Question

Rationalize the difference in boiling points in each pair: (a) ${\left({\mathrm{CH}}_3\right)}_2\mathrm{O}(-{23}^{\circ }\mathrm{C})$ and ${\mathrm{CH}}_3{\mathrm{CH}}_2\mathrm{OH}\left({78}^{\circ }\mathrm{C}\right),$ (b) ${\mathrm{CO}}_2(-{78.5}^{\circ }\mathrm{C})$ and ${\mathrm{CS}}_2\left({46.2}^{\circ }\mathrm{C}\right),(\mathbf{c}){\mathrm{CH}}_3{\mathrm{COCH}}_3\left({50.5}^{\circ }\mathrm{C}\right)$ and ${\mathrm{CH}}_3\mathrm{COOH}\left({101}^{\circ }\mathrm{C}\right)$

Short answer

The differences in boiling points can be rationalized by the intermolecular forces present in each pair of compounds: (a) Ethanol has a higher boiling point than dimethyl ether due to the presence of hydrogen bonds in addition to dipole-dipole interactions. (b) Carbon disulfide has a higher boiling point than carbon dioxide due to stronger van der Waals forces, resulting from its larger, more polarizable atoms. (c) Acetic acid has a higher boiling point than acetone due to the presence of hydrogen bonds in addition to dipole-dipole interactions.

Step-by-step solution

For pair (a), we have dimethyl ether ${\left({\mathrm{CH}}_3\right)}_2\mathrm{O}$ and ethanol ${\mathrm{CH}}_3{\mathrm{CH}}_2\mathrm{OH}$. Both of these compounds are polar and thus have dipole-dipole interactions. However, ethanol also has an -OH group, which can form hydrogen bonds. Dimethyl ether does not have any -OH groups and hence cannot form hydrogen bonds. #Step 2: Explain the difference in boiling points for pair (a)#

Boiling occurs when molecules have enough energy to overcome the intermolecular forces holding them together in the liquid state. Since ethanol can form hydrogen bonds, which are stronger than dipole-dipole interactions, it requires more energy to break these interactions and boil. This is why ethanol has a higher boiling point (${78}^{\circ }\mathrm{C}$) than dimethyl ether ($-{23}^{\circ }\mathrm{C}$). #Step 3: Identify intermolecular forces in pair (b)#

For pair (b), we have carbon dioxide ${\mathrm{CO}}_2$ and carbon disulfide ${\mathrm{CS}}_2$. Both of these are linear molecules, and due to their symmetry, they have no net dipole moment and thus no dipole-dipole interactions. However, carbon disulfide has larger, more polarizable sulfur atoms, which results in stronger van der Waals (London dispersion) forces compared to carbon dioxide. #Step 4: Explain the difference in boiling points for pair (b)#

Since ${\mathrm{CS}}_2$ has stronger van der Waals forces due to its larger, more polarizable atoms, it requires more energy to overcome these forces to boil. This is why carbon disulfide has a higher boiling point (${46.2}^{\circ }\mathrm{C}$) than carbon dioxide ($-{78.5}^{\circ }\mathrm{C}$). #Step 5: Identify intermolecular forces in pair (c)#

For pair (c), we have acetone ${\mathrm{CH}}_3{\mathrm{COCH}}_3$ and acetic acid ${\mathrm{CH}}_3\mathrm{COOH}$. Both of these compounds are polar and have dipole-dipole interactions. However, acetic acid has an -OH group, which can form hydrogen bonds, while acetone does not have any -OH groups and hence cannot form hydrogen bonds. #Step 6: Explain the difference in boiling points for pair (c)#

Since acetic acid can form hydrogen bonds, which are stronger than dipole-dipole interactions, it requires more energy to break these interactions and boil. This is why acetic acid has a higher boiling point (${101}^{\circ }\mathrm{C}$) than acetone (${50.5}^{\circ }\mathrm{C}$).

Key concepts

Intermolecular Forces

Boiling points of substances are greatly influenced by the types of intermolecular forces present. These forces are the attractions that occur between molecules.
Stronger intermolecular forces require more energy to break, resulting in higher boiling points.
The key types of intermolecular forces include:

• Hydrogen bonding: Strongest of the intermolecular forces, occurring when hydrogen is bonded to a highly electronegative atom like nitrogen, oxygen, or fluorine.
• Dipole-dipole interactions: Occur between polar molecules with permanent dipoles.
• Van der Waals forces: A collective term for interactions including London dispersion forces.

Each type has a different strength, impacting substances' boiling points.

Hydrogen Bonding

Hydrogen bonding is a special type of dipole-dipole attraction and significantly raises the boiling points of compounds.
It occurs when hydrogen is directly bonded to small, highly electronegative atoms like oxygen, nitrogen, or fluorine.
For example, in ethanol, the -OH group allows for hydrogen bonding, increasing its boiling point in comparison to dimethyl ether, which lacks such bonding capabilities. Hydrogen bonds are particularly strong because:

• They involve a significant partial charge between hydrogen and the electronegative atom, strengthening their interaction.
• The small size of hydrogen allows close approach between the atoms involved, enhancing the bond strength.

Due to these reasons, substances with hydrogen bonding not only boil at higher temperatures but also have unique properties such as high specific heat and surface tension.

Dipole-Dipole Interactions

Dipole-dipole interactions occur in polar molecules where positive and negative charges attract each other.
These interactions are stronger than van der Waals forces but weaker than hydrogen bonds.
Their presence increases the boiling point compared to non-polar molecules. For instance, acetone experiences dipole-dipole interactions because of the carbonyl group, giving it a higher boiling point than non-polar molecules like ethane.
When discussing dipole-dipole interactions, consider:

• The polarity of the molecules, which depends on shape and electronegativity differences.
• The alignment of the dipoles, with greater effectiveness the closer they can spatially align.

Recognizing these interactions helps understand why some substances require more energy to convert from liquid to gas.

Van der Waals Forces

Van der Waals forces, including London dispersion forces, occur in all molecules but are particularly prominent in non-polar molecules.
These are the weakest intermolecular forces but become significant in larger atoms or molecules.
For example, carbon disulfide, with its larger sulfur atoms compared to carbon dioxide, experiences stronger van der Waals forces, leading to its higher boiling point. Important points about van der Waals forces include:

• They rely on temporary dipoles created by electron cloud fluctuations.
• Polarizability, which measures how the electron cloud's shape can be distorted, strongly impacts these forces.

Understanding van der Waals forces is essential as they explain why even noble gases, with no other intermolecular forces, have boiling points.

Polarizability

Polarizability describes an atom or molecule's ability to distort its electron cloud. More polarizable substances have stronger intermolecular forces.
This property is crucial in understanding why larger atoms and molecules, like sulfur in CS₂ or iodine, have higher boiling points despite being non-polar.
Factors affecting polarizability:

• Atomic size: Larger atoms have more diffused electron clouds, enhancing polarizability.
• Electron count: More electrons allow greater cloud distortion and stronger London dispersion forces.

Higher polarizability generally leads to higher boiling points and viscosity, as stronger intermolecular forces require more energy to overcome. Understanding this helps in predicting and rationalizing the boiling points across different substances.