Problem 67 - Chemical Principles: The Quest for Insight

Question

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 \(\mathrm{CO}_{3}{\underline{\phantom{xx}}}^{2}\); (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 \(\mathrm{CH}_{3} \mathrm{NH}_{2}\).

Step-by-Step Solution

Answer

The longest C-O bond is in CO3 2-, the longest S-O bond is in SO3 2-, and the longest C-N bond is in CH3NH2.

Step 1: Analyze the Lewis Structures for C-O bonds

Begin by drawing Lewis structures for CO, CO2, and CO3 2-. Determine the number of bonds between carbon and oxygen in each molecule: CO has a triple bond, CO2 has two double bonds, and CO3 2- has one double bond and two single bonds due to resonance. More bonds mean shorter bond lengths.

Step 2: Compare Bond Order for C-O bonds

Bond order refers to the number of chemical bonds between a pair of atoms. A higher bond order generally indicates shorter bond length. CO has the highest bond order (3), followed by CO2 (2), and CO3 2- has the lowest (between 1 and 2 due to resonance).

Step 3: Predict Longest C-O bond

Since bond length decreases with increasing bond order, CO3 2- with the lowest average bond order will have the longest C-O bond.

Step 4: Analyze the Lewis Structures for S-O bonds

Repeat the process for sulfur oxides: SO2 has two double bonds, SO3 has three double bonds, and SO3 2- has two double bonds and one single bond due to resonance.

Step 5: Compare Bond Order for S-O bonds

The bond order for SO2 and SO3 is 2 while for SO3 2- it varies between 1 and 2 due to resonance, indicating SO3 2- has the lowest average bond order.

Step 6: Predict Longest S-O bond

Therefore, SO3 2-, with its resonance structures, has the longest average S-O bond.

Step 7: Analyze the Lewis Structures for C-N bonds

Draw Lewis structures for HCN, CH2NH, and CH3NH2. HCN has a triple bond, CH2NH has a double bond, and CH3NH2 has a single bond between carbon and nitrogen.

Step 8: Compare Bond Order for C-N bonds

HCN has a bond order of 3, CH2NH has a bond order of 2, and CH3NH2 has a bond order of 1, denoting a triple, double, and single bond, respectively.

Step 9: Predict Longest C-N bond

Since single bonds are the longest, CH3NH2 will have the longest C-N bond.

Key Concepts

Chemical Bond Order

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 in Molecules

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 and Bond Length

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.