Question

All of the following have a tetrahedral shape except (a) \(\mathrm{SO}_{4}^{2-} ;\) (b) \(\mathrm{XeF}_{4} ;\) (c) \(\mathrm{CCl}_{4} ;\) (d) \(\mathrm{XeO}_{4} ;\) (e) \(\mathrm{NH}_{4}^{+}\)..

Short answer

All the given options except (b) \( \mathrm{XeF}_{4} \) have a tetrahedral shape.

Step-by-step solution

Analysis of SO4-2

The sulfur atom in \( \mathrm{SO}_{4}^{2-} \) has six valence electrons. Each of the four oxygen atoms contributes two more for bonding, making a total of 14 valence electrons. Two electrons will go to fill the S-O bonding orbitals and the remaining ten electrons fill the non-bonding orbitals. Thus, there are four S-O bonding pairs and no lone pairs on the center sulfur atom, which is indicative of a tetrahedral shape.

Analysis of XeF4

Xenon (Xe) has eight valence electrons and each of the four fluorine (F) atoms contributes one for bonding. This makes a total of 12 electrons. Two electrons will go to fill the Xe-F bonding orbitals and the remaining electrons fill the lone pairs. This results in four XeF bonding pairs and 2 lone pairs on the central atom, falling in the octahedral category, but due to the existence of lone pairs, it forms a square planar structure, not a tetrahedral.

Analysis of CCl4

Carbon (C) in \( \mathrm{CCl}_{4} \) has four valence electrons, and each of the four chlorine (Cl) atoms contributes one more for bonding, making a total of eight electrons. These electrons will fill the C-Cl bonding orbitals. Therefore, there are four C-Cl bonding pairs and no lone pairs on carbon, which matches the criteria for a tetrahedral shape.

Analysis of XeO4

Xenon (Xe) also has eight valence electrons, and each of the four oxygen (O) atoms contributes two more for bonding. This forms a total of 16 valence electrons. These electrons will fill the Xe-O bonding orbitals. Therefore, there are four Xe-O bonding pairs and no lone pairs on Xenon, fitting the criteria for a tetrahedral shape.

Analysis of NH4+

Nitrogen (N) in \( \mathrm{NH}_{4}^{+} \) has five valence electrons, and each of the four hydrogen (H) atoms contributes one more for bonding, but one electron is lost due to the +1 charge, making a total of eight electrons. These electrons will fill the N-H bonding orbitals. Hence, there are four N-H bonding pairs and no lone pair on Nitrogen, which also matches the criteria for a tetrahedral shape.

Key concepts

Tetrahedral Shape

The term "tetrahedral shape" refers to a specific molecular geometry where a central atom is bonded to four other atoms in a configuration that resembles a pyramid with a triangular base. This structure is characterized by bond angles of approximately 109.5 degrees. A molecule with a tetrahedral shape is both symmetrical and non-polar, provided all the surrounding atoms are identical.

Tetrahedral geometry arises when there are four bonding pairs and no lone pairs on the central atom. In this spatial arrangement, the electron pairs repel each other equally, distributing themselves symmetrically around the central atom.

• This geometry can be found in molecules like \(\mathrm{CCl}_{4}\) and \(\mathrm{NH}_{4}^{+}\).
• Both of these molecules have four identical atoms or groups attached to the central atom with no lone pairs affecting the geometry.

Bonding Pairs

Bonding pairs are pairs of electrons that are shared between two atoms in a molecule, forming a chemical bond. Each pair of electrons represents one bond. In the context of molecular geometry, the number and arrangement of bonding pairs significantly influence the shape of a molecule.

For instance, in a tetrahedral molecule like \(\mathrm{CCl}_{4}\), the carbon atom uses its four valence electrons to form four bonds with chlorine atoms. This results in four bonding pairs, which spreads evenly around the carbon atom to minimize repulsion, leading to a tetrahedral shape. Similarly, in \(\mathrm{NH}_{4}^{+}\), the nitrogen atom forms four bonds with hydrogen atoms, resulting in four bonding pairs.

• The presence of only bonding pairs and no lone pairs typically results in a symmetrical molecular shape.

Lone Pairs

Lone pairs refer to pairs of valence electrons that are not involved in bonding and remain on a single atom. These electrons can significantly impact the shape of a molecule by altering the repulsion dynamics among electron pairs.

Although tetrahedral shapes generally lack lone pairs on the central atom, the presence of lone pairs can change the molecular geometry drastically. For example, in \(\mathrm{XeF}_{4}\), even though it might initially appear to have a similar structure to tetrahedral molecules, the two lone pairs on xenon force the structure into a square planar shape.

• Lone pairs repulse more strongly than bonding pairs, leading to adjustments in molecular geometry.
• This is why even with four bonding pairs in \(\mathrm{XeF}_{4}\), the presence of lone pairs negates a tetrahedral shape.

Valence Electrons

Valence electrons are the outermost electrons in an atom that can participate in chemical bonding. The number of valence electrons an atom has will determine how many bonds it can form and thus influences the molecular geometry.

For example, sulfur in \(\mathrm{SO}_{4}^{2-}\) has six valence electrons, which it shares with oxygen atoms to form four bonding pairs and no lone pairs, resulting in a tetrahedral shape. On the other hand, xenon in \(\mathrm{XeF}_{4}\) uses its eight valence electrons to form four bonding pairs with fluorine and retains two lone pairs, leading to a different geometry.

• The correct distribution of valence electrons is crucial for predicting the molecular structure.
• This directly affects the shape and symmetry of the molecule, influencing properties like polarity and reactivity.