Question

Predict the electron pair geometry, the molecular shape, and the bond angle for a silicon dioxide molecule, \(\mathrm{SiO}_{2}\), using VSEPR theory.

Short answer

Silicon dioxide (\text{SiO}_{2}) has a linear shape, linear electron geometry, and a bond angle of 180^{\circ}.

Step-by-step solution

Determine the central atom

The central atom in a molecule is typically the one with the lowest electronegativity, which is often a non-hydrogen atom if connected to multiple others. In the case of silicon dioxide, Si (silicon) is the central atom, with O (oxygen) atoms bonded to it.

Count the valence electrons

Each silicon atom has 4 valence electrons, and each oxygen atom has 6 valence electrons. In  ext{SiO}_{2} there are one Si and two O atoms, so the total number of valence electrons is: \[4 + (2 \times 6) = 16 \].

Draw the Lewis structure

In the Lewis structure for  ext{SiO}_{2}, silicon forms double bonds with each oxygen atom. Each double bond accounts for 4 electrons, covering all 16 valence electrons in the structure.

Determine the electron pair geometry

According to the VSEPR theory, electron pairs around a central atom will arrange themselves to minimize repulsion. In  ext{SiO}_{2}, the arrangement of the double bonds means there are no lone electron pairs around the central silicon atom, leading to a linear electron pair geometry.

Determine the molecular shape

The molecular shape of  ext{SiO}_{2} corresponds to the electron pair geometry since there are no lone pairs on the silicon. Therefore, the molecular shape of  ext{SiO}_{2} is also linear.

Predict the bond angle

In a linear geometry according to VSEPR theory, the bond angle is 120^{ ext{degrees}}. However, because  ext{SiO}_{2} forms a perfect line with no lone electron pairs affecting the angles, the bond angle is 180^{ ext{degrees}}.

Key concepts

Electron Pair Geometry

To understand electron pair geometry, it's essential to think about how electrons behave around a central atom. According to the Valence Shell Electron Pair Repulsion (VSEPR) theory, electron pairs arrange themselves to be as far apart as possible. This arrangement helps minimize repulsions caused by electron-electron interactions.

In the case of a silicon dioxide molecule (\( \text{SiO}_2 \)), silicon serves as the central atom with oxygen atoms on either side. This molecule has a linear electron pair geometry. Why? Because each oxygen makes a double bond with silicon, there are no lone pairs on silicon.

• The goal is to achieve a geometry where electron clouds around the central atom experience as little repulsion as possible.

Thus, for \( \text{SiO}_2 \), the linear electron pair geometry ensures that the electrons between silicon and oxygen are balanced and symmetrical.

Molecular Shape

Molecular shape is another key aspect of VSEPR theory. This concept specifically describes the shape formed by the atoms in a molecule, excluding any lone pairs of electrons.

In \( \text{SiO}_2 \), the shape is dictated by the bonding and absence of lone pairs on the central atom, silicon. Since silicon in \( \text{SiO}_2 \) doesn't have any lone pairs, the molecular shape align perfectly with its electron pair geometry, which is linear. This means the atoms line up in a straight line.

• Linear shapes occur when two atoms are bound to a central one, with no lone electron pairs to disrupt symmetry.

For students, always remember that the lack of lone pairs ensures that the electron pair geometry and molecular shape are identical in such scenarios.

Bond Angle

The bond angle is the angle between two bonds originating from the same atom. It is a direct consequence of the electron pair geometry and molecular shape. With \( \text{SiO}_2 \)'s linear configuration, the bond angle can be specifically predicted.

In a linear geometry, the ideal bond angle is 180 degrees. \( \text{SiO}_2 \) achieves this perfect angle due to its linear arrangement of atoms and absence of lone pair repulsion angles, which could have distorted it.

• Bond angles are most affected by lone pairs, which take up more space than bonding pairs, warping angles from their typical values.

Always verify if lone pairs exist, as they lead to adjustments in angles, but in this molecule's case, you're looking at an unaltered, perfect 180 degrees.