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 BF3, CF4, CO2, PF5, and SF6 are all nonpolar despite containing polar bonds because their molecular geometries (trigonal planar, tetrahedral, linear, trigonal bipyramidal, and octahedral respectively) allow the polar bonds to be symmetrically arranged around the central atom in each molecule, causing the bond polarities to cancel each other out and resulting in nonpolar molecules overall.

Step-by-step solution

Identify the central atom

In each of the given molecules, identify the central atom. The central atom is the one that is surrounded by other atoms. - For BF3, the central atom is B (boron). - For CF4, the central atom is C (carbon). - For CO2, the central atom is C (carbon). - For PF5, the central atom is P (phosphorus). - For SF6, the central atom is S (sulfur).

Determine the molecular geometry

In this step, we determine the molecular geometry of each compound using the VSEPR (Valence Shell Electron Pair Repulsion) theory. This theory helps us predict the arrangement of atoms in a molecule based on the repulsion between electron pairs in the valence shell of the central atom. - BF3 has 3 valence electrons around B and no lone pairs, so it forms trigonal planar geometry. - CF4 has 4 valence electrons around C and no lone pairs, so it forms tetrahedron geometry. - CO2 has 2 valence electrons pairs around C and no lone pairs, so it forms a linear geometry. - PF5 has 5 valence electrons around P and no lone pairs, so it forms trigonal bipyramidal geometry. - SF6 has 6 valence electron pairs around S and no lone pairs, so it forms octahedral geometry.

Determine bond polarity

Determine the bond polarity by looking at the electronegativity values of the atoms involved in the bond. A bond will be polar if there is a difference in electronegativity between the two atoms. - B-F bonds in BF3 are polar. - C-F bonds in CF4 are polar. - C-O bonds in CO2 are polar. - P-F bonds in PF5 are polar. - S-F bonds in SF6 are polar.

Analyze the polarity of the entire molecule

Determine if the polar bonds in each molecule cancel each other out, making the entire molecule nonpolar. - In BF3, the trigonal planar geometry means that the three B-F polar bonds are symmetrically located around the central B atom at 120-degree angles. Their polarity cancels each other out, resulting in a nonpolar molecule. - In CF4, the tetrahedral geometry means that the four C-F polar bonds are symmetrically located around the central C atom. Their polarity cancels each other out, resulting in a nonpolar molecule. - In CO2, the linear geometry means that the two polar C-O bonds are symmetrically located around the central C atom. Their polarity cancels each other out, resulting in a nonpolar molecule. - In PF5, the trigonal bipyramidal geometry means that the five P-F polar bonds are symmetrically located around the central P atom. Their polarity cancels each other out, resulting in a nonpolar molecule. - In SF6, the octahedral geometry means that the six S-F polar bonds are symmetrically located around the central S atom. Their polarity cancels each other out, resulting in a nonpolar molecule. In conclusion, all five molecules are nonpolar because their molecular geometries allow the polar bonds to cancel each other out completely.

Key concepts

VSEPR Theory

The Valence Shell Electron Pair Repulsion (VSEPR) theory is crucial for understanding the shape of a molecule. It is based on the idea that electron pairs around a central atom will repel each other and thus arrange themselves as far apart as possible to minimize repulsion. This creates specific molecular shapes.

For instance, the molecule BF₃ is mentioned to have trigonal planar geometry. That's because boron, the central atom, has three electron pairs creating bonds with fluorine atoms. Since there are no lone pairs to repel, the structure is a flat triangle with 120-degree angles between bonds, minimizing repulsion and resulting in this particular shape.

Molecular Geometry

Molecular geometry, which is the three-dimensional arrangement of atoms in a molecule, directly influences a molecule's properties. The VSEPR theory provides a system to predict this geometry. For molecules like CF₄ and SF₆, with four and six bonding pairs respectively, the geometries are tetrahedral and octahedral. The symmetric arrangement of electron pairs around the central atom in these molecules means that their shapes are optimized to reduce electron pair repulsion.

In the context of nonpolarity, even with polar bonds, a molecule's symmetry can lead to an overall nonpolar molecule, as the individual bond polarities cancel each other out.

Bond Polarity

Bond polarity arises from the difference in electronegativity between two atoms involved in a bond. When electrons are not shared equally due to one atom attracting them more strongly, a polar bond is created. Most often, bonds between different types of atoms, like the C-O bonds in CO₂, exhibit polarity.

However, the presence of polar bonds does not necessarily make an entire molecule polar. It's the symmetrical arrangement of these bonds, as explained by VSEPR theory, that can lead to nonpolar molecules despite the presence of individual polar bonds.

Nonpolar Molecules

Nonpolar molecules occur when there is no net dipole moment, meaning the charges are distributed evenly in the molecule. This can happen even in molecules that have polar bonds, as demonstrated by PF₅ and the other examples provided. If the molecule's shape is symmetric, like the trigonal bipyramidal geometry in PF₅, the dipoles from the polar bonds cancel out, resulting in an overall nonpolar molecule.

This concept is key in understanding why certain substances don't mix (like oil and water) and has implications in the properties such as boiling points, solubility, and reactivity.

Electron Pair Repulsion

Electron pair repulsion is the force that shapes molecular geometry. Electron pairs include both the bonding pairs, which are shared between two atoms, and lone pairs, which are not shared. The VSEPR theory states that because electron pairs repel each other, they will arrange themselves to be as far from each other as possible in space.

This phenomenon explains not only the structure of simple molecules but also more complex geometries, where lone pairs can have an even greater repulsive effect than bonding pairs, leading to shapes like the bent structure of water.