Question

Carbon dioxide has a linear geometry and is nonpolar. Yet we know that the molecule exhibits bending and stretching motions that create a dipole moment. How would you reconcile these seemingly conflicting descriptions of \(\mathrm{CO}_{2} ?\)

Short answer

Molecular vibrations in CO_{2} lead to temporary dipole moments despite its overall nonpolar linear geometry.

Step-by-step solution

Understanding Molecular Geometry

Carbon dioxide ( CO_{2} ) is a linear molecule under normal conditions due to its symmetrical arrangement. The carbon atom is situated between two oxygen atoms, making the bond angles 180 degrees.

Understanding Polarity

Each C=O bond in CO_{2} is polar because the oxygen atom is more electronegative than the carbon atom. However, as the molecule is linear and symmetrical, the dipoles cancel each other out, resulting in an overall nonpolar molecule.

Analyzing Molecular Motions

Even though CO_{2} is nonpolar, the molecule can undergo bending and stretching. These vibrational motions break the symmetry temporarily, which can induce a dipole moment.

Reconciliation of Molecular Properties

The temporary dipole moments arise only during vibrational motions. In these motions, the symmetrical nature of CO_{2} is disturbed, allowing for temporary polarization.

Key concepts

Molecular Geometry

In carbon dioxide (\( \mathrm{CO}_2 \)), understanding the molecular geometry is essential. \( \mathrm{CO}_2 \) is a linear molecule. This means that the carbon atom is located between two oxygen atoms with a bond angle of 180 degrees. This straight-line arrangement is due to

• the double bonds between carbon and each oxygen atom,
• and the symmetrical distribution of these atoms around the central carbon atom.

The linear geometry is stable and commonly found in many small molecules. It affects how the molecule interacts with electric fields and light, impacting properties like polarity, which we will discuss next.

Polarity

Polarity determines how a molecule interacts with other molecules and electric fields. In carbon dioxide, each \( \mathrm{C=O} \) bond is polar. This means

• oxygen atoms are more electronegative than carbon atoms,
• leading to a partial negative charge on oxygen and a partial positive charge on carbon.

However, in \( \mathrm{CO}_2 \), these two polar bonds are equal and opposite in direction. Since the molecule is linear, these polarities cancel each other out, resulting in an overall nonpolar molecule. This lack of net polarity means that carbon dioxide doesn't have a permanent dipole moment when in its ground state.

Dipole Moment

The dipole moment is a measure of the polarity of a molecule, indicating a separation of charge. For a molecule like \( \mathrm{CO}_2 \), despite being nonpolar, dipole moments can arise. During certain vibrational motions, like bending or stretching:

• the molecular symmetry is temporarily disrupted,
• creating a temporary dipole moment.

These temporary dipoles can affect how the molecule interacts with external fields and electromagnetic radiation. It's important to realize that these induced dipole moments are not permanent but occur transiently during molecular motions.

Molecular Motions

Molecular motions describe the dynamic aspects of molecules that can influence properties like dipole moments. In the case of \( \mathrm{CO}_2 \), the molecule can engage in vibrational motions such as bending and stretching. These motions:

• temporarily break the molecular symmetry, resulting in transient dipole moments,
• are critical in determining how the molecule absorbs infrared radiation,
• and play a role in how \( \mathrm{CO}_2 \) interacts with other molecules and environments.

Bending motions are particularly interesting because they distort the linear shape, leading to a brief moment where the molecule isn’t symmetrical. Understanding these molecular motions helps in explaining why and how carbon dioxide can exhibit transient polar characteristics despite being a nonpolar molecule overall.