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 lowerboiling 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) At \(-84^{\circ} \mathrm{C}\) both liquids have vapor pressures of \(760 \mathrm{~mm} \mathrm{Hg}\).

Short answer

The correct and modified statements for the two colorless molecular liquids are: (a) The higher-boiling liquid has greater total intermolecular forces than the lower-boiling liquid. (b) The lower-boiling liquid may consist of nonpolar molecules. (c) The lower-boiling liquid may have a lower molecular weight than the higher-boiling liquid. (d) The two liquids have identical vapor pressures at their respective normal boiling points. (e) At \(-84^{\circ} \mathrm{C}\), the lower-boiling liquid has a vapor pressure of 760 mmHg, while the higher-boiling liquid has a lower vapor pressure.

Step-by-step solution

Statement a: Higher boiling liquid and intermolecular forces

The given statement is correct. The higher-boiling liquid has greater total intermolecular forces than the lower-boiling liquid. Boiling occurs when the molecules of a liquid have enough energy to overcome the forces that hold them together. If a liquid has a higher boiling point, this indicates that its intermolecular forces are stronger, and more energy is needed to break these forces.

Statement b: Lower boiling liquid and nonpolar molecules

The given statement is not correct. The modified statement is: The lower-boiling liquid may consist of nonpolar molecules. Nonpolar molecules typically have weaker intermolecular forces, such as London dispersion forces, which would lead to a lower boiling point. However, the presence of other factors, like hydrogen bonding in the higher-boiling liquid, could also lead to the observed difference in boiling point, even if the lower-boiling liquid contains polar molecules.

Statement c: Lower boiling liquid and molecular weight

The given statement is not correct. The modified statement is: The lower-boiling liquid may have a lower molecular weight than the higher-boiling liquid. While molecular weight does influence boiling points, other factors such as the type and strength of intermolecular forces also play a major role. Therefore, it is not necessarily guaranteed that the lower-boiling liquid has a lower molecular weight.

Statement d: Vapor pressures at normal boiling points

The given statement is not correct. The modified statement is: The two liquids have identical vapor pressures at their respective normal boiling points. At its normal boiling point, each liquid's vapor pressure equals the atmospheric pressure, which is around 760 mmHg. Since both liquids are at atmospheric pressure, their vapor pressures will be identical at their respective normal boiling points, but not necessarily at the same temperature.

Statement e: Vapor pressures at -84°C

The given statement is not correct. The modified statement is: At \(-84^{\circ} \mathrm{C}\), the lower-boiling liquid has a vapor pressure of 760 mmHg, while the higher-boiling liquid has a lower vapor pressure. Since the lower-boiling liquid's normal boiling point is at \(-84^{\circ} \mathrm{C}\), its vapor pressure at that temperature will be equal to the atmospheric pressure (760 mmHg). Meanwhile, for the higher-boiling liquid, the vapor pressure at this temperature will be lower than the atmospheric pressure, as it is not yet at its normal boiling point.

Key concepts

Intermolecular Forces

When studying the behavior of liquids, understanding intermolecular forces is key to grasping why substances have different boiling points. Intermolecular forces are the forces of attraction and repulsion between molecules. They are weaker than the intramolecular forces that tie atoms together within a molecule, but these intermolecular attractions or repulsions greatly influence the properties of a substance, including its boiling point.

Three main types of intermolecular forces are present in various compounds:

• London dispersion forces - These are the weakest and occur between all molecules, polar or nonpolar. They become stronger with increased molecular size or mass.
• Dipole-dipole interactions - These occur between polar molecules, with partial positive charges attracting partial negative charges.
• Hydrogen bonds - Not actual bonds, but strong dipole-dipole attractions occurring when hydrogen is bonded to highly electronegative atoms like oxygen, nitrogen, or fluorine.

These forces contribute to the overall intermolecular attractions within a liquid. The stronger these forces are, the more energy is required to separate the molecules and transition to a gas phase, resulting in a higher boiling point. This is why the statement 'The higher-boiling liquid has greater total intermolecular forces than the lower-boiling liquid' is correct.

Vapor Pressure

Vapor pressure is a crucial concept that explains a lot about the boiling point of a substance. It is defined as the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature in a closed system. In simpler terms, it is the pressure created by the gas molecules above a liquid that was once part of the liquid but has evaporated.

As you increase the temperature of a liquid, its vapor pressure increases because more molecules have enough kinetic energy to escape into the vapor phase. When a liquid's vapor pressure equals the ambient (or atmospheric) pressure, the liquid begins to boil. This is why modifications to the statement 'The two liquids have identical vapor pressures at their normal boiling points' are necessary. While it's true that both liquids have the same vapor pressure at their own normal boiling points (which is the ambient pressure), these vapor pressures are not reached at the same temperature, due to differences in the strength of the intermolecular forces in each liquid.

Molecular Weight

Molecular weight plays an intuitive role in the physical properties of substances, including boiling points. It refers to the mass of one mole of a substance and is usually calculated by summing the atomic weights of all the atoms in the molecule. A higher molecular weight often correlates with a higher boiling point because heavier molecules have more electrons, leading to stronger London dispersion forces. As these are a type of intermolecular force, they influence how tightly the molecules are held together.

However, there's an important interplay to consider: while molecules with higher molecular weights tend to have higher boiling points, this is not always the case. Other types of intermolecular forces, like hydrogen bonding and dipole-dipole interactions, can also greatly affect boiling points. That's why the statement 'The lower-boiling liquid has a lower molecular weight than the higher-boiling liquid' is not necessarily true and should be approached with caution. The molecular weight is just one factor that affects boiling point, among others.