Problem 35 - Chemistry: Principles and Reactions

Question

For each of the following pairs, choose the member with the lower boiling point. Explain your reason in each case. (a) \(\mathrm{NaCl}\) or \(\mathrm{PCl}_{3}\) (b) \(\mathrm{NH}_{3}\) or \(\mathrm{AsH}_{3}\) (c) \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}\) or \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OCH}_{3}\) (d) \(\mathrm{HI}(g)\) or \(\mathrm{HCl}(g)\)

Step-by-Step Solution

Answer

(a) NaCl or \(\mathrm{PCl}_{3}\) (b) \(\mathrm{NH}_{3}\) or \(\mathrm{AsH}_{3}\) (c) \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}\) or \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OCH}_{3}\) (d) \(\mathrm{HI(g)}\) or \(\mathrm{HCl(g)}\) Answer: (a) \(\mathrm{PCl}_{3}\) has a lower boiling point than NaCl. (b) \(\mathrm{AsH}_{3}\) has a lower boiling point than \(\mathrm{NH}_{3}\). (c) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OCH}_{3}\) (methoxyethane) has a lower boiling point than \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}\) (propanol). (d) \(\mathrm{HCl(g)}\) has a lower boiling point than \(\mathrm{HI(g)}\).

Step 1: (a) Comparing NaCl and \(\mathrm{PCl}_{3}\)

In this case, we need to compare an ionic compound (NaCl) with a molecular compound (\(\mathrm{PCl}_{3}\)). NaCl has a strong ionic bond between the sodium and chloride ions due to the electrostatic attraction. In contrast, \(\mathrm{PCl}_{3}\) is a covalent compound with weaker dispersion forces between the molecules. Therefore, we expect \(\mathrm{PCl}_{3}\) to have a lower boiling point, because less energy is needed to overcome the weak intermolecular forces compared to the strong ionic bond in NaCl.

Step 2: (b) Comparing \(\mathrm{NH}_{3}\) and \(\mathrm{AsH}_{3}\)

In this case, we need to compare two molecular compounds. \(\mathrm{NH}_{3}\) has a significant difference in electronegativity between nitrogen (3.04) and hydrogen (2.20), which creates a polar molecule with a net dipole moment. This results in the presence of strong hydrogen bonding. In \(\mathrm{AsH}_{3}\), the electronegativity difference between arsenic (2.18) and hydrogen (2.20) is much smaller, so the molecule is considered nonpolar, and the main intermolecular force holding the molecules together is the weaker dispersion forces. Thus, \(\mathrm{AsH}_{3}\) is expected to have a lower boiling point.

Step 3: (c) Comparing \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}\) and $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OCH}_{3}\(

We have to compare two organic molecules, which can form hydrogen bonding: \)\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}\( (propanol) and \)\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OCH}_{3}$ (methoxyethane or ethyl methyl ether). The similar molecular weight and size of both molecules suggest similar dispersion forces. However, propanol has an OH group that can form stronger hydrogen bonds with other molecules, while methoxyethane has an ether OCH3 group, which does not have any hydrogen atoms available to engage in hydrogen bonding directly. So, the intermolecular forces are weaker in methoxyethane, and it is expected to have a lower boiling point than propanol.

Step 4: (d) Comparing \(\mathrm{HI(g)}\) and \(\mathrm{HCl(g)}\)

Both \(\mathrm{HI(g)}\) and \(\mathrm{HCl(g)}\) are diatomic molecules that form polar covalent bonds due to the difference in electronegativity between hydrogen and the respective halogen atom. Therefore, they exhibit dipole-dipole interactions. In this case, we need to consider the atomic size and dispersion forces. The larger atomic radius in iodine than chlorine results in stronger dispersion forces in \(\mathrm{HI(g)}\) compared to \(\mathrm{HCl(g)}\). As a result, \(\mathrm{HCl(g)}\) has weaker dispersion forces and weaker overall intermolecular forces, making its boiling point lower than \(\mathrm{HI(g)}\).

Key Concepts

Intermolecular Forces

Understanding intermolecular forces is crucial for explaining why substances have different boiling points. These forces are the attractions between molecules and can be classified mainly into three types: dispersion forces, dipole-dipole interactions, and hydrogen bonding. Dispersion forces, also known as London forces, are the weakest type and are present in all molecules; they arise due to temporary dipoles as electrons move around the atomic nucleus. Dipole-dipole interactions are stronger than dispersion forces and occur in polar molecules where there is an uneven distribution of electron density. Lastly, hydrogen bonding, a special type of dipole-dipole interaction, occurs when a hydrogen atom is bonded to a highly electronegative atom such as nitrogen, oxygen, or fluorine, making it the strongest among the three types of van der Waals forces.

To determine the boiling point, we consider that substances with stronger intermolecular forces require more energy to break these attractions and, therefore, have higher boiling points. Conversely, substances with weaker intermolecular forces have lower boiling points because the molecules can be separated more easily.

Hydrogen Bonding

When it comes to hydrogen bonding, it's important to recognize its significant role in determining boiling points. This specific type of intermolecular force only occurs in molecules with a hydrogen atom attached to a highly electronegative atom, creating a strong polar bond with a high affinity for bonding with other electronegative atoms. Substances capable of hydrogen bonding, like water (H₂O) or ammonia (NH₃), exhibit much higher boiling points compared to similar-sized molecules that do not form hydrogen bonds.

For instance, in the exercise comparison between NH₃ and AsH₃, NH₃ can form hydrogen bonds due to the presence of a nitrogen atom. This results in a much higher boiling point for NH₃ compared to AsH₃, which does not form hydrogen bonds and relies only on weaker dispersion forces.

Polar and Nonpolar Molecules

Boiling points can also be understood by looking at whether a molecule is polar or nonpolar. Polarity occurs in a molecule when there is an uneven distribution of electrons between atoms with different electronegativities, leading to a molecule with a partial positive end and a partial negative end. Polar molecules, like HCl, experience dipole-dipole interactions because of these partial charges, resulting in a higher boiling point compared to nonpolar molecules with similar molar masses.

Nonpolar molecules, such as AsH₃, have a more even distribution of electron density and often only exhibit dispersion forces, which makes them easier to separate and leads to lower boiling points. In the textbook exercises, the distinction between polar and nonpolar molecules can explain the differences in boiling points between the given substances.

Ionic and Covalent Compounds

Finally, comparing ionic and covalent compounds helps to illustrate why they differ significantly in boiling points. Ionic compounds, like NaCl, are composed of positive and negative ions held together by strong electrostatic forces. These ionic bonds are much stronger than the intermolecular forces present in covalent compounds, giving ionic compounds very high boiling points.

Covalent compounds, on the other hand, are formed by atoms sharing electrons and can be polar or nonpolar. Their boiling points are generally lower than those of ionic compounds because the intermolecular forces in covalent compounds (dispersion forces, dipole-dipole interactions, and hydrogen bonding) are generally weaker than the ionic bonds. For example, in NaCl versus PCl₃, the stronger ionic bonds in NaCl lead to a much higher boiling point than PCl₃'s covalent structure with weaker dispersion forces.