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?

: 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.

: 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.

: 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.

: \(\mathrm{SO}_{2}\) 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.