Problem 39 - Chemistry: The Central Science

Question

(a) What conditions must be met if a molecule with polar bonds is nonpolar? (b) What geometries will signify nonpolar molecules for \(\mathrm{AB}_{2}, \mathrm{AB}_{3}\), and \(\mathrm{AB}_{4}\) geometries?

Step-by-Step Solution

Answer

(a) For a molecule with polar bonds to be nonpolar, the polar bonds must be arranged symmetrically so that their dipoles cancel each other out, resulting in no net dipole moment. (b) The possible nonpolar geometries for the AB2, AB3, and AB4 arrangements are: 1. AB2 - Linear geometry (e.g., CO2) 2. AB3 - Trigonal planar geometry (e.g., BF3) 3. AB4 - Tetrahedral geometry (e.g., CH4)

Step 1: Part (a) - Conditions for Nonpolar Molecules

A molecule with polar bonds may exhibit a net nonpolar characteristic if the polar bonds are arranged symmetrically. If the dipoles of the polar bonds cancel each other out, the overall molecule has no net dipole moment, and it is considered nonpolar. The key is for the bond dipoles to be arranged in such a way that they are equal in magnitude and opposite in direction. This leads to no overall separation of charge and a nonpolar molecule.

Step 2: Part (b) - Nonpolar Geometries for AB2, AB3, and AB4

For molecules with AB2, AB3, and AB4 geometries, we will evaluate possible geometrical arrangements in which bond dipoles cancel out, making the molecule nonpolar. 1. AB2 Geometry: An example of this arrangement is the linear geometry, where there are two electron domains, both are bonding pairs and they are linearly aligned. The bond dipoles will have equal magnitude and opposite direction, resulting in a nonpolar outcome. A classic example of this is CO2, with a 180-degree bond angle and linear geometry. 2. AB3 Geometry: The trigonal planar geometry represents a nonpolar arrangement for the AB3 case. In this case, there are three electron domains - all are bonding pairs arranged in a trigonal planar arrangement around the central atom at a 120-degree bond angle. A typical example of a molecule with such arrangement is BF3. 3. AB4 Geometry: For the AB4 geometry, the nonpolar arrangement possible is the tetrahedral geometry. It has four electron domains, all are bonding pairs evenly distributed in a tetrahedral arrangement around the central atom with bond angles around 109.5 degrees. A well-known example of this nonpolar arrangement is methane (CH4). In each of these geometries, even if there are polar bonds present, the dipoles cancel out due to the symmetric distribution of these bonds, resulting in nonpolar molecules.

Key Concepts

Polar and Nonpolar Bonds

Understanding the difference between polar and nonpolar bonds is critical to grasping the concept of molecule polarity. A polar bond is formed when two atoms with differing electronegativities share electrons unevenly, leading to a partial positive charge on the less electronegative atom and a partial negative charge on the more electronegative atom. Examples of highly polar molecules include water (H2O) and hydrogen fluoride (HF).

Conversely, a nonpolar bond involves atoms with similar or identical electronegativities, which share electrons more or less equally and do not have partial charges. Molecules like nitrogen gas (N2) and methane (CH4) showcase nonpolar bonds. For a molecule with polar bonds to be nonpolar overall, the arrangement of these bonds must allow for the dipoles to cancel out, leading to no net dipole moment in the molecule.

Molecular Geometry

The three-dimensional arrangement of atoms within a molecule, known as molecular geometry, is a decisive factor in determining the polarity of the molecule. The spatial orientation of polar bonds can either cancel out or enhance the molecule’s dipole moments, ultimately defining whether the molecule is polar or nonpolar. For example, the bent shape of water leads to a net dipole due to the asymmetric arrangement of its polar O-H bonds. To identify nonpolar molecules, one must consider both the presence of polar bonds and their geometric arrangement.

Dipole Moment

A dipole moment is a vector quantity that measures the polarity of a molecule. It is represented by an arrow pointing from the positive to the negative pole with a magnitude proportional to the difference in charge and the distance between the charges.

Zero Net Dipole Moment

For a molecule to be nonpolar, the sum of all dipole moments must equate to zero, indicating a symmetric distribution of electrical charge and, consequently, no overall polarity.

Electron Domains

The concept of electron domains around a central atom includes both bond pairs and lone pairs of electrons. For predicting molecular geometry, electron domains are accounted for in the VSEPR (Valence Shell Electron Pair Repulsion) theory, which states that electron pairs repel each other and will arrange themselves as far apart as possible. This outcome could lead to various geometrical structures such as linear, trigonal planar, or tetrahedral, which, when arranged symmetrically, can result in a nonpolar molecule.

Symmetrical Arrangement

A symmetrical arrangement of atoms and electron domains is the key to nonpolarity in molecules with polar bonds. Symmetry in molecular geometry means the polar bonds are distributed in a way that they equally oppose each other's direction, thereby neutralizing the molecule’s polarity. Thus, molecules that exhibit symmetry with respect to their polar bonds, such as carbon dioxide (CO2) with a linear shape or boron trifluoride (BF3) with a trigonal planar shape, will be nonpolar despite having polar bonds.