Question

Order the following species with respect to carbon-oxygen bond length (longest to shortest). $$ \mathrm{CO}, \quad \mathrm{CO}_{2}, \quad \mathrm{CO}_{3}{ }^{2-}, \quad \mathrm{CH}_{3} \mathrm{OH} $$ What is the order from the weakest to the strongest carbonoxygen bond? \(\left(\mathrm{CH}_{3} \mathrm{OH}\right.\) exists as \(\mathrm{H}_{3} \mathrm{C}-\mathrm{OH}\).)

Short answer

The order of the given species from the longest to the shortest carbon-oxygen bond length is: \[ CO_{3}^{2-}, \quad CH_{3}OH, \quad CO_{2}, \quad CO \] And the order from the weakest to the strongest carbon-oxygen bond is: \[ CO_{3}^{2-}, \quad CH_{3}OH, \quad CO_{2}, \quad CO \]

Step-by-step solution

Identifying bond types and resonance structures

First, we will identify the type of bond (single, double, or triple) between carbon and oxygen in each species and determine if any resonance structures exist. Here is the list of species with their respective bond types and resonance structures (if applicable): 1. CO: Triple bond (C≡O), no resonance 2. CO₂: Double bond (O=C=O), no resonance 3. CO₃²⁻: Resonance structure with an average of 1.33 bond order, single and double bonds (O-C=O / O-C-O⁻ / O=C-O⁻) 4. CH₃OH: Single bond (C-O), no resonance

Comparing bond lengths

Now we will compare the bond lengths based on the number of bonds and the presence of resonance structures. We know that as the bond order increases, the bond length decreases. Using this information, we can arrange the species in order from longest to shortest C-O bond length: 1. CO₃²⁻ (1.33 bond order, resonance with single and double bonds) 2. CH₃OH (single bond) 3. CO₂ (double bond) 4. CO (triple bond)

Comparing bond strengths

As mentioned earlier, bond strength increases as the bond order increases. Therefore, we can arrange the species from weakest to the strongest C-O bond using the information from the previous step: 1. CO₃²⁻ (1.33 bond order with resonance) 2. CH₃OH (single bond) 3. CO₂ (double bond) 4. CO (triple bond) The final order for the bond lengths (longest to shortest) is: \[ CO_{3}^{2-}, \quad CH_{3}OH, \quad CO_{2}, \quad CO \] And the order for bond strengths (weakest to strongest) is also: \[ CO_{3}^{2-}, \quad CH_{3}OH, \quad CO_{2}, \quad CO \]

Key concepts

Chemical Bonding

Chemical bonding is the force that holds atoms together in molecules. At its core, it involves the sharing or transfer of electrons between atoms. There are primarily three types of chemical bonds - ionic, covalent, and metallic. Covalent bonds occur when atoms share one or more pairs of electrons, and they can be single, double, or triple bonds depending on how many electron pairs are shared. The strength and length of these bonds are directly affected by the number of shared electrons.

For instance, a single bond involves one pair of shared electrons and is generally longer and weaker than double and triple bonds, which involve two and three pairs of shared electrons, respectively. In molecules like carbon monoxide (CO), a triple bond creates a very strong and short connection between carbon and oxygen, while in methane (CH₃OH), the single bond is longer and weaker. This fundamental concept is essential in understanding the molecular stability, reactivity, and physical properties of substances.

Molecular Geometry

Molecular geometry, also known as molecular structure, refers to the three-dimensional arrangement of atoms within a molecule. It plays a crucial role in defining the physical and chemical properties of a compound, including bond lengths and angles, which ultimately affect the overall stability of a molecule. VSEPR (Valence Shell Electron Pair Repulsion) theory is a model used to predict the shape of individual molecules based on the repulsion of electron pairs around a central atom.

The geometry around a carbon atom bonded to oxygen can vary from linear, as seen in carbon dioxide (CO₂), to bent or angular, as observed in the carbonate ion (CO₃²⁻). These differences in spatial arrangement contribute to the variance in bond lengths and bond strengths, with linear molecules generally featuring shorter and stronger bonds than those with bent configurations. Understanding molecular geometry is key for comprehending the differences in physical attributes and chemical behaviors between different molecules.

Resonance Structures

Resonance structures are a representation of molecules where the bonding cannot be correctly described by a single Lewis structure. These structures are used to depict delocalized electrons within certain molecules that can occupy different positions. When resonance is present, as in the carbonate ion (CO₃²⁻), it indicates that the actual structure is an average of the individual resonance structures.

The concept of resonance suggests that the electron distribution is more stable when it is delocalized over several bonds or atoms. This has a direct impact on bond lengths and strengths; for molecules with resonance, bond lengths are often intermediate between those typical for single and double bonds. Consequently, the bond strength is also affected, resulting in a structure that is stronger than a single bond but not quite as strong as a double bond. The ability to draw and understand resonance structures is an invaluable skill for predicting molecule behavior and bonding characteristics in chemical reactions.