Using the molecular orbital model, write electron...

Using the molecular orbital model, write electron configurations for the following diatomic species and calculate the bond orders. Which ones are paramagnetic? Place the species in order of increasing bond length and bond energy. $$ \text {a} \mathrm{CN}^{+} \quad \text { b. CN } \quad \text { c. } \mathrm{CN}^{-} $$

Using the molecular orbital model, write electron configurations for the following diatomic species and calculate the bond orders. Which ones are paramagnetic? Place the species in order of increasing bond length and bond energy.
$$
\text {a} \mathrm{CN}^{+} \quad \text { b. CN } \quad \text { c. } \mathrm{CN}^{-}
$$

Key Concepts

Molecular Orbital Theory

Molecular Orbital Theory describes how atomic orbitals combine to form molecular orbitals that are spread out over the entire molecule. This theory allows us to explain the bonding, antibonding, and nonbonding interactions between atoms in a molecule, providing a framework to understand electron distribution, bond order, and magnetic properties.

Electron Configuration in Molecular Orbitals

In the context of diatomic molecules, electron configuration is achieved by filling the molecular orbitals with electrons according to their energies using the Aufbau principle. This involves organizing electrons in sigma and pi bonding orbitals, as well as their corresponding antibonding orbitals, and is critical for determining the overall bond order and magnetic behavior of the molecule.

Bond Order

Bond order is a measure of the strength and stability of a chemical bond, calculated as half the difference between the total number of electrons in bonding orbitals and those in antibonding orbitals. A higher bond order generally indicates a stronger, shorter bond with greater bond energy, while a lower bond order suggests a weaker and longer bond.

Paramagnetism

Paramagnetism arises in molecules that have unpaired electrons in their molecular orbitals. The presence of these unpaired electrons causes the molecule to be attracted to an external magnetic field. In the context of molecular orbital theory, assessing the electron configuration helps identify whether any unpaired electrons exist, determining the paramagnetic or diamagnetic nature of the species.

Relationship between Bond Order, Bond Length, and Bond Energy

There exists a direct relationship between bond order, bond length, and bond energy: generally, a higher bond order correlates with a shorter bond length and a higher bond energy, which indicates a stronger bond. Conversely, a lower bond order usually leads to a longer bond length and lower bond energy, reflecting a weaker bond.

Transcript

00:03 In this problem we have three species, cn plus, cn and cn minus.

00:12 The number of balanced electrons in each case is what we will start our problem with.

00:20 So here it's 9, 4 from carbon and 5 from nitrogen.

00:25 Here we lose an electron so it's 8 and here we gain another electron so it's 10 electrons.

00:32 Let's fill this up in.

00:34 Our electronic configuration.

00:38 Sigma 2s 2, sigma star 2s 2, pi 2px equals pi 2, 2pi 2p.

00:48 So this accounts for all the electrons, all the 8 electrons we have.

00:54 Now for cn 2px equals 2pi.

01:02 There's one more electron so it fills up the 2p z.

01:07 So we have one electron here and in this case we have another electron so in cn your sigma 2p z was partially filled and in this case it'll be completely filled so the bond order is number of bonding electrons minus anti -bonding electrons so 1 2 3 4 5 6 6 minus 2 is 4 divided by 2 2 this case 1 2 3 4 5 6 7 to 7 minus 2 is 5 so it will be 2 .5 and in the last case 1 2 4 5 6 7 8 8 minus 2 is 6 divided by 2 will be 3 so the bond order is inversely proportional to the bond length because the higher the bond order, it means that there are more bonds that are holding these two atoms together, are bonding these two atoms together.

02:33 So they will be held closer together.

02:38 And so the bond length obviously will decrease...

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