Which, if any, of these molecules do you expect to be polar: \(\mathrm{CO}_{2}, \mathrm{CS}_{2}\), or \(\mathrm{CSO}\) (carbon is the central atom in all three molecules)? Explain your answer.

We first need to determine the molecular geometry of each molecule since that will help us identify if any cancellation of bond dipoles occurs. 1. \(\mathrm{CO}_{2}\): Carbon has four valence electrons, and oxygen has six. With double bonds between carbon and each oxygen, carbon has a full octet, and each oxygen has a double bond and two lone pairs. Therefore, \(\mathrm{CO}_{2}\) has a linear shape. 2. \(\mathrm{CS}_{2}\): Carbon has four valence electrons, and sulfur has six. With double bonds between carbon and each sulfur, carbon has a full octet, and each sulfur has a double bond and two lone pairs. Therefore, \(\mathrm{CS}_{2}\) also has a linear shape. 3. \(\mathrm{CSO}\): Carbon forms a double bond with sulfur and a double bond with oxygen. Carbon has a full octet, while sulfur and oxygen each have a double bond and two lone pairs. Thus, \(\mathrm{CSO}\) has a bent shape (approximately 120° bond angles) because it has three electron domains around the central carbon atom (VSEPR theory).

To identify if a molecule is polar, we need to evaluate the bond dipoles (electronegativity difference between bonded atoms) within the molecules. 1. \(\mathrm{CO}_{2}\): Oxygen has a higher electronegativity than carbon, so electrons are drawn towards the oxygen, creating bond dipoles. 2. \(\mathrm{CS}_{2}\): Sulfur has a higher electronegativity than carbon, so electrons are drawn towards the sulfur, creating bond dipoles. 3. \(\mathrm{CSO}\): Both oxygen and sulfur have higher electronegativity than carbon, so electrons are drawn towards them, creating bond dipoles in both cases.

Now that we know the shapes and bond dipoles, we can determine which molecules are polar. 1. \(\mathrm{CO}_{2}\): The linear shape of this molecule results in the bond dipoles canceling each other out. Thus, \(\mathrm{CO}_{2}\) is non-polar. 2. \(\mathrm{CS}_{2}\): Similarly, the linear shape of \(\mathrm{CS}_{2}\) results in bond dipoles canceling each other out. So, \(\mathrm{CS}_{2}\) is also non-polar. 3. \(\mathrm{CSO}\): In the bent-shaped \(\mathrm{CSO}\) molecule, bond dipoles from the carbon-sulfur and carbon-oxygen double bonds do not cancel each other out due to their angles and the different electronegativities of sulfur and oxygen. Consequently, \(\mathrm{CSO}\) is polar. To summarize, out of the three molecules, only \(\mathrm{CSO}\) is polar.