Question

Suppose you have two colorless molecular liquids, one boiling at $-{84}^{\circ }\mathrm{C}$, the other at $34{}^{\circ }\mathrm{C},$ and both at atmospheric pressure. Which of the following statements is correct? For each statement that is not correct, modify the statement so that it is correct. (a) The higher-boiling liquid has greater total intermolecular forces than the lower- boiling liquid. (b) The lower-boiling liquid must consist of nonpolar molecules. (c) The lower-boiling liquid has a lower molecular weight than the higher-boiling liquid. (d) The two liquids have identical vapor pressures at their normal boiling points. (e) $\mathrm{At}-84{}^{\circ }\mathrm{C}$ both liquids have vapor pressures of $760\mathrm{mm}\mathrm{Hg}$.

Short answer

The correct statement is (a): The higher-boiling liquid has greater total intermolecular forces than the lower-boiling liquid. The other statements have been corrected as follows: (b) The lower-boiling liquid may consist of nonpolar molecules or have weaker intermolecular forces compared to the higher-boiling liquid. (c) The lower-boiling liquid may have a lower molecular weight than the higher-boiling liquid, but other factors, like the strength of intermolecular forces, also contribute. (d) The two liquids have vapor pressures of 1 atmosphere (760 mm Hg) at their respective normal boiling points. (e) At -84°C, the lower-boiling liquid has a vapor pressure of 760 mm Hg, while the higher-boiling liquid has a lower vapor pressure.

Step-by-step solution

a) Analyzing intermolecular forces of higher and lower-boiling liquids

The statement is correct. The higher-boiling liquid has greater total intermolecular forces than the lower-boiling liquid. This is because stronger intermolecular forces require more energy to break, which corresponds to a higher boiling point.

b) Checking if the lower-boiling liquid consists of nonpolar molecules

The statement is not necessarily correct. While it is true that nonpolar molecules tend to have weaker intermolecular forces and thus lower boiling points, it does not imply that the lower-boiling liquid must consist of nonpolar molecules. Corrected statement: The lower-boiling liquid may consist of nonpolar molecules or have weaker intermolecular forces compared to the higher-boiling liquid.

c) Comparing molecular weight of lower and higher-boiling liquids

The statement is not necessarily correct. Lower molecular weight can contribute to a lower boiling point, but it is not the sole determining factor. The type of intermolecular forces present also plays a significant role in boiling points. Corrected statement: The lower-boiling liquid may have a lower molecular weight than the higher-boiling liquid, but other factors, like the strength of intermolecular forces, also contribute.

d) Comparing vapor pressures of both liquids at their normal boiling points

The statement is incorrect. The vapor pressure of a substance is unique to that substance and depends on temperature. At their normal boiling points, each liquid has a vapor pressure of 1 atmosphere (760 mm Hg), but they have different normal boiling points (-84°C and 34°C). Corrected statement: The two liquids have vapor pressures of 1 atmosphere (760 mm Hg) at their respective normal boiling points.

e) Comparing vapor pressures of both liquids at -84°C

The statement is incorrect. The vapor pressure of a substance depends on the temperature, and it is different for different substances. Only the liquid with a boiling point of -84°C will have a vapor pressure of 760 mm Hg at this temperature. Corrected statement: At -84°C, the lower-boiling liquid has a vapor pressure of 760 mm Hg, while the higher-boiling liquid has a lower vapor pressure.

Key concepts

Boiling Point

The boiling point of a liquid is the temperature at which its vapor pressure equals the atmospheric pressure surrounding the liquid. This is when the liquid turns into vapor. Stronger intermolecular forces in a liquid will result in a higher boiling point because more energy is needed to break these forces. Conversely, weaker intermolecular forces correlate with a lower boiling point.
Understand that while molecular weight influences boiling point, it is not the only factor. Types of intermolecular forces, such as hydrogen bonds or dipole interactions, play a direct role. In the exercise, the liquid boiling at 34°C has stronger intermolecular forces compared to the one boiling at -84°C.
When comparing boiling points, always consider both the types of intermolecular forces and molecular weight.

Molecular Weight

Molecular weight refers to the sum of the atomic weights of all atoms in a molecule. It significantly impacts the physical properties of substances, including boiling points. However, it does not solely dictate the boiling point of a substance.
Lighter molecules may have lower boiling points due to less kinetic energy needed to reach vapor pressure. Yet, even a light molecule can have a high boiling point if it possesses strong intermolecular forces.
In the exercise, suggesting that the lower-boiling liquid must have a lower molecular weight is misleading. Although it can contribute to lower boiling points, intermolecular forces can override the weight effect.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid phase at a given temperature. This property is crucial for determining boiling point conditions. When the vapor pressure of a liquid reaches the surrounding atmospheric pressure, the liquid boils.
It varies with temperature, increasing as temperature increases. This means at higher temperatures, the vapor pressures are greater until they reach boiling point. At their boiling points, both liquids in the problem exert a vapor pressure of 760 mm Hg, though at different temperatures for each.
It's important to remember that vapor pressure is unique to each substance and its temperature, and therefore cannot be directly compared without specifying conditions.

Polar and Nonpolar Molecules

Molecules are classified based on their polarity, which affects their behaviors, including boiling points. Polar molecules have uneven charge distribution, leading to dipole-dipole interactions. These interactions frequently lead to higher boiling points due to stronger intermolecular forces.
Nonpolar molecules lack this charge distribution, generally resulting in weaker Van der Waals forces and, often, lower boiling points. However, exceptions exist since molecular shape and weight also affect boiling behavior.
In the exercise, simply stating the lower-boiling liquid must be nonpolar is too absolute. While nonpolar molecules can imply weaker forces, and thus lower boiling points, other factors must be considered such as specific molecular interactions and conditions.