Why is the \(\mathrm{H}-\mathrm{N}-\mathrm{H}\) angle in \(\mathrm{NH}_{3}\) smaller than the \(\mathrm{H}-\mathrm{C}-\mathrm{H}\) bond angle in \(\mathrm{CH}_{4}\) ? Why is the H-N-H angle in \(\mathrm{NH}_{4}^{+}\) identical to the \(\mathrm{H}-\mathrm{C}-\mathrm{H}\) bond angle in \(\mathrm{CH}_{4} ?\)

Bond angles are a crucial aspect of understanding molecular geometry. They refer to the angles between two adjacent lines representing bonds that a central atom in the molecule makes with its neighbors. In ideal conditions, these angles are determined by the shape that allows for the maximum separation between valence electron pairs, as per VSEPR theory (Valence Shell Electron Pair Repulsion theory). For instance, a perfect tetrahedral molecule would have bond angles of approximately 109.5 degrees.

However, the actual bond angles in molecules can deviate from these ideal values due to the presence of lone pairs or multiple bonds, both of which exert different repulsive forces compared to single bonds. This is the reason why the H-N-H bond angle in NH3 is lesser than the H-C-H bond angle in CH4.

Lone pair repulsion occurs because lone pairs of electrons are slightly closer to the central atom and occupy more space than bonding pairs. This difference arises because lone pairs are only attracted by one nucleus, whereas bonding pairs are attracted by two nuclei. As a result, lone pairs repel each other and bond pairs more strongly, causing the molecules to adjust their shapes accordingly to minimize this repulsion.

For example, the H-N-H angle in NH3 is smaller than the ideal tetrahedral angle due to the presence of a lone pair on nitrogen, which pushes the bonded hydrogen atoms closer together. This concept is a cornerstone for explaining why different molecular geometries exhibit varying bond angles.

Tetrahedral geometry is one of the most common and fundamental molecular shapes where a central atom is bonded to four other atoms placed at the corners of an imaginary tetrahedron. The ideal bond angles in a tetrahedral geometry are 109.5 degrees due to the arrangement that allows for the optimal spatial distribution of the electrons, which minimizes the repulsion between them.

In CH4, each hydrogen atom is bonded to the central carbon atom, creating a perfect tetrahedral geometry with equal bond angles, while in NH4+, the added positive charge effectively balances out the electron distribution, also resulting in a tetrahedral shape with equal bond angles.

The molecular structure of NH3 (ammonia) is based on a trigonal pyramidal geometry, which encompasses a central nitrogen atom bonded to three hydrogen atoms and one lone pair of electrons. The geometry is nearly tetrahedral, but because the lone pair occupies more space, the H-N-H bond angles are approximately 107 degrees, slightly less than the ideal tetrahedral angle. This adjustment maximizes the distance between the lone pair and the bonding pairs, reducing their repulsion as much as possible.

Methane (CH4) is the simplest hydrocarbon with a central carbon atom bonded to four hydrogen atoms. Its structure is a perfect example of tetrahedral geometry where the bond angles between the hydrogen atoms are all equal to approximately 109.5 degrees. This symmetry is due to the absence of lone pairs, allowing for the bonds to spread out evenly in space, equidistant from one another. Methane's geometry is commonly used as a reference point when comparing bond angles in other molecules.

The NH4+ ion, also known as the ammonium ion, has a central nitrogen atom bonded to four hydrogen atoms. The positive charge on the ammonium ion occurs because the nitrogen atom donates one of its electrons, resulting in no lone pairs around the nitrogen. As a consequence, the structure of NH4+ is a regular tetrahedron with bond angles of 109.5 degrees, mirroring those found in the CH4 molecule. The equal bond angles demonstrate a perfect tetrahedral symmetry, which is not distorted because the repulsion between all bonding pairs is uniform.