Question

Consider three molecules: \(\mathrm{A}, \mathrm{B},\) and \(\mathrm{C}\). Molecule A has a hybridization of \(s p^{3} .\) Molecule \(\mathrm{B}\) has two more effective pairs (electron pairs around the central atom) than molecule A. Molecule C consists of two \(\sigma\) bonds and two \(\pi\) bonds. Give the molecular structure, hybridization, bond angles, and an example for each molecule.

Short answer

Molecule A has an \(sp^3\) hybridization, a tetrahedral molecular structure, bond angles of approximately 109.5°, and an example is methane (CH4). Molecule B has an \(sp^3d^2\) hybridization, an octahedral molecular structure, bond angles of 90°, and an example is sulfur hexafluoride (SF6). Molecule C has an \(sp\) hybridization, a linear molecular structure, bond angles of 180°, and an example is carbon dioxide (CO2).

Step-by-step solution

Molecule A

Molecule A has a hybridization of \(sp^3\). This type of hybridization leads to a tetrahedral molecular structure with bond angles of approximately 109.5°. Example: A classic example of an \(sp^3\) hybridized molecule is methane (CH4), with a central carbon atom bonded to four hydrogen atoms.

Molecule B

Molecule B has two more effective pairs (electron pairs around the central atom) than molecule A. Since molecule A has four effective pairs, molecule B must have six effective pairs which corresponds to an \(sp^3d^2\) hybridization. An \(sp^3d^2\) hybridized molecule has an octahedral molecular structure with bond angles of 90°. Example: One example of an \(sp^3d^2\) hybridized molecule is sulfur hexafluoride (SF6), where a central sulfur atom is bonded to six fluorine atoms.

Molecule C

Molecule C consists of two sigma (\(\sigma\)) bonds and two pi (\(\pi\)) bonds. Typically, a molecule with this composition has a double bond. A double bond consists of one \(\sigma\) bond and one \(\pi\) bond. Since there are two double bonds, the central atom is bonded to two other atoms, which means the hybridization of the central atom will be \(sp\). The molecular structure would be linear, with a bond angle of 180°. Example: A common example of a molecule with this structure is carbon dioxide (CO2). In CO2, the central carbon atom forms two double bonds with two oxygen atoms.

Key concepts

Molecular Structure

Molecular structure describes the three-dimensional arrangement of atoms within a molecule. Each arrangement is largely dictated by the type of hybridization the central atom undergoes.
For instance, in molecule A, the central atom is hybridized as \(sp^3\), a configuration that leads to a tetrahedral shape. A familiar example of this is methane \(CH_4\), where the carbon atom sits at the center connected to four hydrogen atoms.
Molecule B, on the other hand, with its \(sp^3d^2\) hybridization, forms an octahedral structure. This means that the central atom is surrounded symmetrically by six other atoms, much like sulfur hexafluoride \(SF_6\).
Lastly, molecule C, with its \(sp\) hybridization, adopts a linear structure typical of molecules with double bonds, like carbon dioxide \(CO_2\). Here, the central atom is linearly arranged with two other atoms through sigma and pi bonds.

Bond Angles

Bond angles are the angles formed between adjacent bonds from the central atom in a molecule. These angles can tell us a lot about the molecule's shape and hybridization.
In molecule A, for example, an \(sp^3\) hybridization results in bond angles of approximately 109.5°. This tetrahedral angle is due to the repulsion between the four regions of electron density around the central atom. Methane \(CH_4\) is a classic example.
Molecule B, with an \(sp^3d^2\) hybridization, showcases bond angles of 90° because of its octahedral structure. This is due to the symmetric distribution of electron pairs around the central atom, as seen in sulfur hexafluoride \(SF_6\).
Molecule C presents a different scenario with its linear shape, resulting in a 180° bond angle. This angle is characteristic of \(sp\) hybridized molecules like carbon dioxide \(CO_2\), where two atoms are directly opposite each other along a straight line.

Electron Pairs

Electron pairs, also known as valence electrons, play a pivotal role in determining a molecule's hybridization and molecular geometry. These pairs can be found in bonded form (shared between atoms) or non-bonded form (lone pairs).
In molecule A, the \(sp^3\) hybridization involves four electron pairs around the central atom. These pairs form bonds, creating a stable tetrahedral shape as seen in \(CH_4\).
Molecule B has six electron pairs due to its \(sp^3d^2\) hybridization. These electron pairs spread out in an octahedral geometry, minimizing electron repulsion in molecules like \(SF_6\).
Molecule C is unique with its two sigma bonds and two pi bonds, typically comprising four regions of electron density around the central atom as found in CO2. This linear arrangement often arises when dealing with double bonds.

Sigma and Pi Bonds

Sigma and pi bonds are fundamental types of covalent bonds you find in molecules. They are distinguished by how the electron clouds overlap between the atoms.
In molecule C, two sigma bonds and two pi bonds suggest the presence of double bonds. A sigma bond (\(\sigma\)) forms when orbitals overlap head-on. This type of overlap is the strongest and most stable, as seen in the axial overlap in CO2's carbon-atom bonds.
Pi bonds (\(\pi\)), on the other hand, occur when orbitals overlap side-by-side. These bonds are found in addition to a sigma bond in double bonds, providing additional strength but less stability than sigma bonds.
Understanding the combination of sigma and pi bonds helps explain the bond formation and stability in molecules like CO2, offering insight into their chemical behavior.