Question

(a) List the following molecules in order of increasing polar-izability: GeCl_ \(_{4}, \mathrm{CH}_{4}, \mathrm{SiCl}_{4}, \mathrm{SiH}_{4},\) and \(\mathrm{GeBr}_{4}\) . (b) Predict the order of boiling points of the substances in part (a).

Short answer

The order of increasing polarizability is: CH₄ < SiH₄ < SiCl₄ < GeCl₄ < GeBr₄. The predicted order of boiling points, based on polarizability, is: CH₄ < SiH₄ < SiCl₄ < GeCl₄ < GeBr₄.

Step-by-step solution

Determine the size and electron cloud structure of the molecules

To order the molecules in terms of polarizability, we must consider the size and electron cloud structure. Larger molecules with more electron diffuseness have a higher degree of polarizability. Let's examine the given molecules: 1. GeCl₄: Germanium tetrachloride is a tetrahedral molecule with a large central atom, Ge, and four chlorine atoms as ligands. 2. CH₄: Methane is a tetrahedral molecule with a small central carbon atom and four hydrogen atoms as ligands. 3. SiCl₄: Silicon tetrachloride is a tetrahedral molecule with a central Si atom (larger than carbon but smaller than germanium) and four chlorine atoms as ligands. 4. SiH₄: Silane is a tetrahedral molecule with a central Si atom and four hydrogen atoms as ligands. 5. GeBr₄: Germanium tetraiodide is a tetrahedral molecule with a large central Ge atom and four bromine atoms as ligands (larger than chlorine).

Order the molecules based on polarizability

Based on the size and electron cloud structure of each molecule, we can order the molecules in terms of increasing polarizability: 1. CH₄: The carbon atom is the smallest among the central atoms present in these molecules, making its electron cloud the least diffuse. 2. SiH₄: The Si atom is larger than the carbon atom in CH₄, but still has small hydrogen atoms as ligands, making it more polarizable than CH₄ but less polarizable than molecules with larger ligands. 3. SiCl₄: The silicon atom is larger and has more diffuse electron cloud due to the larger chlorine atoms as ligands. 4. GeCl₄: Ge is larger than Si and hence, more polarizable. The presence of larger chlorine ligands also increases the polarizability as compared to SiCl₄. 5. GeBr₄: This has an even more diffuse electron cloud due to the presence of larger bromine atoms as ligands compared to GeCl₄. Hence, the order of increasing polarizability is: CH₄ < SiH₄ < SiCl₄ < GeCl₄ < GeBr₄.

Predict the boiling point order

Boiling points are influenced by molecular interactions. More polarizable molecules generally have stronger London dispersion forces (LDF), which lead to higher boiling points. Based on the polarizability order we have determined, we can predict the boiling point order as follows: CH₄ < SiH₄ < SiCl₄ < GeCl₄ < GeBr₄

Key concepts

Molecular Polarizability

Molecular polarizability refers to the tendency of a molecule's electron cloud to distort in response to an external electric field. It plays a significant role in the physical properties of substances, one of which is boiling point. Polarizability increases with the size of the electron cloud and the number of electrons within a molecule.

In the exercise provided, germanium tetrabromide (GeBr₄) has the highest polarizability due to its larger size and greater electron cloud compared to the other molecules listed. Methane (CH₄), being the smallest molecule with the fewest electrons, consequently has the lowest polarizability. The given order from least to most polarizable is: CH₄ < SiH₄ < SiCl₄ < GeCl₄ < GeBr₄. This order reflects increasing molecular size and number of electrons, which lead to an increase in polarizability.

Understanding the concept of polarizability is crucial as it affects other molecular interactions that determine the physical properties of substances, like boiling points, melting points, and solubilities.

Molecular Interactions

Molecular interactions are the forces that act between stable molecules. They are important in determining the physical states and properties of compounds. Common types of molecular interactions include ionic bonds, covalent bonds, hydrogen bonds, dipole-dipole interactions, and London dispersion forces.

Among these, London dispersion forces are the weakest type of van der Waals force and are present in all molecules, affecting the physical properties such as boiling points of substances. They are especially significant in nonpolar molecules where no other stronger forces are present. The polarizability of a molecule is directly related to the strength of its London dispersion forces - the more easily a molecule's electron cloud can be distorted, the stronger the temporary dipoles and induced dipoles that occur, which in turn dictates the strength of the London dispersion forces.

London Dispersion Forces

London dispersion forces (LDF), also known as dispersion forces or induced dipole-induced dipole forces, are a type of very weak intermolecular force. These forces arise due to the momentary uneven distribution of electrons in nonpolar molecules, creating a temporary dipole which then induces a dipole in neighboring molecules.

The strength of London dispersion forces is influenced by the molecule's polarizability. Larger and more heavily electron-bearing species, like GeBr₄ in the exercise, exhibit stronger London dispersion forces compared to smaller and less electron dense species like CH₄.

Impact on Boiling Points

Due to the fact that stronger LDFs lead to an increased attraction between molecules, substances with higher polarizability typically have higher boiling points as more energy is required to overcome these forces during the phase change from liquid to gas. This is why, as indicated in the exercise, the boiling point order corresponds to the polarizability order: CH₄ < SiH₄ < SiCl₄ < GeCl₄ < GeBr₄.