Question

Compare the bond angles in the following molecules: (a) \(\mathrm{CH}_{4}\) (b) \(\mathrm{NH}_{3}\) (c) \(\mathrm{H}_{2} \mathrm{O}\)

Short answer

The bond angle decreases in the series \(\mathrm{CH}_{4}\) (109.5°) > \(\mathrm{NH}_{3}\) (107°) > \(\mathrm{H}_{2}\mathrm{O}\) (104.5°) due to increasing repulsion from lone pairs.

Step-by-step solution

Draw the Lewis structure

The Lewis structure for each molecule is as follows: \n(a) \(\mathrm{CH}_{4}\): Carbon forms four bonds and no lone pairs, making it a regular tetrahedron with Hydrogen. \n(b) \(\mathrm{NH}_{3}\): Nitrogen forms three bonds and one lone pair, forming a trigonal pyramidal shape with Hydrogen. \n(c) \(\mathrm{H}_{2} \mathrm{O}\): Oxygen forms two bonds and two lone pairs, making it a bent shape with Hydrogen.

Determine the Molecular Geometry

Each Lewis structure implies a specific molecular geometry: \n(a) \(\mathrm{CH}_{4}\): Tetrahedral \n(b) \(\mathrm{NH}_{3}\): Trigonal pyramidal \n(c) \(\mathrm{H}_{2} \mathrm{O}\): Bent

Infer the Bond Angle from the Shape

Using the molecular geometry, the bond angle for each compound is: \n(a) \(\mathrm{CH}_{4}\): 109.5° in a tetrahedral shape \n(b) \(\mathrm{NH}_{3}\): 107° in a trigonal pyramidal shape, less than \(\mathrm{CH}_{4}\) due to the presence of a lone pair causing more repulsion. \n(c) \(\mathrm{H}_{2} \mathrm{O}\): 104.5° in a bent shape, the smallest among the three due to the presence of two lone pairs causing more repulsion than the \(\mathrm{NH}_{3}\).

Key concepts

Lewis structures

Lewis structures are diagrams that represent the bonding between atoms within a molecule along with any lone pairs of electrons that might exist. They are a critical first step in predicting the molecular geometry and the subsequent shape of the molecule. In the case of drawing Lewis structures, knowing the valence electrons of each atom is crucial as it helps in determining how atoms bond to fulfill the octet rule or duet rule, depending on the element.
For example, in the molecule

• (CH₄) , Carbon, having four valence electrons, forms single covalent bonds with four hydrogen atoms. There are no lone pairs, resulting in a symmetrical molecule.
• (NH₃) , Nitrogen, with five valence electrons, forms three bonds with hydrogen atoms and retains one lone pair.
• (H₂O) , Oxygen, having six valence electrons, forms two bonds with hydrogen atoms and has two lone pairs.

Accurate Lewis structures allow us to visualize the necessary molecular shape for understanding bond angles and interactions among bonds.

Bond angles

Bond angles are the angles between adjacent lines in a molecular structure that represent bonds in a structural formula. These angles are integral to understanding molecular shape because they directly affect the structure and polarity of the molecule, which in turn influences physical and chemical properties.
The bond angle is determined by the shape of the molecule, which in turn is influenced by the electron-pair repulsion between the atoms.

• In (CH₄) , which has a tetrahedral geometry, the bond angles are approximately 109.5°. This angle allows the bonds to be evenly spaced around the central atom, minimizing repulsion.
• For (NH₃) , the bond angle is slightly less at about 107°, owing to the lone pair on nitrogen causing greater repulsion compared to bonding pairs.
• In (H₂O) , the presence of two lone pairs pushes the hydrogen atoms closer together, reducing the bond angle further to around 104.5°.

Thus, lone pairs play a critical role in determining bond angles due to their increased electron repulsion compared to bonding pairs.

Lone pairs

Lone pairs refer to the pairs of valence electrons that are not shared with another atom and do not participate in bonding. Although they might seem insignificant, they have a vital role in shaping molecular geometry as they exert greater repulsive forces than bonding pairs of electrons. This leads to distortion in idealized angles.

• In (NH₃) (ammonia), the molecule has one lone pair, which compresses the bond angles from an ideal tetrahedral angle of 109.5° to about 107°
• In (H₂O) , where two lone pairs are present, they further compress the bond angles from their idealized form to approximately 104.5°

Lone pairs occupy more space than bonding pairs, which means molecules with lone pairs are generally more angular or non-linear, altering physical and chemical properties due to change in electron geometry.

Tetrahedral

A tetrahedral shape is a subtype of molecular geometry where a central atom is surrounded by four other atoms, forming a shape akin to a pyramid with a triangular base. This structure is symmetrical and leads to bond angles of approximately 109.5°, as seen in (CH₄) .
The tetrahedral molecular geometry arises when a central atom forms four single bonds with surrounding atoms and no lone pairs influence the geometry.

• In carbon tetrachloride (CCl₄) , similar to methane ( CH₄) ,the carbon atom forms four bonds, conforming to a tetrahedral shape with uniform bond angles.

In chemical reactions and physical interactions, substances with a tetrahedral shape exhibit unique properties due to their spatial arrangement, which is both stable and energetically favorable.

Trigonal pyramidal

The trigonal pyramidal shape is a type of molecular geometry that results when there are three bonds and one lone pair on the central atom. This shape takes on a pyramidal structure, as seen in (NH₃) (ammonia).

• The lone pair on the nitrogen atom pushes the hydrogen atoms down, distorting the angle from a perfect tetrahedral arrangement to an angle of about 107°.

Unlike the flat, equilateral layout of a trigonal planar, the geometry of a trigonal pyramidal is a result of the lone pair exerting more repulsion than bonded pairs, creating a 3-dimensional structure. The influence of lone pairs is apparent in their ability to compress bond angles, which has significant implications on the physical properties such as polarity, reactivity, and boiling points.

Bent shape

The bent shape, or angular shape, emerges in molecules where a central atom forms two single bonds and also has two lone pairs. This structure is pivotal in molecules such as (H₂O) , where the oxygen atom holds two bonds with hydrogens and two lone pairs.

• The lone pairs compel the hydrogens to be pushed closer, bending the structure and creating a bond angle that is smaller, around 104.5°.
• This skewed distribution of electrons and angles results in highly polar molecules, signifying uneven charge distribution across the molecule.

The bent shape is vital in dictating physical properties such as solvent interactions, viscosity, and surface tension, making it crucial in fields such as biochemistry and chemical engineering. Understanding how lone pairs affect bond angles in these shapes is key to predicting molecule behavior in diverse environments.