Question

\(\mathrm{CO}_{2}\) Answer: First draw a dot diagram, then examine it via VSEPR: Draw a dot diagram: Apply VSEPR: Determine the molecule's shape: There are two electron The molecule groups \(180^{\circ}\) apart around is linear. the central \(C\) atom. \((S N=2)\)

Short answer

The molecular geometry of the CO2 molecule is determined by drawing its Lewis structure, which shows a central Carbon atom double-bonded to two Oxygen atoms. Applying the VSEPR theory reveals that there are two electron groups around the central Carbon atom, causing them to be \(180^{\circ}\) apart. Therefore, the molecular geometry of CO2 is linear.

Step-by-step solution

Draw the Lewis Structure

First, we need to draw the Lewis structure of the CO2 molecule, which will help us determine the positions of the atoms and the electron pairs around the central atom (Carbon). The molecule has two Oxygen atoms bonded to the central Carbon atom. Carbon has 4 valence electrons, and Oxygen has 6 valence electrons, making a total of 16 electrons in the molecule. The Lewis structure of CO2 is as follows: O=C=O In this Lewis structure: - The central Carbon atom is double-bonded to each of the two Oxygen atoms. - Each Oxygen atoms have two lone pairs of electrons.

Apply the VSEPR Theory

Now we will apply the VSEPR theory to determine the arrangement of electron pairs around the central Carbon atom in the CO2 molecule. In VSEPR theory, the electron pairs around an atom repel each other, so they try to stay as far apart as possible. The bonding pairs (shared by atoms) and lone pairs (not bonded but attached to an atom) around the central atom will define its electron pair geometry. In CO2, the central Carbon atom has two bonding pairs and no lone pairs. We will consider the bonding pairs as electron groups.

Determine the Molecule's Shape

Using VSEPR theory, the molecular geometry is determined by the electron groups around the central Carbon atom. In the CO2 molecule, there are two electron groups, so they try to stay as far apart as possible according to VSEPR theory. They will be \(180^{\circ}\) apart, which means the CO2 molecule has a linear geometry. This explains why the Carbon atom is double-bonded to each of the two Oxygen atoms in a straight line. So, the molecular geometry of the CO2 molecule is linear.

Key concepts

Lewis Structure

The Lewis structure is a way to show the arrangement of valence electrons in a molecule. It's essential for understanding how atoms bond and interact. In the case of \( ext{CO}_2\), drawing the Lewis structure helps visualize the electron distribution. Carbon, which has 4 valence electrons, sits in the center. It's bonded to two Oxygen atoms, each having 6 valence electrons.
- Carbon forms two double bonds with the Oxygen atoms.
- Each Oxygen atom has two lone pairs of electrons.
This depiction not only shows the connectivity of the atoms but also highlights the shared (bonding) and unshared (lone pairs) electrons.

Molecular Geometry

Molecular geometry describes the 3-D arrangement of atom's in a molecule. It's crucial for predicting the molecule's properties and reactivity. VSEPR (Valence Shell Electron Pair Repulsion) theory assists in determining the molecular geometry.
For \( ext{CO}_2\), the molecular geometry is linear.
- Carbon is at the center with Oxygen atoms on either side.
- The molecule forms a straight line with an angle of \(180^\circ\).
This arrangement is due to the repulsion between the electron pairs, pushing them as far apart as possible. Linear geometry in \( ext{CO}_2\) implies no dipole moment, making the molecule nonpolar.

Valence Electrons

Valence electrons are the outer shell electrons involved in bonding. Understanding their roles is key to predicting molecular behavior.
In \( ext{CO}_2\):
- Carbon contributes 4 valence electrons.
- Each Oxygen adds 6, totaling 16 electrons in the molecule.
Valence electrons are arranged to achieve stability, often reflected by the octet rule. This is observed in \( ext{CO}_2\), where each atom reaches a stable configuration through bonding.

Bonding Pairs

Bonding pairs consist of electrons shared between atoms. In simple terms, two atoms share two electrons to form a bond. In a molecular structure like \( ext{CO}_2\), bonding pairs are central to maintaining molecule integrity.
- \( ext{CO}_2\) has two principal types of bonds: double bonds between Carbon and each Oxygen.
- Each double bond involves 4 electrons (2 pairs).
These bonding pairs are crucial in determining the strength and length of bonds. In \( ext{CO}_2\), double bonds contribute to its linear shape and affect its chemical and physical properties.