Question

Consider \(\mathrm{SO}_{2}\) and \(\mathrm{CO}_{2}\). Both have polar covalent bonds. One of these molecules is polar and the other is nonpolar. Which is which and why?

Short answer

\(\mathrm{SO}_{2}\) is a polar molecule because of its bent molecular geometry and the difference in electronegativity between sulfur and oxygen atoms. In contrast, \(\mathrm{CO}_{2}\) is nonpolar due to its linear molecular geometry and the cancellation of bond dipoles, despite the electronegativity difference between carbon and oxygen.

Step-by-step solution

Determine the electronegativity of the atoms in the molecules

: Electronegativity is the ability of an atom to attract the shared electrons in a bond. In both \(\mathrm{SO}_{2}\) and \(\mathrm{CO}_{2}\), there are polar covalent bonds. Oxygen has a higher electronegativity (3.44) than carbon (2.55) and sulfur (2.58), causing an uneven sharing of electrons between the atoms.

Analyze the molecular geometry of the molecules

: To determine the polarity of the entire molecule, we need to analyze the molecular geometry. A molecule's shape is based on the arrangement of its atoms, which can be predicted by the VSEPR (valence shell electron pair repulsion) theory. For \(\mathrm{SO}_{2}\), the central atom is sulfur, which has an expanded octet with six valence electrons, and there are two terminal oxygen atoms. The molecular geometry of \(\mathrm{SO}_{2}\) is a bent (angular) shape, with a bond angle of approximately 120 degrees. For \(\mathrm{CO}_{2}\), the central atom is carbon with four valence electrons, and there are two terminal oxygen atoms. The molecular geometry of \(\mathrm{CO}_{2}\) is linear, with a bond angle of 180 degrees.

Determine the polarity of the molecules based on electronegativity and molecular geometry

: Considering both electronegativity and molecular geometry, we can now determine the polarity of \(\mathrm{SO}_{2}\) and \(\mathrm{CO}_{2}\). In \(\mathrm{SO}_{2}\), the bent geometry combined with the different electronegativities of sulfur and oxygen atoms causes the individual bond dipoles to not cancel each other out, resulting in a net molecular dipole moment. Therefore, \(\mathrm{SO}_{2}\) is a polar molecule. In contrast, \(\mathrm{CO}_{2}\) has a linear geometry, and despite the difference in electronegativity between carbon and oxygen, the bond dipoles are exactly opposite, cancelling each other out. This results in no net molecular dipole moment. Therefore, \(\mathrm{CO}_{2}\) is a nonpolar molecule.

Conclusion

: \(\mathrm{SO}_{2}\) is a polar molecule due to its bent molecular geometry and the difference in electronegativity between sulfur and oxygen atoms, while \(\mathrm{CO}_{2}\) is a nonpolar molecule due to its linear molecular geometry and the cancellation of the bond dipoles, even with the electronegativity difference between carbon and oxygen.

Key concepts

Electronegativity

Electronegativity refers to how strongly an atom can attract electrons towards itself when it is bonded with another atom. It is a crucial aspect when discussing molecular polarity because it dictates how the electrons are distributed between the atoms in a bond. In a molecule, when atoms with different electronegativities bond, the electrons are not shared equally. This leads to the formation of polar covalent bonds.

• The higher the electronegativity of an atom, the more it attracts electrons.
• Oxygen, for example, has a high electronegativity of 3.44, which means it attracts shared electrons more compared to sulfur (2.58) and carbon (2.55).

Abundant in chemistry, the concept of electronegativity helps to predict whether a bond will be nonpolar covalent, polar covalent, or ionic. In the context of \(\mathrm{SO}_{2}\) and \(\mathrm{CO}_{2}\), both molecules contain polar covalent bonds where oxygen's high electronegativity creates a dipole moment. However, the final molecular polarity depends also on the molecular geometry.

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. It influences whether a molecule as a whole will be polar or nonpolar. The geometry is determined by the number of atoms surrounding a central atom, and how they are arranged in space, taking into account the repulsions between electron pairs on the central atom.

• In \(\mathrm{SO}_{2}\), the geometry is bent due to the presence of lone pairs on the sulfur atom, causing the angle between the bonds to register at about 120 degrees.
• In \(\mathrm{CO}_{2}\), the geometry is linear, which means the two oxygen atoms are on opposite sides of the central carbon atom, resulting in an angle of 180 degrees.

These shapes are essential in determining the overall polarity of the molecule. While \(\mathrm{SO}_{2}\)'s bent shape allows for a net dipole moment, making it polar, \(\mathrm{CO}_{2}\)'s linear shape facilitates the cancellation of dipoles, resulting in a nonpolar molecule.

VSEPR Theory

The VSEPR Theory, short for Valence Shell Electron Pair Repulsion Theory, is pivotal for predicting the shape of individual molecules. It postulates that electron pairs surrounding an atom will arrange themselves as far apart as possible to minimize repulsive forces. This theory helps in understanding why molecules adopt their particular shapes, and how these shapes affect their properties.

• In the case of \(\mathrm{SO}_{2}\), sulfur has lone pairs causing the bonds to adopt a bent shape as the pairs push away from each other to minimize repulsion.
• Conversely, \(\mathrm{CO}_{2}\) adopts a linear shape as there are no lone pairs on the central carbon atom, allowing the bonds to align in a straight line, minimizing repulsion effectively.

Thus, VSEPR Theory not only predicts molecular shapes but also helps us infer the physical and chemical characteristics embedded in the molecules' geometry. Understanding VSEPR provides profound insight into how electronegativity and geometry come together to define molecular polarity.