Using your knowledge of Lewis structures, predict which of the following molecules or ions of the set will have the longest indicated bond length: (a) the \(\mathrm{C}-\mathrm{O}\) bond in \(\mathrm{CO}, \mathrm{CO}_{2}\), or \(\mathrm{CO}_{3}{ }^{2}\); (b) the \(\mathrm{S}-\mathrm{O}\) bond in \(\mathrm{SO}_{2}, \mathrm{SO}_{3}\), or \(\mathrm{SO}_{3}^{2}\); (c) the \(\mathrm{C}-\mathrm{N}\) bond in \(\mathrm{HCN}\), \(\mathrm{CH}_{2} \mathrm{NH}\), or \(\mathrm{CH}_{3} \mathrm{NH}_{2}\).

Chemical bond order is a fundamental concept in chemistry that provides insight into the strength and stability of a bond between two atoms. In simple terms, the bond order indicates the number of chemical bonds that connect a pair of atoms. For instance, a single bond has a bond order of 1, a double bond has a bond order of 2, and a triple bond has a bond order of 3.

A higher bond order typically means that the bond is stronger and shorter. For example, a carbon-oxygen triple bond, as in carbon monoxide (CO), is stronger and considerably shorter than a carbon-oxygen double bond in carbon dioxide (CO2), or a single bond as found in carbonate ion (CO3 2-).

In the context of textbook exercises, understanding bond order is critical for predicting properties like bond length. It's important to remember that as the bond order increases, the bond length tends to decrease. This is because the increased number of shared electrons pulls the atoms closer together.

Resonance is a phenomenon that occurs in molecules where the bonding cannot be represented by a single Lewis structure. Molecules or ions exhibit resonance when there are multiple valid Lewis structures, known as resonance forms, that can depict the molecule. These forms differ only in the positions of the electrons, not the positions of the atoms.

The true structure of a resonant molecule is a hybrid of these forms and represents an average of them. A classic example is the carbonate ion (CO3 2-), which has three resonance forms with one double bond and two single bonds, each being equally valid representations. Thus, the actual structure of the carbonate ion is a hybrid with a bond order between 1 and 2 for the carbon-oxygen bonds.

This average effect of resonance often complicates bond length prediction, as it affects the bond order. Since resonance structures distribute the electrons among multiple positions, the overall bond length of a resonant molecule will be an average of the different forms — typically longer than a bond with a higher bond order but shorter than a single bond.

Molecular geometry plays a significant role in determining the bond lengths within a molecule. The spatial arrangement of atoms around a central atom can influence how far apart the surrounding atoms reside from each other. For instance, in a molecule with a linear geometry like carbon dioxide (CO2), the oxygen atoms are further apart from each other compared to a trigonal planar molecule like sulfur trioxide (SO3), which compresses the bonds slightly due to the angular constraints. Likewise, a bent shaped molecule such as water (H2O) has a significantly different bond length compared to a linear molecule like hydrogen peroxide (H2O2), despite both having oxygen-hydrogen bonds.

To assess bond length, it's not only essential to consider bond order but also how the bond angles affect the overall molecular geometry. When comparing molecules with similar connectivities, those with more compact geometries generally have shorter bonds overall, due to the push towards minimizing repulsion between the bonding electron pairs and lone pairs if present.