Question

For which molecular geometries (linear, bent, trigonal planar, trigonal pyramidal, tetrahedral, square planar, T-shaped, seesaw-shaped, trigonal bipyramidal, square pyramidal, octahedral) can an \(\mathrm{AB}_{x}\) molecule be nonpolar if there are (a) two different types of terminal atoms and (b) three different types of terminal atoms?

Short answer

(a) Linear, square planar, octahedral; (b) Generally none, due to lack of symmetry.

Step-by-step solution

Understanding Nonpolar Molecules

To determine whether a molecule is nonpolar, the arrangement of atoms (geometry) must allow for an even distribution of charge, such that any dipole moments cancel out. Therefore, geometries with symmetrical arrangements are likely candidates for nonpolar molecules if the surrounding atoms are identical.

Analyzing Molecular Geometries for Two Terminal Atom Types

For a molecule with two different types of terminal atoms, symmetry is less likely than if they were identical. However, certain geometries still allow for nonpolar configurations if the arrangement is symmetrical. These geometries include linear ( 2 atoms ), square planar, and octahedral (due to their ability to symmetrically distribute molecules around the central atom).

Analyzing Linear Geometry

A linear geometry, such as seen in a molecule AB_2 , is nonpolar if the two different terminal atoms (B) are identical in both directions from the central atom (A). With two different terminal atoms, symmetry does allow for potential cancellation of dipoles if arranged appropriately, resulting in a nonpolar molecule.

Analyzing Square Planar Geometry

In a square planar geometry AB_4 , there can be an array of B atoms symmetrically surrounding an A atom. When two types of terminal atoms are symmetrically placed (e.g., each diagonal or pairwise in alternate positions), the dipoles can cancel out, resulting in a nonpolar molecule.

Analyzing Octahedral Geometry

With an octahedral geometry, an AB_6 molecule with two different terminal atoms can be nonpolar if each set of three different atoms are placed on opposite faces, allowing the dipoles to cancel due to symmetry.

Analyzing Molecular Geometries for Three Terminal Atom Types

For three different types of terminal atoms, achieving nonpolar status is more challenging. Geometries like square planar or octahedral, which allow for symmetric placement of different atoms, can potentially yield a nonpolar molecule if atoms are distributed in a way that allows for symmetry.

Further Analysis for Square Planar with Three Types

In a square planar geometry AB_4 with three types of terminal atoms, achieving nonpolarity is extremely difficult due to the absence of required symmetry to cancel out dipoles completely. Typically, such cases result in a polar molecule.

Conclusion on Nonpolar at Three Terminal Types

With three different types of terminal atoms, it becomes practically impossible to achieve nonpolarity for most geometries due to the complexity of achieving a symmetric distribution necessary to cancel dipoles.

Key concepts

nonpolar molecules

Nonpolar molecules have an even distribution of electron charge, which results in having no overall dipole moment. This typically occurs when the molecule's geometry allows any dipole moments in the molecular bonds to cancel each other out.

For example, a molecule like carbon dioxide (CO extsubscript{2}) is linear and its dipole moments cancel out due to the opposite direction of individual bond dipoles. This leads to a nonpolar molecule overall.

• Nonpolar molecules are usually symmetrical.
• Symmetrical molecule structures promote uniform charge distribution.
• Equal pull on each side of the central atom nullifies the dipole moment.

dipole moments

A dipole moment is a measure of separation of positive and negative charges in a molecule. It is represented as a vector pointing from the positive charge towards the negative charge.

Dipole moments occur when there is an unequal sharing of electrons between atoms. This typically happens in bonds between atoms with differing electronegativities, such as between hydrogen and oxygen in water (H extsubscript{2}O).

• Molecules with higher polarity have greater dipole moments.
• Dipole moments can cancel out in molecules with symmetrical geometries.
• The magnitude of the dipole moment depends on both the charge difference and the distance between the charges.

symmetrical arrangement

A symmetrical arrangement in molecular geometry means that the molecules are arranged in a balanced, even fashion around the central atom. This symmetry can result in the cancellation of dipole moments, leading to a nonpolar molecule.

Examples of symmetrical geometries include linear, square planar, and octahedral arrangements. When atoms are symmetrically arranged, each dipole moment is counterbalanced by another in the opposite direction. This balance results in an overall nonpolar molecule.

• Key for determining nonpolarity is checking symmetry.
• Even distribution of identical surrounding atoms promotes symmetry.
• Structures that allow symmetry include octahedral and square planar.

terminal atoms

Terminal atoms are the atoms located at the ends of a molecule in a linear, two-dimensional, or three-dimensional layout. They are crucial in determining the molecule's overall polarity, as their arrangement and type affect molecular symmetry.

When a molecule has different terminal atoms, it can be challenging to achieve symmetry. However, certain geometries like square planar or octahedral can be designed to distribute different types of terminal atoms symmetrically.

• Identical terminal atoms aid in symmetry, promoting nonpolar nature.
• On varying terminal atoms, symmetry becomes challenging but not impossible.
• Careful arrangement of terminal atoms is essential for dipole cancellation.