\(A\) lone pair of electrons in the valence shell of an atom has a larger effective volume than a bonding electron pair. Lone pairs therefore repel other electron pairs more strongly than do bonding pairs. On the basis of these statements, describe how the bond angles in \(\mathrm{TeF}_{4}\) and \(\mathrm{BrF}_{5}\) deviate from those found in a trigonal bipyramid and an octahedron, respectively. Sketch the molecular shapes of \(\mathrm{TeF}_{4}\) and \(\mathrm{BrF}_{5}\) and indicate these deviations on your drawing.

Understanding the Valence Shell Electron Pair Repulsion (VSEPR) theory is fundamental when examining molecular shapes. The VSEPR theory predicts the arrangement of electron pairs around a central atom based on the idea that electron pairs in the valence shell repel each other and will arrange themselves as far apart as possible to minimize this repulsion. Consequently, the spatial arrangement of atoms in a molecule is influenced.

Due to their negative charges, both bonding pairs (shared electrons between atoms) and lone pairs (non-bonded electrons) repel one another. However, lone pairs exert a greater repulsive force as compared to bonding pairs. This is because lone pairs are closer to the nucleus and less shielded by bonding electrons, hence having a larger effective volume. As a result, their influence on the geometry of the molecule is more pronounced, often leading to deviations from idealized shapes such as the trigonal bipyramid or octahedron.

For instance, a molecule like TeF4 that would otherwise adopt a trigonal bipyramidal structure (if all electron pairs were bonding) will change its shape to accommodate the lone pair, leading to different observed bond angles and molecular shape.

Electron pair geometry provides a three-dimensional sketch of the arrangement of electron pairs, both bonding and lone pairs, around a central atom. It acts as a foundational step towards predicting the actual shape of the molecule. The VSEPR theory suggests that electron pair geometry will be influenced by the number of electron pairs. Each geometry aims to maximize distance between electron pairs to reduce repulsion.

In the case of TeF4, the central tellurium atom is surrounded by five regions of electron density: four fluoride atoms and one lone pair. According to VSEPR theory, the electron pair geometry for five regions of electron density is typically a trigonal bipyramid. Likewise, BrF5, with six regions of electron density - five fluoride atoms and one lone pair - would have an electron pair geometry resembling an octahedron.

Yet, the presence of lone pairs tends to distort this geometry. In reality, for TeF4, the lone pair will take an equatorial position, being more spread out and causing the molecule to take on a see-saw shape instead of a perfect trigonal bipyramid. This also applies to BrF5, where the lone pair's presence modifies the octahedral arrangement into a square pyramidal shape.

Bond angle deviation refers to the departure from ideal bond angles in a molecule's electron pair geometry due to the presence of lone pairs. Lone pairs occupy more space and exert greater repulsion than bonding pairs, resulting in adjacent bond angles being compressed.

For a molecule with a trigonal bipyramidal electron pair geometry, like TeF4, the expected bond angles without any distortion would be 120° in the equatorial plane and 180° between the axial positions. However, the presence of a lone pair in the equatorial position leads to bond angles slightly less than 120°. Additionally, the axial positions may experience reduced angles as well due to increased equatorial repulsion.

Similarly, an octahedral molecule like BrF5 is expected to have bond angles of 90° and 180°. Yet, the insertion of a lone pair causes the surrounding F atoms to experience a geometry shift. The resulting shape, a square pyramid, has bond angles of less than 90° between the base and the sides, and somewhat less than 180° across the opposite sides of the base. Through these adaptations, the geometry effectively minimizes electron pair repulsion, albeit at the cost of ideal angles.