Question

Consider the methane molecule. (a) Draw the methane molecule showing its tetrahedral shape, using lines, solid wedges, and dashed wedges to show three-dimensionality. (b) Draw the methane molecule inscribed inside ? tetrahedron such that the \(\mathrm{H}\) atoms touch the vertices of the tetrahedron. (c) Why is it better for methane to have \(109.5^{\circ}\) bond angles rather than \(90^{\circ}\) bond angles?

Short answer

To represent the methane molecule (\(CH_4\)), depict the carbon atom at the center of a tetrahedron and the hydrogen atoms at the vertices, with lines and wedges indicating three-dimensional bonds. The methane molecule is inscribed inside a tetrahedron, with vertices shared between the molecule and the polyhedron. The \(109.5^{\circ}\) bond angles are energetically more favourable than \(90^{\circ}\) angles, due to the valence shell electron pair repulsion (VSEPR) theory, which minimizes repulsion and maintains stability in the molecule.

Step-by-step solution

(Drawing the methane molecule)

To draw the methane molecule (\(CH_4\)), first, place the carbon atom (\(C\)) at the center and the four hydrogen atoms (\(H\)) at the vertices of a tetrahedron. Represent the bonds between the atoms using lines, solid wedges, and dashed wedges to show three-dimensionality. Solid wedges indicate the bonds coming out of the plane towards you, while dashed wedges indicate the bonds going behind the plane.

(Inscribing methane inside a tetrahedron)

Draw a tetrahedron, placing its vertices at the four hydrogen atoms of the methane molecule. The edges of this tetrahedron will connect the hydrogen atoms. This way, you'll have both, the methane molecule and the tetrahedron, sharing the same vertices. Consequently, the methane molecule can be regarded as inscribed inside the tetrahedron.

(Explaining the bond angles)

The bond angles in methane are approximately \(109.5^{\circ}\), and not \(90^{\circ}\), because of the tetrahedral shape. This shape allows for the maximum possible separation between the hydrogen atoms, which is essential for minimizing electron-electron repulsion, as per the valence shell electron pair repulsion (VSEPR) theory. If the bond angles were equal to \(90^{\circ}\), that would mean the hydrogen atoms would be closer together, leading to increased repulsion and instability of the molecule. Therefore, having a bond angle of \(109.5^{\circ}\) is energetically more favourable for methane.

Key concepts

Tetrahedral Shape

The methane molecule, with the chemical formula \(CH_4\), adopts a unique three-dimensional shape known as the tetrahedral shape. In this configuration, the central carbon atom is surrounded by four hydrogen atoms positioned at the corners of a tetrahedron. This arrangement allows the molecule to maintain symmetry and maximize the distance between the hydrogen atoms.

To visualize this, imagine a pyramid with a triangular base. The carbon atom is at the center, and the hydrogen atoms are located at each vertex of the pyramid. This shape is key to understanding methane's molecular properties and why it behaves the way it does in chemical reactions.

Bond Angles

In a tetrahedral molecule like methane, the bond angles between the atoms are approximately \(109.5^{\circ}\). These angles are crucial in keeping the molecule stable.

If the angles were smaller, like \(90^{\circ}\), the hydrogen atoms would be closer together, increasing the repulsive forces between them. The \(109.5^{\circ}\) bond angles ensure each hydrogen atom is evenly spaced, minimizing repulsion and resulting in a more energetically favorable state.

This natural spacing is essential for maintaining the structural integrity of the molecule.

Valence Shell Electron Pair Repulsion

The Valence Shell Electron Pair Repulsion (VSEPR) theory helps predict the shape of the methane molecule. According to VSEPR, electron pairs around a central atom will position themselves as far apart as possible to minimize repulsion.

In methane, there are four bonding pairs of electrons around the carbon atom. The tetrahedral arrangement is the best configuration to minimize these electron pair repulsions, resulting in bond angles of \(109.5^{\circ}\).

This theory is foundational for understanding why molecules adopt certain shapes and is widely used in chemistry to predict molecular geometry.

Electron Repulsion

Electron repulsion is a critical concept in understanding molecular shapes. Electrons, being negatively charged, naturally repel each other. In a molecule like methane, minimizing this repulsion is key.

By adopting a tetrahedral shape, the molecule maximizes the distance between hydrogen atoms, reducing the repulsive forces between the electrons in the bonds.

This decreased repulsion leads to a more stable molecule, which is why the tetrahedral shape with \(109.5^{\circ}\) angles is energetically preferred over tighter angles such as \(90^{\circ}\).

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. For methane, this geometry is tetrahedral, giving it symmetry and stability.

The molecular geometry is determined by the number of electron pairs and bonds around the central atom. In the case of methane, four bonds result in a perfectly tetrahedral shape.

This geometric configuration is not just theoretical; it plays a crucial role in how the molecule interacts, bonds, and reacts with other substances. Understanding molecular geometry helps chemists predict and explain the behavior of different molecules.