Problem 48 - Chemistry and Chemical Reactivity

Question

Compare the carbon-oxygen bond lengths in the formate ion \(\left(\mathrm{HCO}_{2}^{-}\right),\) in methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right),\) and in the carbonate ion \(\left(\mathrm{CO}_{3}^{2-}\right) .\) In which species is the carbon-oxygen bond predicted to be longest? In which is it predicted to be shortest? Explain briefly.

Step-by-Step Solution

Answer

Methanol has the longest; carbonate ion has the shortest carbon-oxygen bond.

Step 1: Identify the Bond Orders

Discuss the bond order of the carbon-oxygen bonds in each compound. In \(\text{HCO}_2^-\), the bond order is an average between single and double bonds due to resonance. In \(\text{CH}_3\text{OH}\), the bond is a carbon-oxygen single bond. In \(\text{CO}_3^{2-}\), the bond order is higher than one due to resonance among three equivalent bonds.

Step 2: Determine the Relationship between Bond Length and Bond Order

Remember that higher bond orders correspond to shorter bond lengths. A single bond is longer than a double bond, which is longer than a bond with a higher order.

Step 3: Apply Bond Order to Estimate Bond Lengths

Since methanol \(\text{CH}_3\text{OH}\) has a carbon-oxygen single bond, it should have the longest bond length. The carbonate ion \(\text{CO}_3^{2-}\) has partial double bonds due to resonance, making its bonds shorter. The formate ion \(\text{HCO}_2^-\) has a bond order between one and two, indicating an intermediate bond length.

Step 4: Conclusion

Therefore, the carbon-oxygen bond in methanol is predicted to be longest, while in carbonate ion, it is predicted to be shortest due to the highest bond order.

Key Concepts

Carbon-Oxygen Bonds

Carbon-oxygen bonds play a crucial role in many chemical compounds and understanding their properties, such as bond length and order, is essential. Bond length refers to the distance between the nuclei of the bonded atoms. In general, the bond order is inversely related to bond length, meaning that the higher the bond order, the shorter the bond length will be.

In organic and inorganic chemistry, different compounds demonstrate varying carbon-oxygen bonds:

• In methanol ( ext{CH}_3 ext{OH}), the carbon-oxygen bond is a single bond. As single bonds have lower bond order, they are generally longer.
• In the carbonate ion ( ext{CO}_3^{2-}), resonance structures result in partial double bonds, leading to a higher bond order and consequently shorter bond lengths.
• In the formate ion ( ext{HCO}_2^-), resonance creates an average bond order between single and double bonds, leading to bond lengths that are intermediate.

This variability in bond types highlights the significance of evaluating bond order to predict and understand bond lengths in various chemical systems.

Resonance Structures

Resonance structures are used to represent molecules where electron distribution can be expressed in multiple ways. These structures depict the delocalization of electrons across more than one position within a molecule. Importantly, resonance doesn't mean that these structures exist separately, but rather, they are a useful way to show a more accurate picture of electron distribution, which is a "hybrid" of all possible structures.

Take the carbonate ion ( ext{CO}_3^{2-}) for example. It contains three equivalent resonance structures, in which the position of double bonds shifts between the three oxygen atoms. This delocalization allows each carbon-oxygen bond to have a partial double-bond character, increasing the bond order and making the bond lengths equal and shorter than a typical C-O single bond.

In the formate ion ( ext{HCO}_2^-), resonance is also present but involves two structures leading to a bond order averaging between single and double bonds. This results in a carbon-oxygen bond length that is not as short as in ext{CO}_3^{2-} but not as long as a pure single bond.

The utilization of resonance structures provides a deeper understanding of molecular behavior and properties such as bond lengths and reactivity.

Chemical Bonding Concepts

Chemical bonding is a central concept in chemistry that explains how atoms combine to form molecules. An essential aspect of chemical bonding is the concept of bond order, which is critical for understanding molecular geometry and stability.

Bond order is a measure of the number of chemical bonds between a pair of atoms. It's calculated as the difference between the bonding and antibonding electrons divided by two. Generally, a higher bond order indicates a stronger, more stable bond and shorter bond length.

• A single bond (bond order of 1) holds atoms further apart than a double bond (bond order of 2).
• Triple bonds (bond order of 3) are even shorter and stronger than double bonds.
• Compounds like ext{CO}_3^{2-} exhibit resonance, resulting in bond orders that are not whole numbers but fractional, due to shared multiple resonance structures.

The information about bond orders helps predict physical properties, reactivity, and other characteristics of substances. Understanding these concepts is crucial when examining complex molecules in various fields, including organic chemistry, materials science, and biochemistry.