Question

In each pair of bonds, predict which is shorter. (a) \(\mathrm{B}-\mathrm{Cl}\) or \(\mathrm{Ga}-\mathrm{Cl}\) (b) \(\mathrm{Sn}-\mathrm{O}\) or \(\mathrm{C}-\mathrm{O}\) (c) \(\mathrm{P}-\mathrm{S}\) or \(\mathrm{P}-\mathrm{O}\) (d) \(\mathrm{C}=\mathrm{O}\) or \(\mathrm{C}=\mathrm{N}\)

Short answer

(a) B-Cl is shorter, (b) C-O is shorter, (c) P-O is shorter, (d) C=O is shorter.

Step-by-step solution

Analyze Atomic Size

Compare the atomic sizes of the central atoms in each pair of bonds because smaller atoms generally form shorter bonds. For (a), B is smaller than Ga. For (b), C is smaller than Sn. For (c), O is smaller than S.

Consider Bond Order

Higher bond orders typically lead to shorter bonds due to increased electron sharing. For (d), C=O and C=N both have a double bond, so this factor may not significantly differentiate them directly.

Compare Bond Length Trends

For (a), the smaller size of B compared to Ga suggests that B-Cl will be shorter than Ga-Cl. For (b), C-O, involving smaller C compared to Sn, will be shorter than Sn-O. For (c), due to O being smaller and having stronger bonds generally, P-O is likely shorter than P-S. In (d), due to oxygen's higher electronegativity, C=O is typically shorter than C=N.

Key concepts

Atomic Size

Atomic size refers to the dimensions of an atom, usually measured by the atomic radius. It plays a crucial role in determining bond length, which is the distance between the centers of two bonded atoms. Atoms with smaller atomic sizes tend to form shorter bonds because their nuclei are closer together, allowing the shared electrons to exert a stronger binding force.

For instance:

• Boron (B) is smaller than Gallium (Ga), which means a boron-chlorine (B-Cl) bond is shorter than a gallium-chlorine (Ga-Cl) bond.
• Carbon (C) has a smaller atomic size compared to Tin (Sn), hence a carbon-oxygen (C-O) bond is shorter than a tin-oxygen (Sn-O) bond.
• Similarly, Oxygen (O) is smaller than Sulfur (S), so phosphorus-oxygen (P-O) bonds are shorter than phosphorus-sulfur (P-S) bonds.

By understanding atomic size, you can intuitively predict which bonds will generally be shorter.

Bond Order

Bond Order describes the number of chemical bonds between a pair of atoms. It provides insight into the stability and length of a bond. Higher bond orders indicate more shared electron pairs, thus stronger and typically shorter bonds.

Consider this:

• Single bonds (bond order 1) are generally longer than double bonds (bond order 2) and triple bonds (bond order 3). This is due to the fact that more shared electrons bring the atoms closer together.
• In the example of C=O and C=N from the exercise, both bonds are double bonds, implying that only bond order wouldn't distinguish their lengths significantly unless considering other factors like electronegativity.

By connecting bond order to bond length, you gain a better grasp of bond strength and structural predictions.

Electronegativity

Electronegativity refers to an atom's ability to attract and hold electrons within a chemical bond. It can affect bond length indirectly, especially when comparing bonds of the same order, such as those between carbon-oxygen (C=O) and carbon-nitrogen (C=N).

Points to note:

• Oxygen is more electronegative than nitrogen. This means it attracts electrons more strongly, creating a tighter bond. As a result, a C=O bond is usually shorter than a C=N bond.
• Higher electronegativity can lead to shorter bond lengths because the highly electronegative atom pulls shared electrons closer.

This concept helps predict and explain bond length differences in molecules with similar bond structures.

Chemical Bonding

Chemical bonding refers to the lasting attraction between atoms that enables the formation of chemical compounds. Bonds can be ionic, covalent, or metallic, but in the context of bond length, we focus on covalent bonds, where electrons are shared between atoms.

Covalent bond length depends on:

• Atomic Size: Smaller atoms form shorter covalent bonds due to closer nuclei.
• Bond Order: More bonds (higher bond order) mean shorter distances between bonded atoms as they share more electrons.
• Electronegativity: Bonds with highly electronegative atoms can have shorter distances due to tighter electron attractions.

Grasping these aspects of chemical bonding is key to understanding why different bonds have different lengths. It allows us to predict molecular structures and their properties accurately.