Question

Which of the following substances has the highest polarizability: \(\mathrm{CH}_{4}, \mathrm{H}_{2}, \mathrm{CCl}_{4}, \mathrm{SF}_{6}, \mathrm{H}_{2} \mathrm{~S} ?\)

Short answer

CCl extsubscript{4} has the highest polarizability.

Step-by-step solution

Understand Polarizability

Polarizability refers to how easily the electron cloud of a molecule can be distorted by an electric field. It generally increases with the number of electrons and the size of the atom or molecule.

Analyze the Size and Number of Electrons

Check the molecular size and electron content of each molecule: - **CH extsubscript{4}**: Methane, a small molecule with 10 electrons (4 from C and 6 from 4 H). - **H extsubscript{2}**: Molecular hydrogen, extremely small, with only 2 electrons. - **CCl extsubscript{4}**: Carbon tetrachloride, larger size with 74 electrons (6 from C and 68 from 4 Cl). - **SF extsubscript{6}**: Sulfur hexafluoride, a large molecule with 70 electrons (16 from S and 54 from 6 F). - **H extsubscript{2}S**: Hydrogen sulfide, with 18 electrons (16 from S and 2 from 2 H).

Compare Molecular Sizes

Larger molecules with more electrons are generally more polarizable. - **CCl extsubscript{4}** and **SF extsubscript{6}** are the largest in size and contain the highest number of electrons compared to the other molecules listed.

Determine the Most Polarizable Substance

Between **CCl extsubscript{4}** and **SF extsubscript{6}**, **CCl extsubscript{4}** is more polarizable because chlorine atoms have larger atomic radii than fluorine atoms, making carbon tetrachloride more easily distortable.

Key concepts

Molecular Size

When discussing polarizability, molecular size plays a vital role. Bigger molecules have larger volumes, allowing for the electron cloud to be more easily influenced by an external force.
For instance, carbon tetrachloride (\(\mathrm{CCl}_4\)) and sulfur hexafluoride (\(\mathrm{SF}_6\)) are relatively large molecules. Their sizable structures mean that their electron clouds cover more space, which makes those clouds easier to distort.
On the other hand, smaller molecules like methane (\(\mathrm{CH}_4\)) and hydrogen (\(\mathrm{H}_2\)), have less volume, resulting in a negligible distortion of their electron clouds.
Thus, molecular size can greatly influence the ease at which a molecule's electron cloud reacts to external forces.

Electron Cloud Distortion

Electron cloud distortion refers to how the cloud of electrons around a molecule reacts when exposed to an electric field. This can cause the molecule to become polarized, leading to temporary changes in molecular behavior.
The extent to which a cloud is distorted depends on several factors:

• Size of the electron cloud: Bigger clouds are more spread out and thus more easily distorted.
• Nuclear hold: A strong nuclear force can hold the electron cloud tightly around the nucleus and resist distortion.

For carbon tetrachloride (\(\mathrm{CCl}_4\)), having a larger electron cloud compared to hydrogen, makes its electron cloud prone to distortion.
This effect is crucial in understanding how chemical interactions can be affected by external factors.

Number of Electrons

The number of electrons a molecule holds is another key factor in determining its polarizability. More electrons mean a larger electron cloud, as mentioned before, which makes the molecule more susceptible to distortion.
In our examples:

• \(\mathrm{CCl}_4\) has 74 electrons, signifying a hefty electron cloud ready to be distorted.
• \(\mathrm{SF}_6\) is just behind, with 70 electrons, hence still quite polarizable.
• Comparing these to \(\mathrm{H}_2\) with just 2 electrons, it's clear why larger numbers of electrons increase polarizability.

Thus, more electrons correlate with increased polarizability due to easier electron cloud deformation.

Molecular Comparison

Directly comparing molecules can give insights into their relative polarizabilities. In a collection of differing molecule sizes and electron numbers:

• \(\mathrm{CH}_4\) and \(\mathrm{H}_2\), with their smaller electron counts and sizes, are less polarizable.
• \(\mathrm{CCl}_4\) and \(\mathrm{SF}_6\) emerge as leaders in polarizability due to their extensive electron clouds and larger molecular frameworks.
• The distinction between \(\mathrm{CCl}_4\) and \(\mathrm{SF}_6\) is refined using additional factors like atomic radii.

In this comparison, it becomes clear that both size and electron number determine a molecule's response to external fields. Picking the most polarizable molecule often involves striking the balance between these factors.

Electric Field Effect on Molecules

Understanding how electric fields interact with molecules is crucial for explaining phenomena like polarizability. An electric field can influence molecules by adjusting the distribution of their charges.
Key effects include:

• Distorting the electron cloud, leading to induced dipoles.
• Weakening chemical bonds if distortion is extensive.

With \(\mathrm{CCl}_4\), for example, its considerable electron cloud and larger molecular size allow significant interactions with electric fields.
Such fields can stretch the cloud more easily compared to a smaller molecule like \(\mathrm{H}_2\), which stands up better to disturbances due to its compact structure. By appreciating these dynamics, one can appreciate finer molecular interactions in chemistry.