Problem 54 - Chemistry The Central Science In Si Units

Question

Consider the formate ion, \(\mathrm{HCO}_{2}^{-}\), which is the anion formed when formic acid loses an \(\mathrm{H}^{+}\) ion. The \(\mathrm{H}\) and the two \(\mathrm{O}\) atoms are bonded to the central C atom. (a) Draw the best Lewis structure(s) for this ion. (b) Are resonance structures needed to describe the structure? (c) Would you predict that the \(\mathrm{C}-\mathrm{O}\) bond lengths in the formate ion would be longer or shorter relative to those in \(\mathrm{CO}_{2}\) ?

Step-by-Step Solution

Answer

The best Lewis structure for \(\mathrm{HCO}_2^-\) involves resonance between two forms. The C-O bonds are longer than in \(\mathrm{CO}_2\).

Step 1: Determine Total Valence Electrons

Calculate the total number of valence electrons available for the \(\mathrm{HCO}_2^-\) ion. Hydrogen contributes 1, carbon 4, each oxygen 6, and the negative charge adds an extra electron, summing up to a total of 18 valence electrons.

Step 2: Create Initial Skeleton Structure

Arrange the atoms with hydrogen and the two oxygen atoms bonded to the central carbon. Place single bonds (2 electrons each) between the carbon atom and each of the three other atoms.

Step 3: Complete the Octets of Outer Atoms

Fill the octets for the two oxygen atoms by adding lone pairs. You will need 6 electrons per oxygen atom (excluding the bond with carbon), so 12 electrons are used to satisfy the octets of both oxygens.

Step 4: Assign Remaining Electrons to Central Atom

Place any remaining electrons on the central carbon atom. After placing lone pairs on oxygen, you will have 2 electrons left, which are initially added to carbon.

Step 5: Form Double Bond to Satisfy Octet Rule

Convert one lone pair from an oxygen into a double bond with carbon to satisfy carbon's octet rule. Choose one oxygen to share its lone pair with carbon, forming a double bond.

Step 6: Consider Resonance Structures

Determine if resonance structures are necessary. Since there are two possible ways to position the double bond (with either oxygen), the formate ion has two resonance structures.

Step 7: Compare C-O Bond Lengths with CO2

In \(\mathrm{CO}_2\), each C-O bond is a double bond, resulting in shorter bond lengths. For \(\mathrm{HCO}_2^-\), each C-O bond exists as a resonance hybrid of a single and a double bond, making the bonds longer than a pure double bond but shorter than a single bond.

Key Concepts

Lewis Structure of the Formate Ion

Understanding the Lewis structure for the formate ion \(\mathrm{HCO}_2^-\) is crucial to visualizing the distribution of electrons around the molecule. Let's explore this step by step.To start, the total number of valence electrons available is 18. Here's how: hydrogen provides 1 electron, carbon contributes 4, each oxygen 6, and the extra negative charge adds 1 more electron.Next, the skeleton structure is organized with carbon at the center, bonded to hydrogen and the two oxygen atoms. Initially, we use single bonds, each accounting for 2 electrons, which leaves us with 12 electrons.The outer atoms, in this case, the oxygens, should have complete octets. To do so, we distribute the remaining electrons, giving each oxygen 6 electrons to complete their octets (excluding the bond). After this process, we are left with 2 electrons, which initially sit on the carbon atom.Since carbon needs an octet too, we convert a lone pair from an oxygen to form a double bond with carbon. This adjustment satisfies carbon's requirement for 8 electrons around it.

Resonance Structures

In some molecules, a single Lewis structure can't fully illustrate electron distribution. The formate ion is a perfect example of resonance, which means multiple structures can describe the same molecule. For the formate ion, once we've established one Lewis structure, it's apparent that there are two places where we can form a double bond. This happens because the double bond can be placed with either of the oxygen atoms. However, this does not mean that the molecule is constantly switching between these forms. Instead, it is often best described as a resonance hybrid, which effectively means that the actual structure is a blend or average of the resonance forms. Due to this hybrid nature, the double-bond character is shared between the two C-O bonds.
Resonance structures often show up in various chemical species and are key to understanding the true nature of atomic interactions and bond lengths, as they affect the molecule's stability and reactivity.

C-O Bond Length in the Formate Ion

Bond lengths are important to understanding molecular shape and function. They vary based on the types of bonds present, like single, double, or even triple bonds.In carbon dioxide, each carbon-oxygen bond is a double bond, resulting in shorter bond lengths due to stronger overlapping between the bonding orbitals. However, in the formate ion, the situation is a little different due to resonance.In \(\mathrm{HCO}_2^-\), each C-O bond is neither purely single nor purely double. Instead, the bond length is an intermediate, due to its nature as a resonance hybrid. The average bond order, which is a measure of bond strength, in a resonance situation may be around 1.5 for formate ion, symbolizing this intermediate length.Overall, the C-O bond lengths within the formate ion are longer than the typical double bond found in \(\mathrm{CO}_2\), but notably shorter than a typical single bond. Understanding this helps predict how the formate ion interacts in different chemical environments.