Problem 44 - Chemistry and Chemical Reactivity

Question

Give the bond order for each bond in the following molecules or ions: (a) \(\mathrm{CN}^{-}\) (b) \(\mathrm{CH}_{3} \mathrm{CN}\) (c) \(\mathrm{SO}_{3}\) (d) \(\mathrm{CH}_{3} \mathrm{CH}=\mathrm{CH}_{2}\)

Step-by-Step Solution

Answer

(a) 3, (b) C≡N is 3, C–C is 1, (c) 1.33, (d) C=C is 2, C–C is 1.

Step 1: Understanding Bond Order

Bond order is the number of chemical bonds between a pair of atoms. Higher bond order indicates a stronger, shorter bond. It can be determined from a molecule's molecular orbital diagram or resonance structures.

Step 2: Determine Bond Order for CN⁻

The cyanide ion (\(\mathrm{CN}^-\)) has a triple bond between carbon and nitrogen. Its bond order is 3 because triple bonds consist of three shared pairs of electrons.

Step 3: Determine Bond Order for CH₃CN

In acetonitrile (\(\mathrm{CH}_3\mathrm{CN}\)), the C≡N bond is a triple bond with a bond order of 3. The C–C bond to the methyl group is a single bond with a bond order of 1.

Step 4: Determine Bond Order for SO₃

In sulfate (\(\mathrm{SO}_3\)), each sulfur-oxygen bond can be represented as 1.33 using resonance theory. It is derived from three resonance structures where one S=O double bond is rotated among the three oxygen atoms.

Step 5: Determine Bond Order for CH₃CH=CH₂

In propene (\(\mathrm{CH}_3\mathrm{CH}=\mathrm{CH}_2\)), the C=C bond has a bond order of 2 because it is a double bond, while each C–C bond in the chains is a single bond with a bond order of 1.

Key Concepts

Molecular Orbital Theory

Molecular orbital theory offers a way to understand how atoms form chemical bonds by combining atomic orbitals to create molecular orbitals. This theory is crucial when determining bond order, which reflects the strength and stability of a bond.
Bond order is calculated using the formula:\[ \text{Bond Order} = \frac{(\text{Number of bonding electrons}) - (\text{Number of antibonding electrons})}{2} \]
In molecular orbital theory:

• Bonding orbitals: Lower energy orbitals that are more stable and help hold atoms together.
• Antibonding orbitals: Higher energy orbitals that are less stable and, if occupied, weaken the bond.

This theory can precisely depict

• the bonding and antibonding interactions,
• resulting in a detailed picture of the electron arrangement in a molecule.

Through these interactions, students can accurately determine bond order, aiding in the prediction of molecular properties like bond length and bond strength.

Resonance Structures

Resonance structures provide another perspective on how molecules achieve stability. They are different ways to draw the arrangement of electrons in a molecule that cannot be represented by a single structural formula alone.
These structures are particularly important when the bonding in a molecule cannot be adequately described by one Lewis structure.

• In molecules with resonance, electrons are delocalized over several atoms.
• This delocalization increases stability, as seen in molecules like sulfate (\( \text{SO}_3 \)), where resonance creates equivalent bond orders.
• Instead of distinct bonds, resonance portrays partial bonds with averaged bond orders.

When determining bond order using resonance:

• Each bond's electrons in all resonant forms are averaged.
• For example, in sulfate, bonds often exhibit a fractional bond order.

This highlights the resonance effect in distributing electrons and increasing molecular stability.

Chemical Bonds

Chemical bonds are the attractive forces holding atoms together in molecules. Three primary types of chemical bonds are ionic, covalent, and metallic bonds.
Our focus here mainly revolves around covalent bonds, where atoms share pairs of electrons:

• Single Bonds: Consist of one shared pair of electrons, having a bond order of 1.
• Double Bonds: Involve two shared pairs, resulting in a bond order of 2.
• Triple Bonds: Involve three shared pairs, giving a bond order of 3.

A higher bond order indicates a stronger, shorter bond. Short bonds tend to be stronger and hold more energy, which means they are harder to break. The balance of these electron-sharing interactions defines how the molecule forms and its reactive nature. Different bond types and strengths can determine the physical properties of substances, such as hardness, electrical conductivity, and melting point.

Triple Bond

Triple bonds are a specific form of covalent bond where three electron pairs are shared between two atoms, resulting in a bond order of 3.
Characteristics of Triple Bonds:

• Strong and Short: Because of the three electron pairs, these bonds hold a very high level of stability and strength.
• Commonly found: In molecules like cyanide (\( \text{CN}^- \)) and acetonitrile (\( \text{CH}_3\text{CN} \)) where the carbon-nitrogen bond is a triple bond.
• Bond Length: These are the shortest among single, double, and triple bonds.
• Electron Sharing: Triple bonds involve extensive sharing, sometimes leading to unique chemical properties.

Triple bonds are densest in terms of electron presence between bonded atoms. They contribute significantly to the strength and reactivity of substances, making understanding them vital in both organic and inorganic chemistry.