Question

Arrange these substances in order of increasing boiling point. Explain your reasoning. (a) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}\) (c) \(\mathrm{CBr}_{3} \mathrm{CBr}_{2} \mathrm{CBr}_{3}\) (d) \(\mathrm{CH}_{3} \mathrm{OCH}_{3}\)

Short answer

Order: Propane < Dimethyl ether < Ethanol < Hexabromoethane

Step-by-step solution

Identify Intermolecular Forces

Begin by identifying the types of intermolecular forces present in each substance. - (a) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) - Contains hydrogen bonding due to the \(-OH\) group.- (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}\) - Contains only London dispersion forces as it is a non-polar alkane.- (c) \(\mathrm{CBr}_{3} \mathrm{CBr}_{2} \mathrm{CBr}_{3}\) - Contains London dispersion forces and potentially some dipole-dipole interactions due to the high polarizability of bromine.- (d) \(\mathrm{CH}_{3} \mathrm{OCH}_{3}\) - Contains dipole-dipole interactions due to the ether linkage.

Assess Molecular Weight and Shape

Evaluate the molecular weights and shapes, as they affect the boiling points due to dispersion forces.- (a) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) is light and has a hydrogen bond, which is a strong intermolecular force.- (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}\) is a small non-polar molecule with relatively weak dispersion forces.- (c) \(\mathrm{CBr}_{3} \mathrm{CBr}_{2} \mathrm{CBr}_{3}\) has a much higher molecular weight due to the many bromine atoms, enhancing London dispersion forces.- (d) \(\mathrm{CH}_{3} \mathrm{OCH}_{3}\) has moderate molecular weight and some polar characteristics due to the ether oxygen.

Rank by Strength of Intermolecular Forces

Rank the molecules based on the strength of their intermolecular forces, as stronger forces result in higher boiling points.- (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}\) only has weak London dispersion forces.- (d) \(\mathrm{CH}_{3} \mathrm{OCH}_{3}\) has dipole-dipole interactions, which are stronger than dispersion forces.- (a) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) demonstrates hydrogen bonding, stronger than dipole-dipole.- (c) \(\mathrm{CBr}_{3} \mathrm{CBr}_{2} \mathrm{CBr}_{3}\) has very strong dispersion forces due to its size and polarizability.

Finalize Order of Increasing Boiling Points

Compile your reasoning into an order based on increasing boiling point:- First is \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}\), due to weakest London forces.- Followed by \(\mathrm{CH}_{3} \mathrm{OCH}_{3}\) due to dipole-dipole forces.- Then \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) due to hydrogen bonding strength.- Finally, \(\mathrm{CBr}_{3} \mathrm{CBr}_{2} \mathrm{CBr}_{3}\) due to strong dispersion forces from its large molecular size.

Key concepts

Hydrogen Bonding

Hydrogen bonding is a special type of intermolecular force that occurs when hydrogen is bonded to electronegative atoms like oxygen, nitrogen, or fluorine. This creates a strong dipole where the hydrogen atom becomes partially positive and the electronegative atom becomes partially negative. The hydrogen atom then forms a "bridge" with other electronegative atoms in nearby molecules, creating a sturdy bond.

In the context of boiling points, substances with hydrogen bonding typically have higher boiling points. This is because more energy is required to break these strong intermolecular forces.

For example, in (a) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\), the presence of the \(-\mathrm{OH}\) group means hydrogen bonding is at play, making it a prime example. This specific bond is stronger than many other types of forces. Thus, elevating the boiling point of substances exhibiting these bonds. This is why alcohols like ethanol generally have high boiling points.

London Dispersion Forces

London dispersion forces, or simply dispersion forces, are often found in all types of molecules, both polar and nonpolar. These forces are a result of temporary fluctuations in the electron distribution within molecules or atoms, which creates instantaneous dipoles.

These dipoles then induce similar temporary dipoles in neighboring molecules, causing them to attract each other weakly.

The strength of London dispersion forces increases with larger or more polarizable molecules. For example, (c) \(\mathrm{CBr}_{3} \mathrm{CBr}_{2} \mathrm{CBr}_{3}\), with its large bromine atoms, has significantly stronger dispersion forces compared to smaller molecules. This is because larger atoms like bromine have a greater electron cloud that can more easily be distorted, leading to stronger instantaneous dipoles.
The result is usually higher boiling points, as seen in large, heavy molecules exhibiting strong dispersion forces.

Dipole-Dipole Interactions

Dipole-dipole interactions occur in polar molecules where there is a permanent separation of charge, creating positive and negative ends. These molecules align themselves such that opposite charges attract, resulting in an intermolecular force.

This force is stronger than London dispersion forces but usually weaker than hydrogen bonds. Example: (d) \(\mathrm{CH}_{3} \mathrm{OCH}_{3}\), or dimethyl ether, exhibits dipole-dipole interactions due to its structure. The presence of an oxygen atom gives rise to a polar bond, leading to a separation of charge. With dipole-dipole interactions, dimethyl ether demonstrates moderate boiling points, higher than non-polar substances like alkanes but lower than molecules capable of hydrogen bonding.

Understanding these interactions helps us predict molecular behavior based on structural properties.