Question

You have samples of four compounds: dimethyl ether, methane, difluoromethane, and ethanol. You measure the boiling points of the compounds as \(-128^{\circ} \mathrm{C},-52^{\circ} \mathrm{C}\) \(-25^{\circ} \mathrm{C},\) and \(78^{\circ} \mathrm{C},\) but then lose the labels for each sample. Make the following predictions: (a) Which compound boils at \(-128^{\circ} \mathrm{C} ?(\mathbf{b})\) Which boils at \(-52^{\circ} \mathrm{C} ?(\mathbf{c})\) Which boils at \(-25^{\circ} \mathrm{C} ?(\mathbf{d})\) Which boils at \(78^{\circ} \mathrm{C} ?\)

Short answer

(a) Methane boils at \(-128^{\circ} \mathrm{C}\) due to weak London dispersion forces. (b) Dimethyl ether boils at \(-52^{\circ} \mathrm{C}\) due to dipole-dipole interactions and stronger dispersion forces. (c) Difluoromethane boils at \(-25^{\circ} \mathrm{C}\) because of its dipole-dipole interactions. (d) Ethanol boils at \(78^{\circ} \mathrm{C}\) due to strong hydrogen bonding.

Step-by-step solution

Identifying the dominant intermolecular forces in each compound

Begin by determining the molecular structures of each compound: 1. Dimethyl ether (\(\mathrm{CH_3OCH_3}\)): An oxygen atom is present, which forms a polar bond with the two carbon atoms. There are no hydrogen bonds present. 2. Methane (\(\mathrm{CH_4}\)): The electrons are distributed symmetrically around carbon, so it is a nonpolar molecule with London dispersion forces. 3. Difluoromethane (\(\mathrm{CH_2F_2}\)): The electronegative fluorine atoms create a polar molecule, but there are no hydrogen bonds. 4. Ethanol (\(\mathrm{CH_3CH_2OH}\)): The hydroxyl group (\(\mathrm{-OH}\)) on the molecule allows for hydrogen bonding.

Compare boiling points due to intermolecular forces

Generally, the hierarchy of intermolecular forces in relation to boiling points is as follows: hydrogen bonding > dipole-dipole > London dispersion forces. Now, let's determine which compound corresponds to each boiling point: (a) A boiling point of \(-128^{\circ} \mathrm{C}\) is very low and indicates weak intermolecular forces. Methane has the weakest forces, London dispersion forces, so it is most likely the compound that boils at this temperature. (b) A boiling point of \(-52^{\circ} \mathrm{C}\) is still low, but notably higher than \(-128^{\circ} \mathrm{C}\). This indicates a compound with stronger intermolecular forces. Both dimethyl ether and difluoromethane have dipole-dipole interactions, however, dimethyl ether has a slightly larger molar mass and might exhibit stronger dispersion forces. Therefore, this boiling point is likely for dimethyl ether. (c) With a boiling point of \(-25^{\circ} \mathrm{C}\), we can infer that this compound has stronger intermolecular forces than the previous two. The remaining compound with dipole-dipole interactions, difluoromethane, is the likely candidate for this boiling point. (d) Lastly, the boiling point of \(78^{\circ} \mathrm{C}\) is significantly higher than the others, indicating very strong intermolecular forces. Ethanol exhibits hydrogen bonding, the strongest type of intermolecular force among these compounds, and is therefore the compound with this boiling point. In conclusion, we have matched the boiling points to the compounds as follows: dimethyl ether at \(-128^{\circ} \mathrm{C}\), methane at \(-52^{\circ} \mathrm{C}\), difluoromethane at \(-25^{\circ} \mathrm{C}\), and ethanol at \(78^{\circ} \mathrm{C}\).

Key concepts

Boiling Points

The boiling point of a substance is the temperature at which its liquid phase transforms into the gas phase. This transition occurs when the vapor pressure of the liquid equals the external pressure surrounding the liquid. Boiling points are essential because they give insight into the strength of the intermolecular forces holding the molecules together.

When molecules have strong intermolecular forces, such as hydrogen bonds or dipole-dipole interactions, they require more energy to break these forces apart, resulting in higher boiling points. Conversely, molecules with weaker forces, like London dispersion forces, will have lower boiling points because they need less energy to convert from liquid to gas. When analyzing different substances, it is important to consider their molecular structure to understand the types of intermolecular forces present.

Knowing the boiling point can help predict a compound's behavior in various chemical processes and its applications in real-world situations, such as cooking, refrigeration, or chemical separation techniques.

Dimethyl Ether

Dimethyl ether, with the formula \(\mathrm{CH_3OCH_3}\), is a simple ether containing an oxygen atom bonded to two methyl groups. It is a polar molecule due to the oxygen atom, which creates a slight separation of charge, although it does not engage in hydrogen bonding.

This molecule primarily experiences dipole-dipole interactions, which arise due to the positive and negative ends of polar molecules attracting each other. Additionally, it experiences London dispersion forces, but these are weaker compared to its dipole-dipole interactions. These intermolecular forces collectively result in dimethyl ether having a moderate boiling point compared to nonpolar or hydrogen-bonding compounds.

Despite being a gas at room temperature, dimethyl ether is used in various industrial applications due to its properties, including as a propellant in aerosol products and as a potential clean-burning alternative fuel.

Methane

Methane, \(\mathrm{CH_4}\), is a nonpolar molecule owing to its symmetrical tetrahedral structure, where four hydrogen atoms are evenly spaced around a central carbon atom. In this arrangement, any differences in electronegativity are canceled out, leading to an overall nonpolar molecule.

As methane lacks permanent dipoles, it interacts primarily through London dispersion forces, which are the weakest type of intermolecular forces. These forces arise due to momentary shifts in electron density, creating brief, tiny dipoles that induce similar shifts in neighboring molecules. As a result, methane has a very low boiling point, requiring little energy to transform from a liquid to a gas.

Methane is a significant component of natural gas, used extensively as a fuel source for energy production and heating. Despite its low boiling point, its abundance and energy content make it a vital component in global energy infrastructure.

Ethanol

Ethanol, with the formula \(\mathrm{CH_3CH_2OH}\), includes a hydroxyl group that engages in hydrogen bonding—one of the strongest intermolecular forces. This group consists of an oxygen atom bonded to a hydrogen atom, allowing ethanol molecules to form strong attractions with each other and other polar molecules.

In addition to hydrogen bonding, ethanol also experiences dipole-dipole interactions and London dispersion forces, but its ability to hydrogen bond is the primary contributor to its relatively high boiling point. Because a greater amount of energy is needed to overcome the hydrogen bonds, ethanol transitions to a gaseous state at a significantly higher temperature compared to weaker-bonding substances.

Ethanol is used widely in industries ranging from beverage production to pharmaceuticals, and as a biofuel in cars. Its strong intermolecular interactions and versatility make it a valuable substance in many applications.