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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 N鈧�, the electron configuration is (蟽鈧乻)虏(蟽*鈧乻)虏(蟽鈧俿)虏(蟽*鈧俿)虏(蟺鈧俻)鲁(蟽*鈧俻)鹿, with one electron moving from the 蟺鈧俻 orbital to the 蟽*鈧俻 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 N鈧�

In N鈧�, both nitrogen atoms contribute a total of 10 valence electrons. The molecular orbitals involved in this case are: 蟽鈧乻, 蟽*鈧乻, 蟽鈧俿, 蟽*鈧俿, 蟺鈧俻, 蟺*鈧俻, 蟽鈧俻, and 蟽*鈧俻. 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, N鈧� has the electron configuration: (蟽鈧乻)虏(蟽*鈧乻)虏(蟽鈧俿)虏(蟽*鈧俿)虏(蟺鈧俻)鈦�. In this configuration, there are 8 electrons in bonding orbitals (蟽鈧乻, 蟽鈧俿, 蟺鈧俻) and 4 electrons in antibonding orbitals (蟽*鈧乻, 蟽*鈧俿). The bond order of N鈧� 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 蟺鈧俻, moves to the lowest unoccupied molecular orbital (LUMO), which is 蟽*鈧俻. The new electron configuration in the first excited state would be: (蟽鈧乻)虏(蟽*鈧乻)虏(蟽鈧俿)虏(蟽*鈧俿)虏(蟺鈧俻)鲁(蟽*鈧俻)鹿.
04

Bond Order in the First Excited State

In this excited state configuration, there are now 7 electrons in bonding orbitals (蟽鈧乻, 蟽鈧俿, 蟺鈧俻) and 5 electrons in antibonding orbitals (蟽*鈧乻, 蟽*鈧俿, 蟽*鈧俻). The bond order of N鈧� in the first excited state is (7-5)/2 = 1.
05

Comparison of Ground State vs. Excited State Properties

In the ground state, N鈧� 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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Most popular questions from this chapter

Which of the following statements concerning \(\mathrm{SO}_{2}\) is (are) true? a. The central sulfur atom is \(s p^{2}\) hybridized. b. One of the sulfur-oxygen bonds is longer than the other(s). c. The bond angles about the central sulfur atom are about \(120^{\circ} .\) d. There are two \(\sigma\) bonds in \(\mathrm{SO}_{2}\) . e. There are no resonance structures for SO.

Cyanamide \(\left(\mathrm{H}_{2} \mathrm{NCN}\right),\) an important industrial chemical, is produced by the following steps: $$ \begin{array}{c}{\mathrm{CaC}_{2}+\mathrm{N}_{2} \longrightarrow \mathrm{CaNCN}+\mathrm{C}} \\ {\mathrm{CaNCN} \stackrel{\mathrm{Acid}}{\longrightarrow} \mathrm{H}_{2} \mathrm{NCN}} \\\ {\mathrm{Cyanamide}}\end{array} $$ Calcium cyanamide (CaNCN) is used as a direct-application fertilizer, weed killer, and cotton defoliant. It is also used to make cyanamide, dicyandiamide, and melamine plastics: a. Write Lewis structures for \(\mathrm{NCN}^{2-}, \mathrm{H}_{2} \mathrm{NCN}\) , dicyandiamide, and melamine, including resonance structures where appropriate. b. Give the hybridization of the C and N atoms in each species. c. How many \(\sigma\) bonds and how many \(\pi\) bonds are in each species? d. Is the ring in melamine planar? e. There are three different \(C-N\) bond distances in dicyandiamide, \(\mathrm{NCNC}\left(\mathrm{NH}_{2}\right)_{2}\) , and the molecule is nonlinear. Of all the resonance structures you drew for this molecule, predict which should be the most important.

Use the localized electron model to describe the bonding in \(\mathrm{H}_{2} \mathrm{CO}(\text { carbon is the central atom })\)

Using an MO energy-level diagram, would you expect \(\mathrm{F}_{2}\) to have a lower or higher first ionization energy than atomic fluorine? Why?

The oxyanion of nitrogen in which it has the highest oxidation state is the nitrate ion \(\left(\mathrm{NO}_{3}^{-}\right) .\) The corresponding oxyanion of phosphorus is \(\mathrm{PO}_{4}^{3-}\) . The \(\mathrm{NO}_{4}^{3-}\) ion is known but is not very stable. The \(\mathrm{PO}_{3}-\) ion is not known. Account for these differences in terms of the bonding in the four anions.
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