs. Excited State Properties

In the ground state, N₂ has a bond order of 2 and is a very stable molecule. In the first excited state, the bond order is reduced to 1, which means that the stability of the N-N bond is decreased. In addition, as the excited state has a higher energy than the ground state, the molecule will be more reactive, and its chemical properties might change, making the molecule more susceptible to displacement or addition reactions. Finally, since the excited electrons are in higher energy orbitals, they are more likely to participate in chemical reactions or absorb energy from light or heat.

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