The \(\mathrm{CO}_{2}\) (OCO) and OCS molecules are both linear. Both have polar bonds. \(\mathrm{CO}_{2}\) does not have a dipole moment (that is, the dipole moment is zero). Why does OCS have a dipole moment?

In the realm of chemistry, the concept of bond polarity is central to understanding the behavior of molecules. Bond polarity arises when two atoms with different electronegativities form a bond, leading to an unequal sharing of electrons. The more electronegative atom pulls the shared electrons closer, resulting in a partial negative charge (\textsl{\textdelta}-), while the less electronegative atom acquires a partial positive charge (\textsl{\textdelta}+).

For instance, in carbon dioxide (\textsl{CO}\(_{2}\)) and carbonyl sulfide (OCS), the bonds between carbon and oxygen (C-O) are polar because oxygen is more electronegative than carbon. However, the C-S bond in OCS is also polar, with the electrons being closer to carbon due to sulfur's lower electronegativity compared to carbon.

Understanding this concept is pivotal when analyzing why certain molecules, despite having polar bonds, may not exhibit a dipole moment as a whole. This leads us to explore molecular geometry, which plays an integral role in determining whether the polarities of individual bonds result in a net dipole moment for the entire molecule.

The spatial arrangement of atoms in a molecule, known as molecular geometry, is a crucial factor in defining the molecule's properties, including its dipole moment. The geometry dictates how bond polarities contribute to the overall polarity of the molecule.

In a molecule like \textsl{CO}\(_{2}\), a linear geometry ensures that the polarities of the two identical C-O bonds perfectly oppose each other. As a result, they effectively cancel out, leaving \textsl{CO}\(_{2}\) with no net dipole moment. This cancellation is a geometric consequence, not one based on the lack of bond polarity.

On the other hand, OCS, though also linear, consists of different atoms with varied electronegativities at each end of the molecule. This asymmetric distribution of electronegativities means that even with a linear shape, the differing bond polarities cannot cancel each other out perfectly, leading to a molecule with a net dipole moment. Hence, molecular geometry is the decisive detail when determining which molecules will be polar or nonpolar.

Electronegativity is a measure of an atom's ability to attract and hold onto electrons within a chemical bond. The Pauling scale, created by Linus Pauling, is commonly used to quantify this property. Higher electronegativity values indicate a greater ability to attract electrons, which is the underlying cause of bond polarity.

In a bonded pair, the atom with higher electronegativity will exhibit a greater pull on the shared electrons, creating an uneven electron distribution. This is precisely the case in polar bonds found within molecules like \textsl{CO}\(_{2}\) and OCS, where oxygen's higher electronegativity relative to carbon and sulfur shapes the bond's polarity.

Understanding the concept of electronegativity enables us to predict which bonds will be polar and to anticipate the overall polarity of molecules based on their geometry and the relative electronegativities of their constituent atoms.