Problem 23 - General Chemistry: Principles and Modern Applications

Question

The concept of formal charge helped us to choose the more plausible of the I ewis structures for \(\mathrm{NO}_{2}^{+}\) given in expressions (10.14) and \((10.15) .\) Can it similarly help us to choose a single Lewis structure as most plausible for \(\mathrm{CO}_{2} \mathrm{H}^{+} ?\) Explain.

Step-by-Step Solution

Answer

By drawing the possible Lewis structures for \(\mathrm{CO}_{2} \mathrm{H}^{+}\) and assessing the formal charges on each atom within these structures, one can identify the most plausible structure as the one where the formal charges on individual atoms are lowest and closest to zero.

Step 1: Draw Possible Structures

First, start by drawing all possible Lewis structures for \(\mathrm{CO}_{2} \mathrm{H}^{+}\). This molecule has 13 total valence electrons, so these electrons need to be distributed in such a way that every atom has a complete octet (apart from hydrogen, which only requires two electrons).

Step 2: Calculate Formal Charges

Calculate the formal charges for each atom in each structure. The formal charge is calculated using the formula: Formal charge = [No. of valence electrons in the free atom] – [No. of non-bonding electrons + 1/2 the number of bonding electrons]. Apply this formula to each atom in the structures.

Step 3: Evaluate Structures Based on Formal Charges

The most plausible Lewis structure will be the one in which the atoms bear the least formal charge possible, because formal charge is an indication of the electron distribution in a molecule. Structures in which formal charges are closest to zero will be more plausible.

Key Concepts

Lewis Structures

Lewis structures are a visual representation of molecules that show how atoms are connected and how valence electrons are distributed around them. When drawing Lewis structures, start by determining the total number of valence electrons available in the molecule. For example, in \(\mathrm{CO}_{2} \mathrm{H}^{+}\), there are 13 valence electrons in total.The next step involves arranging these electrons to ensure that every atom reaches a stable configuration. Typically, most atoms aim for an octet, or eight valence electrons. However, hydrogen is an exception and is stable with just two electrons. Drawing multiple possible Lewis structures helps in exploring various ways atoms can bond.While multiple structures might be possible, we need a method to decide which is the most stable. This where the concept of formal charge comes in handy. Reviewing the possible structures for their respective formal charges allows us to determine the most stable Lewis structure for a molecule.

Valence Electrons

Valence electrons are the outermost electrons of an atom and are crucial in chemical bonding. They determine how atoms bond with one another to form molecules. Consider them as the active players during bond formation. These are the electrons used in making the Lewis structures. In a neutral atom, the number of valence electrons corresponds to an element's group number in the periodic table. For instance:

• Carbon, found in group 14, has four valence electrons.
• Oxygen, located in group 16, has six valence electrons.
• Hydrogen, in group 1, has one valence electron.

You tally up the valence electrons for all the atoms in a molecule to determine how many electrons should be represented in the Lewis structure. This tallying helps not only in structuring each of the possible Lewis configurations but also in ensuring that the drawn structures are chemically valid.

Electron Distribution

Electron distribution in molecules involves placing electrons around atoms in a way that satisfies the electron demand for each atom. In Lewis structures, electrons are distributed as lone pairs or shared as bonding pairs between atoms. A good Lewis structure will strive to:

• Complete the octet for atoms that require it (note, hydrogen is an exception).
• Minimize formal charges across the molecule to enhance stability.

When electrons are distributed ideally, molecules achieve a stable electronic arrangement. The formal charge is an essential factor in achieving optimal electron distribution. By calculating the formal charge — which considers valence electrons, non-bonding electrons, and bonding electrons shared by the atom — we can gauge whether the electrons are distributed in a way that maintains chemical stability. Structures with a total charge near zero or those that place negative charges on more electronegative atoms are generally more stable. Ultimately, correct electron distribution reflects the molecule's readiness to achieve stability with its observed structure.