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? \(\left(\mathrm{CH}_{3} \mathrm{OH} \text { exists as } \mathrm{H}_{3} \mathrm{C}-\mathrm{OH} .\right)\)

Short answer

The order of species with respect to carbon-oxygen bond length (longest to shortest) is CO₃²⁻, CH₃OH, CO₂, CO, and the order from the weakest to the strongest carbon-oxygen bond is CH₃OH, CO₃²⁻, CO₂, CO.

Step-by-step solution

Determine the molecular structure and the types of bonds

First, let's determine the molecular structure and the types of bonds of each species given: 1. CO (Carbon monoxide) - This molecule consists of a triple bond between carbon and oxygen atoms. 2. CO₂ (Carbon dioxide) - This molecule has two double bonds between the central carbon atom and the two oxygen atoms. 3. CO₃²⁻ (Carbonate ion) - This polyanion has a negative charge of 2 and contains a carbon atom at the center, which is bonded to three oxygen atoms using resonance structures consisting of one double bond and two single bonds. 4. CH₃OH (Methanol) - This molecule consists of a single bond between carbon and oxygen (C-O).

Compare the types of bonds and bond lengths

Knowing the bond types in each species, we can compare their bond lengths as follows: - Triple bond (C≡O) in CO is shorter than a double bond (C=O). - Double bond (C=O) in CO₂ is shorter than a single bond (C-O). - Resonance structures in CO₃²⁻ ion contain one double bond (C=O) and two single bonds (C-O); the actual bond length is intermediate between a double and single bond. - Single bond (C-O) in CH₃OH

Order the species according to bond length

Based on the bond length comparisons, we can order the given species from the longest to the shortest carbon-oxygen bond lengths: CO₃²⁻ > CH₃OH > CO₂ > CO

Determine the order of carbon-oxygen bond strength

Bond strength is inversely proportional to bond length. Therefore, we can order the species from the weakest to the strongest carbon-oxygen bond: CH₃OH < CO₃²⁻ < CO₂ < CO In summary, the order of species with respect to carbon-oxygen bond length (longest to shortest) is CO₃²⁻, CH₃OH, CO₂, CO, and the order from the weakest to the strongest carbon-oxygen bond is CH₃OH, CO₃²⁻, CO₂, CO.

Key concepts

Molecular Structure

Understanding the molecular structure is key to predicting the lengths and strengths of bonds in a molecule or ion. Each molecule has a characteristic shape and bonding pattern that is a result of the atoms it contains and how they are connected.

In carbon monoxide (CO), the connection between carbon and oxygen is a triple bond, which involves the sharing of three pairs of electrons. Carbon dioxide (CO₂) on the other hand comprises two double bonds between carbon and oxygen atoms. These multiple bonds are shorter and stronger than single bonds, a pattern that can usually be applied to other molecules as well.

The carbonate ion (CO₃²⁻), with its negative two charge, has a central carbon atom bonded to three oxygen atoms. Unlike the straightforward bonding in CO and CO₂, the carbonate ion exhibits a phenomenon called resonance, which we'll explore in a later section. Lastly, methanol (CH₃OH) consists of a single bond between carbon and oxygen, which typically results in longer and weaker bonds when compared to multiple bonds.

The connectivity and types of bonds in these molecules or ions dictate their physical and chemical properties including, but not limited to, bond lengths and bond strengths.

Chemical Bonding

Chemical bonding is the force that holds atoms together in a molecule. At its core, bonding involves the interaction of atoms' valence electrons to achieve greater stability. Bonds vary in nature – some are covalent, where electrons are shared between atoms, while others are ionic, involving the transfer of electrons.

In our discussion of carbon-oxygen bonds, we are looking at covalent bonding. In a covalent bond, the number of shared electron pairs determines the bond order – single, double, or triple – with triple bonds being the strongest and shortest due to increased electron sharing and resulting greater attraction between atoms. This concept explains the progressive increase in bond strength and decrease in bond length as we move from the single bond in methanol through the double bonds in carbon dioxide to the triple bond in carbon monoxide.

Providing Stability

Atoms engage in bonding to reach a more stable electronic configuration. The octet rule, although not universally applicable, serves as a useful guideline: atoms tend to share, donate, or receive electrons to complete their outermost valence shell with eight electrons, mirroring the stability of noble gases. Methanol, carbon dioxide, and carbon monoxide exemplify different ways in which carbon and oxygen atoms can achieve stable electronic configurations through bonding.

Resonance Structures

Resonance structures are a way to depict molecules where multiple correct ways to draw a molecule exist, each differing only in the position of electrons, not the placement of atoms. It is a concept used in molecular orbital theory to describe the delocalization of electrons within a molecule.

In the case of the carbonate ion (CO₃²⁻), resonance structures are particularly informative. The actual molecule doesn't have one carbon-oxygen double bond and two single bonds; instead, the double bond character is spread over all three carbon-oxygen bonds, making them equivalent. The resonance in CO₃²⁻ means that the bond lengths are intermediate between what one would expect for a single and a double bond.

Understanding Delocalization

Delocalization is key to resonance. Rather than being held in one specific location, certain electrons are spread out over multiple adjacent atoms. This results in a stabilization of the molecule and often affects molecular properties like bond length, as seen in the carbonate ion. It's important to recognize that resonance structures are not different states of the molecule but rather a combined representation of the molecule's actual electronic structure, which is often somewhere in between the possible resonance forms.