Question

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.

Short answer

Out of the three given molecules $\mathrm{CO}_{2}$, $\mathrm{CS}_{2}$, and $\mathrm{CSO}$, only $\mathrm{CSO}$ is polar. The linear shape of $\mathrm{CO}_{2}$ and $\mathrm{CS}_{2}$ results in the bond dipoles canceling each other out, making them non-polar. In contrast, the bent shape and differing electronegativities in $\mathrm{CSO}$ prevent bond dipoles from canceling, making it a polar molecule.

Step-by-step solution

Determine the molecule's shape

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).

Determine individual bond dipoles

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.

Evaluate the overall molecular polarity

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.

Key concepts

Molecular Geometry

Understanding the shape of a molecule is crucial to determining its properties, including polarity. Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. This geometry influences how molecules interact with each other, especially in chemical reactions.
For instance, let's look at linear versus bent geometries. A linear shape, as in \(\mathrm{CO}_{2}\), means the atoms are arranged in a straight line. This is contrasted with a bent shape, seen in \(\mathrm{CSO}\), which resembles a V or an angle.
Why does this matter? Because a molecule's shape affects how the electrons are distributed. In turn, this impacts the molecule's polarity. A linear shape may allow dipoles to cancel out, leading to a non-polar molecule. However, a bent shape can prevent such cancellation, resulting in a polar molecule.

Bond Dipoles

Bond dipoles happen because different atoms attract electrons with varying strength. This is dictated by electronegativity, which we'll get into later. For now, know that a bond dipole is essentially the separation of electric charge between two atoms.
Consider a bond between carbon and oxygen. Oxygen is more electronegative, pulling electrons closer and creating a 'dipole'. This dipole is directional and often represented by an arrow pointing towards the more electronegative atom.
How do these dipoles impact polarity? Well, in molecules like \(\mathrm{CO}_{2}\), the symmetrical linear shape causes these dipoles to cancel each other out. They pull equally and in opposite directions. On the other hand, in \(\mathrm{CSO}\), the bent structure means the dipoles add up, creating an overall polarity.

Electronegativity

Electronegativity is the measure of an atom's ability to attract and hold onto electrons. It’s a key player in determining bond polarity. Generally, the more electronegative an atom, the stronger it pulls on shared electrons.
To give you some perspective, oxygen is one of the most electronegative elements, and it significantly affects bond behavior in molecules like \(\mathrm{CO}_{2}\) and \(\mathrm{CSO}\). Sulfur also has a high electronegativity but less so than oxygen.
This difference in electronegativity between bonded atoms sets up a dipole. In a molecule, these dipoles dictate whether the entire molecule will be overall polar or non-polar. If the configuration allows dipoles to counteract each other, you get a non-polar molecule like \(\mathrm{CO}_{2}\). In asymmetric configurations like \(\mathrm{CSO}\), these dipoles reinforce one another, leading to a polar molecule.

VSEPR Theory

The VSEPR Theory, or Valence Shell Electron Pair Repulsion Theory, explains the shapes of molecules. It relies on the idea that electron pairs around a central atom will arrange themselves as far apart as possible to minimize repulsion and stabilize the molecule.
This is how you determine if a molecule's geometry is linear, bent, trigonal, or otherwise. The theory helps us predict not just shape but also angles between atoms.
For example, in \(\mathrm{CO}_{2}\), there are two double bonds spreading electrons evenly across a straight line, making it linear. The \(\mathrm{CSO}\) molecule, with different atoms bonded to the central carbon, forms a bent shape because of its lone pairs and electron repulsions.
VSEPR is incredibly helpful in predicting how molecular geometry affects dipoles and overall polarity, which are essential for understanding molecular behavior.