Question

The molecules \(\mathrm{BF}_{3}, \mathrm{CF}_{4}, \mathrm{CO}_{2}, \mathrm{PF}_{5}\), and \(\mathrm{SF}_{6}\) are all nonpolar, even though they all contain polar bonds. Why?

Short answer

The molecules \(\mathrm{BF}_{3}, \mathrm{CF}_{4}, \mathrm{CO}_{2}, \mathrm{PF}_{5}\), and \(\mathrm{SF}_{6}\) are all nonpolar because their symmetric geometric arrangement leads to the cancellation of their polar bond's dipole moments. Even though each molecule has polar bonds, due to differences in electronegativity, the various geometries (planar trigonal, tetrahedral, linear, trigonal bipyramidal, and octahedral) ensure that the dipole moments balance each other out, resulting in overall nonpolar molecules.

Step-by-step solution

(Step 1: Understanding polarity)

Polar molecules have an uneven distribution of electron density, leading to positive and negative ends or poles. Electronegativity differences between bonding atoms cause polar bonds. However, a molecule may be nonpolar if the polar bonds within it cancel each other out due to symmetry.

(Step 2: Examining \(\mathrm{BF}_{3}\))

\(\mathrm{BF}_{3}\) has a central B atom with 3 F atoms evenly spaced around it, forming a planar trigonal geometry. This geometry is symmetric, and even though B-F bonds are polar due to the difference in electronegativity, their dipole moments cancel each other out. Thus, the entire molecule is nonpolar.

(Step 3: Examining \(\mathrm{CF}_{4}\))

\(\mathrm{CF}_{4}\) has a central C atom with 4 F atoms forming a tetrahedral geometry. The F atoms are symmetrically arranged around the C atom, and the dipole moments of the polar C-F bonds cancel each other out. This results in a nonpolar \(\mathrm{CF}_{4}\) molecule.

(Step 4: Examining \(\mathrm{CO}_{2}\))

\(\mathrm{CO}_{2}\) has a central C atom with 2 O atoms double-bonded to it, forming a linear geometry. The polar C-O bonds have their dipole moments directly opposite each other as they are 180 degrees apart, which cancels each other out. Therefore, \(\mathrm{CO}_{2}\) is nonpolar.

(Step 5: Examining \(\mathrm{PF}_{5}\))

\(\mathrm{PF}_{5}\) has a central P atom with 5 F atoms distributed in a trigonal bipyramidal geometry. The axial PF bonds are 180 degrees apart, and the equatorial PF bonds form a planar triangle, both with equal dipole moments. This symmetric arrangement of atoms causes the cancellation of the dipole moments, resulting in a nonpolar \(\mathrm{PF}_{5}\) molecule.

(Step 6: Examining \(\mathrm{SF}_{6}\))

\(\mathrm{SF}_{6}\) has a central S atom with 6 F atoms distributed in an octahedral geometry. The F atoms are arranged symmetrically around the S atom, and their dipole moments cancel each other out. Thus, the overall molecule is nonpolar. In conclusion, all these molecules have a symmetric arrangement of atoms that causes the cancellation of the dipole moments created by the polar bonds, which makes them nonpolar molecules.

Key concepts

Polar and Nonpolar Molecules

A fundamental concept in chemistry is the classification of molecules based on their polarity—a feature that dictates how molecules interact with other substances.

A polar molecule exhibits an uneven distribution of electron density, leading to distinct positive and negative regions within the molecule. This imbalance results in a molecule that has poles, much like a magnet with a north and south pole. In contrast, nonpolar molecules have an even distribution of electrons, producing no significant charge across the molecule.

These characteristics hinge on the presence of polar bonds within the molecules. Polar bonds occur due to a difference in electronegativity between two atoms bonded together; the more electronegative atom pulls the electrons closer, acquiring a slight negative charge, while the other atom becomes slightly positive. However, even molecules with polar bonds can be overall nonpolar if their molecular geometry ensures that these polarities cancel each other out.

• Water (H_2O) is a classic example of a polar molecule due to its V-shaped geometry and polar O-H bonds.
• Carbon dioxide (CO_2) though comprising polar bonds, is a nonpolar molecule because of its linear shape that allows the dipoles to cancel out.

Understanding this concept helps explain a molecule's solubility, boiling point, and reactivity—the crux of many chemical phenomena.

Electronegativity

At the heart of molecular polarity lies electronegativity, a chemical property that describes an atom's ability to attract and hold onto electrons. Electronegativity values range across the periodic table, with fluorine being the most electronegative element.

When two atoms form a bond, the difference in their electronegativities dictates the bond's character. A large difference implies a polar bond, with the more electronegative atom pulling electrons towards itself. Conversely, when the difference is negligible, the bond is considered nonpolar.

The Electronegativity Scale

The Pauling scale is commonly used to quantify electronegativity. The scale helps predict bond polarity and, consequently, molecular polarity. When the electronegativity difference is greater than 0.5, covalent bonds tend to be polar.

• Bonding between elements with similar electronegativities (e.g., H_2) results in nonpolar covalent bonds.
• Bonding between elements with dissimilar electronegativities (e.g., HCl) results in polar covalent bonds.

By mastering electronegativity, students can predict molecular behavior and interactions, essential for understanding chemistry at a deeper level.

Molecular Geometry

The spatial arrangement of atoms in a molecule, known as the molecular geometry, impacts a molecule's properties, including its polarity.

Even with polar bonds, a molecule's shape can result in a nonpolar overall character if the molecular geometry allows for an even distribution of charge. This is pivotal in understanding why molecules like BF_3 and SF_6 are nonpolar despite containing polar bonds.

Common Molecular Geometries

VSEPR (Valence Shell Electron Pair Repulsion) theory is a useful tool for predicting molecular geometries. It states that electron pairs around a central atom will arrange themselves as far apart as possible to minimize repulsion.

• Linear: Molecules like CO_2 are nonpolar because their dipole moments cancel out in a straight line.
• Tetrahedral: Molecules like CH_4 have no net dipole moment due to their symmetrical shape.
• Trigonal Pyramidal and Bent: These shapes often lead to polar molecules due to an asymmetrical distribution of charges.

Analyzing a molecule's geometry is thus integral to determining its behavior, especially when it comes to polarity, and provides insights that go beyond merely knowing its constituent atoms.