Problem 72 - General Chemistry: Principles and Modern Applications

Question

Comment on the similarities and differences in the molecular structure of the following four-atom species: \(\mathrm{NO}_{3}^{-}, \mathrm{CO}_{3}^{2-}, \mathrm{SO}_{3}^{2-},\) and \(\mathrm{ClO}_{3}^{-}\).

Step-by-Step Solution

Answer

The NO3-, CO3^2-, SO3^2-, and ClO3- ions all have similar molecular geometry (trigonal planar) and the same number of total atoms and valence electrons. The species differ considering the central atom and the number of electrons it contributes. Each species has resonance structures which explain their equal bond lengths.

Step 1: Matter Composition

First, identify the atoms that make up each species: NO3- is made up of one Nitrogen atom and three Oxygen atoms. CO3^2- is composed of one Carbon atom and three Oxygen atoms. Similarly, SO3^2- consists of one Sulfur atom and three Oxygen atoms, while ClO3- contains one Chlorine atom and three Oxygen atoms.

Step 2: Identify the Charge

Next, identify the charge on each species due to loss or gain of electrons, NO3- has a charge of -1, CO3^2- and SO3^2- both have charges of -2, and ClO3- has a charge of -1.

Step 3: Determine the Molecular Geometry

All of these molecules have a central atom bonded to three other atoms, resulting in a trigonal planar molecular geometry, in which the atoms make a flat triangle with the central atom in the middle.

Step 4: Assess the Bond Length

NO3-, CO3^2-, SO3^2-, and ClO3- have double bonds and single bonds which resonate, meaning the actual bond lengths are equal and somewhere between a single and double bond length. These resonance structures explain why the bond lengths are the same within each molecule.

Step 5: Contrast the Species

Each species differ in the central atom and the number of electrons it contributes. But, all of them have the same number of total atoms, molecular geometry, resonance structures, equal bond lengths and also, the same number of total valence electrons (24 each).

Key Concepts

Molecular Geometry

Molecular geometry is an essential concept in understanding how molecules are shaped. It's determined by the number and arrangement of bonds around a central atom. In the case of \(\mathrm{NO}_{3}^{-}\), \(\mathrm{CO}_{3}^{2-}\), \(\mathrm{SO}_{3}^{2-}\), and \(\mathrm{ClO}_{3}^{-}\), all four molecules exhibit trigonal planar molecular geometry.
The central atom is bonded to three oxygen atoms in a flat triangle arrangement. This is due to the presence of three electron domains around the central atom, allowing for a 120-degree separation angle.
In molecular geometry:

• Bond angles are informed by electron repulsion
• This maximizes distance and minimizes repulsion between bonded atoms

Understanding molecular geometry helps in predicting molecule behavior and interaction in chemical reactions.

Resonance Structures

Resonance structures depict different ways electrons can be arranged in molecules. They showcase delocalization, where electrons are shared across multiple bonds. For molecules like \(\mathrm{NO}_{3}^{-}\), \(\mathrm{CO}_{3}^{2-}\), \(\mathrm{SO}_{3}^{2-}\), and \(\mathrm{ClO}_{3}^{-}\), resonance is key to understanding equal bond lengths.
Each molecule can depict resonance by drawing structures with alternating single and double bonds, indicating electron flow. This results in:

• Equal bond lengths within the molecule
• Stabilization of the molecule due to electron delocalization
• A more accurate description of charge distribution across bonds

By using resonance, we can explain why these similar molecules have uniform bond characteristics.

Trigonometry Planar Geometry

The term 'trigonometry planar geometry' refers to the mathematical principles applied in planar shapes. In chemistry, it helps explain molecular shapes like the trigonal planar structure found in our four molecules.
This application of trigonometry helps determine specific angles, like those observed in molecules with similar binding groups.

• In a trigonal planar shape, all bond angles are approximately 120 degrees.
• The use of trigonometry ensures accurate predictions of molecular shapes.

By understanding the trigonometry behind molecular shapes, we can visualize and anticipate how molecules interact in space, which is crucial for reactions and compound formation.

Valence Electrons

Valence electrons are the outermost electrons that participate in chemical bonding. They determine the reactivity and bond formation for an element or compound.
For \(\mathrm{NO}_{3}^{-}\), \(\mathrm{CO}_{3}^{2-}\), \(\mathrm{SO}_{3}^{2-}\), and \(\mathrm{ClO}_{3}^{-}\), each species contains 24 valence electrons.
This similar count across all four compounds arises from the sum of valence electrons from the central and surrounding atoms along with any additional electrons from the charge.

• More valence electrons facilitate multiple bonding scenarios.
• Less valence electrons mean fewer possibilities for complex bond formation.

The balance of valence electrons stabilizes molecules, influences molecular geometry, and affects resonance forms.

Bond Length

Bond length is the average distance between the nuclei of two bonded atoms. It offers insights into bond strength and molecular stability.
In molecules with resonance, such as \(\mathrm{NO}_{3}^{-}\), \(\mathrm{CO}_{3}^{2-}\), \(\mathrm{SO}_{3}^{2-}\), and \(\mathrm{ClO}_{3}^{-}\), bond lengths are influenced by a blend of single and double bonding.
This resonance effect produces equal bond lengths that are somewhere between typical single and double bonds:

• Shorter bond lengths often indicate stronger bonds.
• Resonance equalizes bond lengths for consistent structural integrity.

Understanding bond length helps in predicting molecular behavior, reactivity, and the energy required to break or form bonds.