Question

If we assume that the energy-level diagrams for homonuclear diatomic molecules shown in Figure $9.43$ can be applied to heteronuclear diatomic molecules and ions, predict the bond order and magnetic behavior of (a) ${\mathrm{CO}}^{+}$, (b) ${\mathrm{NO}}^{-}$, (c) ${\mathrm{OF}}^{+}$, (d) ${\mathrm{NeF}}^{+}$.

Short answer

(a) CO+: Bond order = 1.5, Paramagnetic (b) NO-: Bond order = 2, Paramagnetic (c) OF+: Bond order = 2, Paramagnetic (d) NeF+: Bond order = 2, Diamagnetic

Step-by-step solution

Determine the total number of valence electrons

For each diatomic molecule or ion, add the number of valence electrons from each atom and modify the total according to the charge on the ion: (a) CO+: (C has 4 valence electrons + O has 6 valence electrons) - 1 (for +1 charge) = 9 valence electrons (b) NO-: (N has 5 valence electrons + O has 6 valence electrons) + 1 (for -1 charge) = 12 valence electrons (c) OF+: (O has 6 valence electrons + F has 7 valence electrons) - 1 (for +1 charge) = 12 valence electrons (d) NeF+: (Ne has 8 valence electrons + F has 7 valence electrons) - 1 (for +1 charge) = 14 valence electrons

Fill the molecular orbitals using the energy-level diagram

For each diatomic molecule or ion, fill the molecular orbitals according to the energy-level diagram, starting with the lowest energy level and applying the Pauli Exclusion Principle (each orbital can hold up to 2 electrons with opposite spins) and Hund's Rule (when filling degenerate orbitals, fill them singly before pairing electrons). The order for filling orbitals is: σ1s, σ*1s, σ2s, σ*2s, π2px=π2py, σ2pz, π*2px=π*2py, σ*2pz. (a) CO+: 9 valence electrons (σ1s)^2(σ*1s)^2(σ2s)^2(σ*2s)^2(π2px)^1 (b) NO-: 12 valence electrons (σ1s)^2(σ*1s)^2(σ2s)^2(σ*2s)^2(π2px )^2(π2py )^2(σ2pz)^1 (c) OF+: 12 valence electrons (σ1s)^2(σ*1s)^2(σ2s)^2(σ*2s)^2(π2px )^2(π2py )^2(σ2pz)^1 (d) NeF+: 14 valence electrons (σ1s)^2(σ*1s)^2(σ2s)^2(σ*2s)^2(π2px)^2(π2py)^2(σ2pz)^2(π*2px )^1(π*2py )^1

Determine the bond order

For each diatomic molecule or ion, calculate the bond order using the formula: Bond order = (Number of electrons in bonding orbitals - Number of electrons in antibonding orbitals) / 2 (a) CO+: (6 - 3) / 2 = 1.5 (b) NO-: (8 - 4) / 2 = 2 (c) OF+: (8 - 4) / 2 = 2 (d) NeF+: (10 - 6) / 2 = 2

Determine the magnetic behavior

For each diatomic molecule or ion, decide if it is diamagnetic or paramagnetic: - Diamagnetic: All electrons are paired - Paramagnetic: There are unpaired electrons (a) CO+: Paramagnetic (1 unpaired electron in π2px) (b) NO-: Paramagnetic (1 unpaired electron in σ2pz) (c) OF+: Paramagnetic (1 unpaired electron in σ2pz) (d) NeF+: Diamagnetic (no unpaired electrons)

Final Answer

(a) CO+: Bond order = 1.5, Paramagnetic (b) NO-: Bond order = 2, Paramagnetic (c) OF+: Bond order = 2, Paramagnetic (d) NeF+: Bond order = 2, Diamagnetic

Key concepts

Bond Order

Bond order is a concept used to determine the stability and strength of a chemical bond within a molecule. It is calculated using the formula: $$\text{Bond order}=\frac{(N_b-N_a)}{2}$$where $N_b$ is the number of electrons in bonding orbitals, and $N_a$ is the number of electrons in antibonding orbitals.

• A higher bond order usually indicates a stronger and more stable bond.
• A bond order of zero often means no bond will form between the atoms in a molecule.

For heteronuclear diatomic molecules like CO⁺ and NO^-, you can visualize the bond order by using their energy-level diagrams.
Here's an example for CO⁺ with 9 valence electrons: Using the filling order, we obtain:

• Bonding electrons = 6
• Antibonding electrons = 3
• Bond order = $(6-3)/2=1.5$

This calculation shows that CO⁺ has a bond order of 1.5, indicating a relatively stable bond, but not as strong as a double bond.
Understanding bond order helps in predicting the molecule's behavior during chemical reactions.

Magnetic Behavior

Magnetic behavior of molecules is determined by the arrangement and number of unpaired electrons in their molecular orbitals.

• Diamagnetic: All electrons are paired in their orbitals. This means the molecule is not attracted to a magnetic field.
• Paramagnetic: The presence of one or more unpaired electrons causes the molecule to be attracted to a magnetic field.

To determine the magnetic behavior, fill in the molecular orbitals and check for any unpaired electrons.
Let's take NO^- as an example:

• It has 12 valence electrons.
• The orbital filling results in one unpaired electron in the $\sigma 2p_z$ orbital.
• This results in a paramagnetic behavior.

In contrast, NeF⁺ has 14 valence electrons, with all electrons paired. Therefore, it is diamagnetic.
Determining magnetic behavior is crucial for understanding the physical properties of the molecule.

Valence Electrons

Valence electrons are the outermost electrons of an atom and are crucial in determining how atoms interact during chemical reactions.
In the context of molecular orbital theory, we need to account for these electrons to understand the molecule's electronic structure.

• For ions like CO⁺, we adjust the total valence electrons by considering the charge ( 10 - 1 = 9).
• This ensures that the energy-level diagram reflects the accurate distribution of electrons in molecular orbitals.

Each atom contributes its valence electrons:

• Oxygen typically brings 6, while nitrogen provides 5.
• For NO^-, account for the extra electron from the negative charge, giving a total of 12 valence electrons.

Understanding valence electrons is the first step in building the molecular orbital diagram, which further helps to predict both bond order and magnetic behavior.
Through these calculations, students can grasp how fundamental electron configurations influence molecular properties.