Question

(a) What is meant by the term polarizability? (b) Which of the following atoms would you expect to be most polarizable: $\mathrm{N}$, $\mathrm{P},$ As, $\mathrm{Sb}$ ? Explain. (c) Put the following molecules in order of increasing polarizability: ${\mathrm{GeCl}}_4$, ${\mathrm{CH}}_4$, ${\mathrm{SiCl}}_4,{\mathrm{SiH}}_4$, and ${\mathrm{GeBr}}_4$. (d) Predict the order of boiling points of the substances in part (c).

Short answer

(a) Polarizability is the ability of an atom or molecule to form instantaneous dipoles due to the distortion of electron clouds under the influence of an external electric field. (b) Sb (antimony) atom is the most polarizable among N, P, As, and Sb because it has the largest atomic size and electron cloud. (c) The order of increasing polarizability for the given molecules is: CH4 < SiH4 < SiCl4 < GeCl4 < GeBr4. (d) The boiling points will follow the same trend as polarizability: CH4 < SiH4 < SiCl4 < GeCl4 < GeBr4.

Step-by-step solution

Part (a): Defining Polarizability

Polarizability is the ability of a molecule or atom to form instantaneous dipoles under the influence of an external electric field. It is the degree to which the electron cloud around an atom or a molecule can be distorted or shifted, leading to the creation of a temporary partial charge distribution (instantaneous dipoles). The greater the polarizability, the more easily the electron cloud can be distorted.

Part (b): Comparing Polarizability of N, P, As, and Sb

Generally, polarizability increases with an increase in atomic size and the number of electrons (due to a larger electron cloud). Comparing the given elements N, P, As, and Sb, their atomic radii increase down the periodic table, resulting in the following order: N < P < As < Sb. Therefore, Sb (antimony) is the most polarizable among the four elements because it has the largest atomic size and electron cloud.

Part (c): Arranging Molecules in Order of Increasing Polarizability

To arrange the given molecules in increasing order of polarizability, we can consider the atomic sizes of the central atoms and the presence of more polarizable halogen atoms (such as Br and Cl). Based on these factors, the order of increasing polarizability will be: CH4 < SiH4 < SiCl4 < GeCl4 < GeBr4 This order is determined by considering larger central atoms with larger electron clouds (Si and Ge in comparison to C) and the presence of larger halogens (Br vs Cl).

Part (d): Predicting Boiling Points of Molecules

The boiling points of substances are strongly influenced by their intermolecular forces: stronger forces yield higher boiling points. Since polarizability is related to the strength of the London dispersion forces, larger polarizable molecules will have stronger dispersion forces and, consequently, higher boiling points. Based on the increasing polarizability order obtained in part (c), the order of boiling points will also follow the same trend: CH4 < SiH4 < SiCl4 < GeCl4 < GeBr4

Key concepts

Understanding Intermolecular Forces

Intermolecular forces are the forces that mediate interaction between molecules, including attractions and repulsions. These forces are responsible for the physical properties of substances, such as their phase, melting points, boiling points, and solubility. The key types of intermolecular forces include London dispersion forces, dipole-dipole interactions, and hydrogen bonding.

London dispersion forces are present in all molecules, whether they are polar or nonpolar. These forces arise due to instantaneous dipoles that occur when electrons in an electron cloud are unevenly distributed at a given moment in time. Polarizability plays a critical role in determining the strength of these dispersion forces. Molecules with large electron clouds and high polarizability induce stronger London dispersion forces.

Dipole-dipole interactions occur between polar molecules with permanent dipoles. These interactions are stronger than London dispersion forces and affect the boiling points of polar substances. Hydrogen bonding, a specific type of dipole-dipole interaction, occurs when hydrogen is bonded to a highly electronegative atom, significantly affecting the boiling points of compounds like water.

Atomic Size and Electron Cloud Influence on Polarizability

Polarizability is highly dependent on the size of the atom and the expanse of its electron cloud. Larger atoms have more loosely held electrons, which can be more easily induced into forming temporary dipoles. As atoms increase in size, the valence electrons are farther from the nucleus and experience less electrostatic pull from the positively charged core.

This increased distance weakens the hold on the electrons, making larger atoms intrinsically more polarizable. Additionally, the larger volume of the electron cloud offers more space for the electrons to shift when subjected to an external electric field. It's noteworthy to mention that molecules with larger atomic sizes and more electrons have an easier time distorting their electron clouds, resulting in an increased polarizability which contributes to stronger intermolecular forces and higher boiling points.

Periodic Trends in Polarizability

The polarizability of atoms and molecules follows specific trends within the periodic table. Moving down a group, polarizability increases due to the growth in atomic size and the electron cloud. For example, in group 15 where nitrogen (N), phosphorus (P), arsenic (As), and antimony (Sb) reside, antimony (Sb) is the most polarizable, as it is the largest and possesses the most extensive electron cloud.

Moving across a period from left to right, polarizability generally decreases as atoms become smaller and the effective nuclear charge increases, tightening its control over the electrons. Consequently, the ability of the atomic electron cloud to be distorted and form instantaneous dipoles reduces, leading to decreased polarizability. Understanding this trend is vital as it helps predict and explain the physical properties of different elements and compounds, such as their phase at room temperature, melting points, and boiling points.

Molecular Boiling Points and Polarizability

Boiling points of molecules are intimately connected to their intermolecular forces, which in turn have a direct correlation with polarizability. A higher polarizability suggests stronger intermolecular forces, especially London dispersion forces, resulting in higher boiling points. Molecules like methane (CH4) with low polarizability possess weak dispersion forces and boil at lower temperatures.

As you compare molecules with different central atoms or varying halogens, you observe a trend that those with larger atomic sizes and more polarizable halogens (like Ge and Br) exhibit higher boiling points. For example, in the order of increasing polarizability (CH4 < SiH4 < SiCl4 < GeCl4 < GeBr4), the boiling points follow suit. This is because these molecules have larger electron clouds allowing them to induce stronger temporary dipoles and more potent London dispersion forces. This link between molecular structure, polarizability, and boiling points is key when predicting and explaining the thermal properties of chemical compounds.