Question

Consider the \(\mathrm{CCl}_{4}\) molecule. a) Are the \(\mathrm{C}-\mathrm{Cl}\) bonds in \(\mathrm{CCl}_{4}\) polar? b) Where is the center of positive charge? c) Where is the center of negative charge? d) Why is the dipole moment zero for \(\mathrm{CCl}_{4}\) ?

Short answer

a) Yes, the \(\mathrm{C}-\mathrm{Cl}\) bonds in \(CCl_4\) are polar due to the difference in electronegativity between Cl and C. b) The center of positive charge in \(CCl_4\) is on the Carbon atom. c) The center of negative charge is distributed among the Chlorine atoms. d) Despite the \(\mathrm{C}-\mathrm{Cl}\) bonds being polar, the dipole moment of \(CCl_4\) is zero due to the tetrahedral molecular geometry, causing the bond dipoles to offset each other.

Step-by-step solution

Determining Polarity

A covalent bond between two atoms is polar when the atoms have different electronegativities. Chlorine(Cl) is more electronegative than Carbon(C), hence electrons are pulled more towards Chlorine which results in a partial negative charge(\(\delta^-\)) on Cl and a partial positive charge(\(\delta^+\)) on Carbon(C). Thus, the \(\mathrm{C}-\mathrm{Cl}\) bonds in \(CCl_4\) are polar.

Locating the Center of Positive Charge

The center of positive charge in a molecule is usually located on the atom with the lowest electronegativity because it tends to lose electron density to other atoms. In the case of \(CCl_4\), the Carbon atom has a lower electronegativity than Chlorine, hence it carries the partial positive charge (\(\delta^+\)). Thereby, the Carbon atom is the center of positive charge.

Locating the Center of Negative Charge

The center of negative charge in a molecule is located on the atom that is more electronegative since it attracts electron density towards it. In \(CCl_4\), the Chlorine atoms are more electronegative and thus carry the partial negative charge (\(\delta^-\)). Therefore, the center of negative charge is distributed among the Chlorine atoms.

Understanding the Zero Dipole Moment

The dipole moment of a molecule is a measure of its overall polarity. It is dependent upon both the magnitude of the charges and the geometry of the molecule. In the case of \(CCl_4\), even though the \(\mathrm{C}-\mathrm{Cl}\) bonds are polar, the tetrahedral geometry of the molecule causes the bond dipoles to cancel each other out due to symmetry. As a result, the net dipole moment is zero.

Key concepts

Polar Covalent Bonds

Let's consider the nature of polar covalent bonds by examining a molecule of carbon tetrachloride (\(CCl_4\)). In chemistry, the term 'polar' refers to a separation of electric charge leading to a molecule or its chemical groups having an electric dipole moment, with a partially positive charge on one end and a partially negative charge on the other.

The idea is pretty straightforward: when two atoms in a molecule have different electronegativities, the bonding electrons aren't shared equally. Instead, they spend more time closer to the atom with the higher electronegativity. In the case of \(CCl_4\), the chlorine atoms are more electronegative than the carbon atom. Because of this, the \(C-Cl\) bonds are indeed polar, with the electrons being pulled slightly towards the chlorine atoms endowing them with a partial negative charge (\(\delta^-\)), and a corresponding partial positive charge (\(\delta^+\)) on the carbon atom.

Electronegativity

Electronegativity is a measure of how strongly an atom can attract or hold onto electrons when it is part of a compound. It's a crucial concept when discussing polar covalent bonds because it explains why certain atoms become partially negative or partially positive.

In many molecules, such as \(CCl_4\), differences in electronegativity between the carbon and chlorine atoms create poles, or ends, that have differing charges, just like a magnet. This occurs because chlorine, being more electronegative, hoards more of the electron density for itself, leaving the less electronegative carbon with a deficiency of electrons, and therefore, a slight positive charge. The Pauling scale is the most commonly used scale for electronegativity, with higher values indicating greater electronegativity.

• Chlorine's electronegativity: ~3.16 on the Pauling scale.
• Carbon's electronegativity: ~2.55 on the Pauling scale.

This difference can be visualized like a tug-of-war, where chlorine is the stronger team pulling the 'rope' (electrons) towards itself.

Dipole Moment

The dipole moment is a vector quantity that measures the polarity of a molecule. Imagine it as an arrow pointing from the positive pole to the negative pole, with its length representing the magnitude of the charge separation and the polarity of the bond. The unit for dipole moment is the debye (\(D\)).

For individual bonds, the dipole moment will point from the less electronegative atom to the more electronegative atom, indicating the direction the electron density is skewed. However, in the \(CCl_4\) molecule, although each \(C-Cl\) bond has a dipole moment, they all cancel out due to the molecule's symmetrical shape, resulting in a net dipole moment of zero. This may seem counterintuitive since the bonds are polar, but the symmetry of the molecule's tetrahedral geometry means that all the individual dipole moments point in opposite directions and nullify one another.

Molecular Geometry

The molecular geometry or shape of a molecule plays a key role in determining its overall polarity. When we say that a molecule like \(CCl_4\) is tetrahedral, we’re describing the spatial arrangement of its atoms—a central carbon atom with four chlorine atoms at equal distances and angles from it.

This particular geometry is crucial in understanding why, despite having polar covalent bonds, the \(CCl_4\) molecule itself isn't polar. Although you have regions of partial positive and negative charges due to the polar bonds, the symmetrical arrangement allows the dipoles to cancel out. Consequently, no side of the molecule is overall more negative or positive, and we say that the molecule is nonpolar with a zero dipole moment. In contrast, other shapes like bent or trigonal pyramidal can lead to non-cancelling dipole moments and overall polarity in molecules.