Problem 81 - Chemistry The Central Science In Si Units

Question

Determine the electron configurations for \(\mathrm{CN}^{+}, \mathrm{CN},\) and \(\mathrm{CN}^{-} .(\mathbf{a})\) Which species has the strongest \(\mathrm{C}-\mathrm{N}\) bond? (b) Which species, if any, has unpaired electrons?

Step-by-Step Solution

Answer

(a) CN⁺ has the strongest C-N bond. (b) CN has unpaired electrons.

Step 1: Determine the Total Electrons

First, find the total number of electrons for each species. The molecule CN is composed of carbon (C), which has 6 electrons, and nitrogen (N), which has 7 electrons. Therefore, the CN molecule has 13 electrons. For CN⁺, lose one electron to get 12 electrons, and for CN⁻, gain one electron to get 14 electrons.

Step 2: Determine Molecular Orbitals for CN

To determine the bonding and molecular orbitals, order the molecular orbitals for CN as: \[ 1σ^2, 1σ^{*2}, 2σ^2, 2σ^{*2}, (π2p_x)^2, (π2p_y)^2, 3σ^2 \] CN has a total of 13 electrons: \[ 1σ^2, 1σ^{*2}, 2σ^2, 2σ^{*2}, (π2p_x)^2, (π2p_y)^2, 3σ^1 \]

Step 3: Analyze CN⁺ (12 Electrons)

CN⁺ has one less electron than CN. Fill the molecular orbitals with 12 electrons: \[ 1σ^2, 1σ^{*2}, 2σ^2, 2σ^{*2}, (π2p_x)^2, (π2p_y)^2 \] All orbitals are filled with paired electrons.

Step 4: Analyze CN⁻ (14 Electrons)

CN⁻ has one more electron than CN. Fill the molecular orbitals with 14 electrons: \[ 1σ^2, 1σ^{*2}, 2σ^2, 2σ^{*2}, (π2p_x)^2, (π2p_y)^2, 3σ^2 \] All orbitals are filled with paired electrons.

Step 5: Determine Bond Strength

The bond strength often correlates with the bond order, calculated as: \\[ ext{Bond Order} = rac{ ext{(Number of electrons in bonding orbitals)} - ext{(Number of electrons in anti-bonding orbitals)}}{2} \] - CN⁺: Bond Order = 3- CN: Bond Order = 2.5- CN⁻: Bond Order = 2CN⁺ has the highest bond order, indicating the strongest C-N bond.

Step 6: Identify Unpaired Electrons

Identify unpaired electrons by checking each molecular orbital. - CN⁺: All paired - CN: One unpaired (3σ^1) - CN⁻: All paired Thus, CN has one unpaired electron.

Key Concepts

Molecular Orbitals

Molecular orbitals are special regions in a molecule where electrons reside. These orbitals are formed by the combination of atomic orbitals from bonded atoms. In a diatomic molecule like CN , orbital interactions can be categorized into bonding and anti-bonding types. Bonding orbitals are stabilizing and hold electrons that increase the strength of the bond, while anti-bonding orbitals tend to weaken the bond by decreasing stability.
Understanding the arrangement and filling of these molecular orbitals allows us to predict the molecule's properties, such as bond order and the presence of unpaired electrons. For the CN molecule and its ions, the molecular orbitals are filled in the sequence:

• 1σ, 1σ^*, 2σ, 2σ^*: These are the lower-energy orbitals that fill first and contribute to bond strength.
• π2p_x, π2p_y: These orbitals hold electrons involved in pi -bonding, commonly seen in multiple bonds such as double or triple bonds.
• 3σ: The highest energy orbital considered here, which may contain unpaired electrons in some species.

Bond Order

Bond order is a crucial concept in determining the strength of a bond between two atoms. It is derived from the number of electrons in bonding molecular orbitals instead of anti-bonding ones. The formula to calculate the bond order is:\[\text{Bond Order} = \frac{\text{(Number of electrons in bonding orbitals)} - \text{(Number of electrons in anti-bonding orbitals)}}{2}\]The bond order tells us how many chemical bonds exist between two atoms. A higher bond order generally indicates a stronger and more stable bond. In the case of CN, CN⁺, and CN^-:

• CN⁺ has a bond order of 3, showing it's the strongest with a triple bond.
• CN has a bond order of 2.5, indicating a bond strength between a double and a triple bond.
• CN^- has a bond order of 2, equivalent to a double bond and the weakest among the three species discussed.

Bond order is a valuable tool in predicting how likely a molecule is to react chemically.

Unpaired Electrons

Unpaired electrons are single electrons located in an atomic or molecular orbital. These electrons are significant because they impart unique chemical reactivity and magnetic properties to a molecule.
When examining CN species and its ions:

• CN has one unpaired electron. This unpaired electron resides in the 3σ orbital, making CN paramagnetic, which means it's slightly attracted to a magnetic field.
• Both CN⁺ and CN^- have all their electrons paired. These ions exhibit diamagnetic properties, meaning they are slightly repelled by a magnetic field.

The presence of unpaired electrons in a molecule can influence its chemical reactions. They often play crucial roles in reactions that involve reductions, oxidations, or radical formation.

Chemical Bonding

Chemical bonding involves the interaction of atomic orbitals to form molecular orbitals. This interaction is fundamental to the formation of molecules and how they stabilize.
In the context of CN, CN⁺ , and CN^-, the key type of chemical bonding is covalent bonding.
Covalent bonds occur when two atoms share electrons. In these species:

• The C-N bond lengthens or shortens based on the balance of electrons in bonding versus anti-bonding orbitals.
• The difference in bond orders among CN species indicates variations in the sharing of electrons between the carbon and nitrogen atoms.
• Electrons in bonding orbitals contribute to the covalent bond strength, while electrons in anti-bonding orbitals can weaken the interaction by decreasing overlap between atomic orbitals.

Understanding these concepts of chemical bonding helps explain the stability and reactivity differences between these similar molecules. This becomes especially relevant in practical applications like designing materials or predicting reaction pathways in chemistry.