Question

Explain why \(\mathrm{CO}_{2}\) and \(\mathrm{CCl}_{4}\) are both nonpolar even though they contain polar bonds.

Short answer

\(\mathrm{CO}_{2}\) and \(\mathrm{CCl}_{4}\) are nonpolar because their symmetrical geometries (linear and tetrahedral, respectively) allow the dipole moments of the polar bonds to cancel each other out, resulting in a net dipole moment of zero.

Step-by-step solution

Identify Molecular Geometry

Understand that the polarity of a molecule is determined by the shape of the molecule and the distribution of charges. For \(\mathrm{CO}_{2}\), the molecule is linear with oxygen atoms on either side of the central carbon, which results in any polar bonds cancelling out due to symmetry. \(\mathrm{CCl}_{4}\) has a tetrahedral structure with the chlorine atoms symmetrically arranged around the central carbon atom. This arrangement also allows the polarities of the individual \(C-Cl\) bonds to cancel out.

Examine Electronegativity

Consider the differences in electronegativity to determine if the bonds are polar. Oxygen is more electronegative than carbon, which makes the \(C=O\) bonds in \(\mathrm{CO}_{2}\) polar. Chlorine is also more electronegative than carbon, making the \(C-Cl\) bonds in \(\mathrm{CCl}_{4}\) polar.

Assess the Net Dipole Moment

Because of the symmetrical geometries of both molecules, the individual dipole moments of the polar bonds point in opposite directions and are of equal magnitude. They therefore cancel each other out, resulting in a net dipole moment of zero for each molecule. A net dipole moment of zero means that the molecules are nonpolar.

Key concepts

Molecular Geometry

Understanding the shape of a molecule, known as its molecular geometry, is crucial in determining its polarity. This concept is illustrated by comparing two different molecules, carbon dioxide (\r\(\mathrm{CO}_2\)) and carbon tetrachloride (\r\(\mathrm{CCl}_4\)), both of which contain polar bonds but are nonpolar as whole molecules. In \r\(\mathrm{CO}_2\), the geometry is linear with an equal distribution of charge across the molecule. As a result, the polar bonds directly oppose each other and cancel out the dipole moments. Likewise, \r\(\mathrm{CCl}_4\) possesses a tetrahedral structure with chlorine atoms equally distributed around the central carbon. This symmetry ensures that any one polar bond's dipole moment is balanced by another, leading to an overall nonpolar molecule.

To simplify, imagine molecular geometry as the arrangement of 'tug of war' teams: if the teams are evenly matched in strength and positioned symmetrically, the rope does not move, symbolizing a nonpolar molecule. However, if one team is stronger or the teams are unevenly positioned, the rope shifts towards the stronger side, representing the occurrence of a net dipole in polar molecules.

Electronegativity

Electronegativity refers to an atom's ability to attract and hold onto electrons. When looking at a chemical bond, if one atom has significantly higher electronegativity than the other, it will pull the shared electrons towards itself more strongly, creating a polar bond. For instance, oxygen has a greater electronegativity than carbon, resulting in the \r\(C=O\) bonds of \r\(\mathrm{CO}_2\) being polar. Similarly, chlorine's electronegativity is higher than carbon's, giving the \r\(C-Cl\) bonds in \r\(\mathrm{CCl}_4\) a polar characteristic.

The disparity in electronegativity is like a game of tug of war where participants have different levels of strength. The stronger participant (more electronegative atom) pulls the rope (electrons) towards them, which can create an uneven charge distribution. However, this doesn't always result in a polar molecule; as seen in \r\(\mathrm{CO}_2\) and \r\(\mathrm{CCl}_4\), the geometry can compensate for the uneven charge distribution, resulting in nonpolarity.

Net Dipole Moment

The net dipole moment measures the overall polarity of a molecule and is the vector sum of all individual bond dipoles within a molecule. It is determined by both the magnitude and direction of each bond's dipole moment. In cases where the bonds are arranged symmetrically—as with \r\(\mathrm{CO}_2\) and \r\(\mathrm{CCl}_4\)—the dipole moments of each polar bond cancel each other out because they have equal magnitude and are pointed in opposite directions. This results in a net dipole moment of zero, classifying both \r\(\mathrm{CO}_2\) and \r\(\mathrm{CCl}_4\) as nonpolar molecules.

Using the 'tug of war' analogy again, if each team pulls with equal force in opposite directions, no team wins and the rope stays in the middle. This equilibrium is analogous to a molecule having a net dipole moment of zero. Because both geometry and electronegativity define the directions and strengths of the individual dipoles, it's important to consider them together to understand the molecule's overall polarity.