Question

The correct order of increasing \(\mathrm{C}-\mathrm{O}\) bond length of \(\mathrm{CO}, \mathrm{CO}_{3}^{2-}, \mathrm{CO}_{2}\) is (a) \(\mathrm{CO}_{3}^{2-}<\mathrm{CO}_{2}<\mathrm{CO}\) (b) \(\mathrm{CO}_{2}<\mathrm{CO}_{3}^{2}<\mathrm{CO}\) (c) \(\mathrm{CO}<\mathrm{CO}_{3}^{2-}<\mathrm{CO}_{2}\) (d) \(\mathrm{CO}<\mathrm{CO}_{2}<\mathrm{CO}_{3}^{2}\)

Short answer

The correct order is (d): \(\text{CO} < \text{CO}_2 < \text{CO}_3^{2-}\).

Step-by-step solution

Understanding Bond Length

Bond length generally decreases with increasing bond order. The bond order is determined by the number of chemical bonds between a pair of atoms.

Comparing Bond Orders

Calculate the bond order for each type of molecule. - For \(\text{CO}\), it is a triple bond, so its bond order is 3.- For \(\text{CO}_2\), the structure is linear composed of two double bonds, so the bond order of each C-O is 2.- For \(\text{CO}_3^{2-}\), we have resonance structures with a bond order of \(\frac{4}{3}\) for each C-O bond.

Determine Bond Length Order

Since bond length is inversely related to bond order, the order of increasing bond length from shortest to longest will be from the highest bond order to the lowest. Thus, the order is: \(\text{CO} (3) < \text{CO}_2 (2) < \text{CO}_3^{2-} (\frac{4}{3})\).

Select Correct Answer

Based on the analysis, the correct order of increasing C-O bond length is given by option (d): \(\text{CO} < \text{CO}_2 < \text{CO}_3^{2-}\).

Key concepts

Bond Length

Bond length refers to the distance between the nuclei of two atoms bonded together. It serves as one of the primary determinants of molecular shape and size. Generally, bond length decreases when the bond order increases. When atoms share more electrons, or in other words, form multiple bonds, they are brought closer together. Some key points to keep in mind include:

• Triple bonds are generally shorter than double bonds.
• Double bonds are typically shorter than single bonds.
• Bond length can affect the stability and reactivity of a molecule.

When studying molecular structures like CO, CO₂, and CO₃²⁻, it's important to remember that differences in bond length arise from the varying bond orders of carbon and oxygen in each molecule.

Bond Order

Bond order is a crucial concept when it comes to understanding chemical bonding and molecular geometry. It quantifies the number of chemical bonds between a pair of atoms. Bond order helps predict both the strength and the length of a bond. The higher the bond order, the greater the electron cloud overlap, resulting in a stronger and shorter bond. Here are some insights:

• A bond order of 3, as seen in CO, indicates a triple bond.
• CO₂ has a bond order of 2, resulting from two double bonds in a linear structure.
• CO₃²⁻ has a fractional bond order of 4/3 due to resonance structures, indicating a bond between that of a double and a single bond.

Understanding bond order not only clarifies bond length but also provides insights into the chemical properties of molecules.

Resonance Structures

Resonance structures offer a way to depict a molecule that has multiple feasible structures contributing equally to the actual electronic distribution. These structures don't exist individually but are hypothetical extremes that enhance our understanding of electron distribution. In molecules like CO₃²⁻, resonance is pivotal in explaining the bond characteristic. Consider the following:

• The carbonate ion ( CO₃²⁻) displays three resonance forms.
• Each form shows different placements of double and single bonds, which lead to an averaged bond order.
• Resonance contributes to lower energy and increased stability.

In essence, resonance allows for a more accurate representation of a molecule's actual electron arrangement and bond characteristics.

C-O Bond Order

The C-O bond order is central to establishing the properties of compounds like CO, CO₂, and CO₃²⁻. This specific measurement is derived directly from the types of bonds present between carbon and oxygen. In carbon monoxide (CO), the C-O bond order is 3, representing a strong, short, triple bond. In carbon dioxide (CO₂), the bond order is 2, attributed to its double bonds. Finally, in the carbonate ion (CO₃²⁻), resonance structures generate a bond order of 4/3 for each C-O bond, creating a longer bond than seen in CO or CO₂. Understanding the C-O bond order aids in predicting the following:

• Molecular geometry and reactivity.
• Physical properties like bond strength and length.
• Comparative stabilities of different carbon-oxygen compounds.

The bond order directly influences the chemical behavior and characteristics of these molecules, showcasing the importance of this parameter in chemical bonding.