Question

Describe the shapes of \(\mathrm{BF}_{3}\) and \(\mathrm{BH}_{4}^{-}\). Assign the hybridisation of boron in these species.

Short answer

\(\text{BF}_3\) is trigonal planar with \(sp^2\) hybridisation. \(\text{BH}_4^-\) is tetrahedral with \(sp^3\) hybridisation.

Step-by-step solution

Determine the Shape of \(\text{BF}_3\)

Boron trifluoride (\(\text{BF}_3\)) is a molecule where boron is the central atom bonded to three fluorine atoms. Since it has three bonding pairs and no lone pairs, \(\text{BF}_3\) adopts a trigonal planar shape according to VSEPR (Valence Shell Electron Pair Repulsion) theory.

Identify Hybridisation in \(\text{BF}_3\)

For \(\text{BF}_3\), boron has three regions of electron density, which leads to \(\text{sp}^2\) hybridisation. This results in one \(s\) and two \(p\) orbitals mixing to form three equivalent \(sp^2\) hybrid orbitals arranged in a plane, 120° apart from each other.

Determine the Shape of \(\text{BH}_4^-\)

In the \(\text{BH}_4^-\) ion, boron is bonded to four hydrogen atoms. The electronic geometry is tetrahedral due to the four areas of electron density, and there are no lone pairs to affect the shape. Hence, \(\text{BH}_4^-\) is tetrahedral.

Identify Hybridisation in \(\text{BH}_4^-\)

For \(\text{BH}_4^-\), boron has four regions of electron density necessitating \(\text{sp}^3\) hybridisation. This involves the mixing of one \(s\) and three \(p\) orbitals to create four equivalent \(sp^3\) hybrid orbitals, forming a tetrahedral shape.

Key concepts

VSEPR Theory

The VSEPR theory, or Valence Shell Electron Pair Repulsion theory, is a key model used to determine the geometrical arrangement of atoms around a central atom in a molecule. This theory hinges on the premise that electron pairs around a central atom will arrange themselves in such a way as to minimize repulsion, maximizing the distance between them. This results in particular geometric shapes for molecules.

• For instance, in the molecule \(\text{BF}_3\), boron serves as the central atom with three electron pair regions (bonding pairs), which spread out evenly in a plane to form a trigonal planar shape with 120° angles between bonds.
• In contrast, \(\text{BH}_4^-\) involves four regions of bonding pairs around boron, leading to a tetrahedral arrangement with bond angles of approximately 109.5°.

Understanding VSEPR helps us predict molecular geometry and anticipate molecular behavior during chemical reactions.

Hybridisation

Hybridisation is a critical concept that explains the arrangement of electrons around a central atom, and it corresponds to the observed molecular geometry. During hybridisation, atomic orbitals mix to form new equivalent hybrid orbitals which are ideal for forming bonds and accommodating lone pairs.

For \(\text{BF}_3\), the boron atom undergoes \(\text{sp}^2\) hybridisation:

• The boron uses one \(s\) and two \(p\) orbitals to create three \(sp^2\) hybrid orbitals which lie in a plane.
• These hybrid orbitals arrange themselves 120° apart, perfect for forming three equivalent bonds with fluorine, resulting in a trigonal planar shape.

In \(\text{BH}_4^-\), boron undergoes \(\text{sp}^3\) hybridisation:

• Here, one \(s\) and three \(p\) orbitals mix to form four equivalent \(sp^3\) orbitals.
• This hybridisation results in a tetrahedral geometry where the hybrid orbitals are directed towards the four hydrogen atoms.

Electron Density

Electron density is a term describing the probability of finding electrons in a particular region around an atom. It plays a pivotal role in determining the shape and hybridisation of molecules. The areas of electron density include both bonding pairs and lone pairs of electrons.

• In \(\text{BF}_3\), boron has three regions of electron density surrounding it, all bonding pairs, which leads to a trigonal planar arrangement.
• For \(\text{BH}_4^-\), boron is surrounded by four regions of electron density, all bonding pairs as well, which leads to a tetrahedral shape.

By understanding electron density, we can predict the spatial arrangement of atoms in a molecule, which is crucial for explaining molecular reactivity and properties.

Trigonal Planar

A trigonal planar shape is a type of molecular geometry where one atom is positioned at the center and three atoms form an equilateral triangle around it in a single plane. This shape results in bond angles of exactly 120°.In \(\text{BF}_3\), the trigonal planar geometry arises due to the boron's three bonding pairs, with no lone pairs to alter this arrangement. The planarity and equal bond angles are direct outcomes of the \(\text{sp}^2\) hybridisation, which allows the formation of three equivalent \(sp^2\) hybrid orbitals. This symmetrical arrangement is crucial for understanding the molecule's polarity and interactions with other molecules.

Tetrahedral Shape

The tetrahedral shape is a common molecular geometry where a central atom is surrounded by four atoms, positioned at the vertices of a tetrahedron. This arrangement results in bond angles of approximately 109.5° and is characteristic of \(\text{sp}^3\) hybridisation.

In the \(\text{BH}_4^-\) ion, the tetrahedral shape is achieved because boron is bonded to four hydrogen atoms, with each bond representing a region of electron density. The lack of lone pairs allows the symmetrical distribution of the bonded atoms, creating an optimized spatial arrangement.

• This geometry is critical for various organic compounds and explains the stability and reactivity of tetrahedral molecules in chemical reactions.
• The \(\text{sp}^3\) hybridisation is a result of mixing one \(s\) and three \(p\) orbitals, ensuring all orbital engagements are equivalent in energy and shape, accommodating the four hydrogen atoms perfectly around boron.