Question

The molecule having zero dipole moment is: (a) \(\mathrm{CCl}_{4}\) (b) \(\mathrm{H}_{2} \mathrm{O}\) (c) \(\mathrm{HCl}\) (d) \(\mathrm{CHCl}_{2}\)

Short answer

The molecule with a zero dipole moment is \(\mathrm{CCl}_{4}\).

Step-by-step solution

Understanding Dipole Moment

A molecule will have a zero dipole moment when the individual dipoles from bond polarities cancel each other out, meaning the molecule is symmetrical, and any charge separation is balanced out.

Analyzing CCl4

The molecule \\(\text{CCl}_4\) has a tetrahedral shape with chlorine atoms symmetrically distributed around the central carbon atom. This symmetry allows the dipoles from each \(\text{C--Cl}\) bond to cancel out, resulting in an overall zero dipole moment.

Analyzing H2O

The water molecule \(\text{H}_2\text{O}\) has a bent shape due to the two lone pairs on oxygen, resulting in an asymmetric distribution of charge. The dipoles do not cancel out, and it has a non-zero dipole moment.

Analyzing HCl

\(\text{HCl}\) is a diatomic molecule with a significant electronegativity difference between hydrogen and chlorine. This causes a dipole moment to arise from the unequally distributed charge, hence it has a non-zero dipole moment.

Analyzing CHCl2

\(\text{CHCl}_2\) has a tetrahedral geometry like \(\text{CCl}_4\), but chlorine atoms are not symmetrically arranged. The asymmetry in the molecule results in an overall non-zero dipole moment.

Conclusion

Among the options, only \(\text{CCl}_4\) is completely symmetrical allowing all dipole moments to cancel out, hence it is the molecule with a zero dipole moment.

Key concepts

Understanding Molecular Symmetry

Molecular symmetry plays a crucial role in determining the dipole moment of a molecule. When we talk about symmetry, we're referring to how molecule parts are arranged in space. In a symmetrical molecule, the atoms are positioned in such a manner that their individual bond dipoles counteract each other. This balanced arrangement neutralizes the molecule's overall dipole moment. One example of this is the molecule \(\text{CCl}_4\), which is perfectly symmetrical with four chlorine atoms evenly distributed around a central carbon atom. As a result, the dipoles from each carbon-chlorine bond cancel out.

The Principle of Dipole Cancellation

Dipole cancellation occurs when the dipole moments of individual bonds in a molecule counterbalance each other. This results in a net dipole moment of zero. For dipole cancellation to be effective, molecular symmetry is essential. Understanding this principle helps in predicting whether a molecule is polar or non-polar. In symmetrical molecules like \(\text{CCl}_4\), dipole cancellation happens because the vector sum of the individual bond dipoles is zero. Without symmetry, as seen with \(\text{CHCl}_2\), a molecule can have bonded atoms, but any lack of symmetry disrupts complete dipole cancellation, resulting in a non-zero dipole moment.

Differences: Polar vs Non-Polar Molecules

A molecule's polarity is determined by its shape and the distribution of electrical charges across it. Polar molecules have a significant difference in electronegativity between bonded atoms, leading to a partial charge separation. This is evident in molecules like \(\text{H}_2\text{O}\) and \(\text{HCl}\), where the more electronegative atom pulls the shared electrons closer. Non-polar molecules, on the other hand, exhibit no overall charge separation. These molecules, such as \(\text{CCl}_4\), have their individual dipole moments cancel out due to their symmetry, creating a molecule with no net dipole moment.

Exploring Tetrahedral Geometry

Tetrahedral geometry is a common molecular shape where a central atom is connected to four peripheral atoms at the corners of a tetrahedron. This geometry is seen in molecules like \(\text{CCl}_4\), where the central carbon atom forms four bonds aimed symmetrically around it. Each bond angle is approximately 109.5 degrees, making the tetrahedral shape highly symmetrical. Due to this symmetry, the dipoles of each bond tend to cancel out, especially if identical atoms surround the central atom, resulting in a non-polar molecule. However, if the surrounding atoms are not identical, as in \(\text{CHCl}_2\), the symmetry is disrupted and the molecule may become polar.