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 from the weakest to the strongest carbon-oxygen bond is CH₃OH, CO₃²⁻, CO₂, and CO.

Step-by-step solution

Understand the molecular structures

We start by analyzing the structures of CO, CO₂, CO₃²⁻, and CH₃OH. Here is a brief description of each: 1. CO (Carbon monoxide) is a simple molecule with a triple bond between carbon and oxygen atoms. 2. CO₂ (Carbon dioxide) is a linear molecule with two double bonds, one between carbon and each oxygen atom. 3. CO₃²⁻ (Carbonate ion) is a polyatomic ion with one carbon atom connected to three oxygen atoms in a resonance structure where two oxygen atoms are double bonded to the carbon atom, and one is single bonded. 4. CH₃OH (Methanol) has a single bond between carbon and oxygen atoms, as well as three single C-H bonds and one O-H bond.

Compare bond lengths

Based on the molecular structures, we can now order the species by carbon-oxygen bond length: 1. CO with a triple bond generally has the shortest bond length. 2. CO₂ with a double bond has the intermediate bond length. 3. CO₃²⁻ has a resonance structure with both single and double bonds to the oxygen atoms, which gives it an effective bond length that lies between single and double bonds. 4. CH₃OH has a single bond between its carbon and oxygen atoms, which results in the longest bond length. Thus, the order from the longest to the shortest carbon-oxygen bond length is: CH₃OH, CO₃²⁻, CO₂, CO.

Determine bond strength

The strength of a chemical bond is inversely related to bond length - that is, longer bonds are generally weaker, while shorter bonds are stronger. Based on our order of bond lengths, we can now order the species from the weakest to the strongest carbon-oxygen bond: Weakest: CH₃OH < CO₃²⁻ < CO₂ < CO : Strongest So, the order from the weakest to the strongest carbon-oxygen bond is CH₃OH, CO₃²⁻, CO₂, and CO.

Key concepts

Chemical Bond Strength

Understanding the strength of a chemical bond is critical for studying the behavior of molecules. Bond strength is intimately related to the bond length; the distance between the nuclei of two bonded atoms. Generally, shorter bond lengths imply stronger bonds, as the atoms are held together more tightly by the attraction between their nuclei and the shared electrons.

The bond strength can vary depending on the type of bond and the atoms involved. For example, a triple bond, such as in carbon monoxide (CO), is shorter and stronger than a double bond found in carbon dioxide (CO₂). The strength decreases further in a single bond, such as in methanol (CH₃OH). A fascinating aspect of bond strength is its inverse relationship with bond length, which provides insights into the molecule's reactivity and stability.

In the exercise, by knowing that CH₃OH has the longest carbon-oxygen bond length, it can be inferred that it also has the weakest bond. Conversely, the molecule CO, with the shortest bond length, possesses the strongest carbon-oxygen bond. This information is not only important for understanding reactions but also crucial in applications like material science and drug design, where bond strength can influence the properties of a substance.

Molecular Structure

The molecular structure of a compound determines not only its bond lengths and bond strengths but also its physical and chemical properties. In our exercise, the various carbon-oxygen bond lengths are influenced by how the carbon and oxygen atoms are arranged in space.

For instance, CO₂'s linear shape with symmetrical double bonds to the oxygen atoms results in a moderate bond length. Methanol (CH₃OH), on the other hand, has a tetrahedral geometry around the carbon atom which contributes to a longer carbon-oxygen bond length. The molecular structure defines the angles between bonds, the rotation of molecules, and the distribution of electrons, all essential for understanding how a molecule will interact with others. Additionally, the concept of molecular geometry is fundamental in areas such as pharmacology, where the shape of a molecule can determine its biological activity.

Resonance Structure

Resonance structures provide insight into molecules like CO₃²⁻, where the actual molecular structure is a hybrid of multiple valid Lewis structures. In terms of carbon-oxygen bond length, resonance has a significant impact as it leads to bond lengths that are averages of the different possible structures. For the carbonate ion (CO₃²⁻), resonance causes the carbon-oxygen bonds to have lengths that are between a single bond and a double bond.

Understanding resonance is important for predicting the behavior of molecules and the delocalization of electrons within them, which affects their stability, acidity, and reactivity. The concept is particularly useful in organic chemistry and biochemistry, where resonance can explain the characteristics of complex organic molecules. Explaining resonance with structures that contribute to the final hybrid provides students a clearer understanding of how these intermediate forms play a role in determining the properties of the molecule.