Question

Suppose you have two colorless molecular liquids A and B whose boiling points are \(78^{\circ} \mathrm{C}\) and \(112^{\circ} \mathrm{C}\) respectively and both are 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) Both A and \(B\) are liquids with identical vapor pressure at room temperature of \(25^{\circ} \mathrm{C} .(\mathbf{b})\) Liquid A must consist of nonpo- (c) Both lar molecules with lower molecular weight than B. liquids A and \(B\) have higher total intermolecular forces than water. (d) Liquid \(\mathrm{A}\) is more volatile than liquid \(\mathrm{B}\) because it has a lower boiling point. (e) At \(112^{\circ} \mathrm{C}\) both liquids have a vapor pressure of \(1 \mathrm{~atm}\).

Short answer

Both liquid A and B have different vapor pressures at room temperature of \(25^{\circ}\mathrm{C}\), which depends on their molecular structures and intermolecular forces. Liquid A has a lower boiling point than B, but we cannot infer the type of molecule or molecular weight from the boiling points alone. Liquids A and B have different boiling points, which is related to the strength of their intermolecular forces, but we cannot compare their forces with water without additional information. Liquid A is more volatile than liquid B because it has a lower boiling point, indicating weaker intermolecular forces and greater volatility. At \(112^{\circ}\mathrm{C}\), liquid B has a vapor pressure of 1 atm, but we cannot determine the vapor pressure of liquid A without additional information.

Step-by-step solution

Statement (A) Correctness and Correction

Statement (A) says that both liquid A and B have identical vapor pressure at room temperature of \(25^{\circ}{\rm C}\). This statement is not necessarily correct since we are provided with only boiling points (not enough information). A correct statement could be: "Both liquid A and B have different vapor pressures at room temperature of \(25^{\circ}\mathrm{C}\), which depends on their molecular structures and intermolecular forces."

Statement (B) Correctness and Correction

Statement (B) says that liquid A must consist of nonpolar molecules with lower molecular weight than B. This statement is not correct because we cannot infer the type of molecule from the boiling point. A correct statement could be: "Liquid A has a lower boiling point than B, but we cannot infer the type of molecule or molecular weight from the boiling points alone."

Statement (C) Correctness and Correction

Statement (C) says that both liquids A and B have higher total intermolecular forces than water. This statement is not correct since we cannot infer this information from the given boiling points. A correct statement could be: "Liquids A and B have different boiling points, which is related to the strength of their intermolecular forces, but we cannot compare their forces with water without additional information."

Statement (D) Correctness and Correction

Statement (D) says that liquid A is more volatile than liquid B because it has a lower boiling point. This statement is correct. A lower boiling point is an indication of weaker intermolecular forces, which results in a higher vapor pressure and greater volatility.

Statement (E) Correctness and Correction

Statement (E) says that at \(112^{\circ}\mathrm{C}\) both liquids have a vapor pressure of 1 atm. This statement is not correct as we know that liquid B has a boiling point of \(112^{\circ}\mathrm{C}\), which means that its vapor pressure is 1 atm at this temperature, but we have no information on the vapor pressure of liquid A at this temperature. A correct statement could be: "At \(112^{\circ}\mathrm{C}\), liquid B has a vapor pressure of 1 atm, but we cannot determine the vapor pressure of liquid A without additional information."

Key concepts

Vapor Pressure

Vapor pressure is an important concept when understanding the behavior of liquids. It refers to the pressure exerted by the vapor of a liquid when it is in equilibrium with its liquid phase at a specific temperature.
The higher the vapor pressure, the more readily a liquid evaporates into a gaseous state. Thus, vapor pressure is intimately linked to the boiling point of a liquid.

• Liquids with higher vapor pressure have a lower boiling point because they require less heat to convert into vapor.
• Conversely, liquids with lower vapor pressure have higher boiling points.

These relationships help explain why in our case, liquid A has a lower boiling point than liquid B. Liquid A would have a higher vapor pressure at any given temperature, including room temperature. This is why it is more volatile compared to liquid B.

Intermolecular Forces

Intermolecular forces are the forces of attraction or repulsion between molecules. They play a central role in determining a liquid's properties such as boiling point and vapor pressure.
Stronger intermolecular forces result in higher boiling points because more energy is required to separate the molecules from each other. This would mean a lower vapor pressure due to the “stickiness” of the molecules.

• Molecules with strong hydrogen bonding, for example, generally exhibit higher boiling points.
• Weaker van der Waals forces result in lower boiling points.

In the context of our exercise, the different boiling points of liquids A and B suggest variations in their intermolecular forces. Liquid A, with its lower boiling point, likely has weaker intermolecular attractions than liquid B.

Volatility

Volatility refers to how easily a liquid transforms into a gas. A substance's volatility is directly tied to both its vapor pressure and boiling point.

• Highly volatile liquids have high vapor pressures at a given temperature and low boiling points, indicating weaker intermolecular forces and easier transition into a vapor state.
• Low volatility is characteristic of substances with low vapor pressures and high boiling points, suggesting stronger intermolecular forces.

In our discussion, liquid A is noted for being more volatile than liquid B because its lower boiling point means it can vaporize more readily. This is a useful characteristic in applications where rapid evaporation is desired, such as in fuel or volatile solvents.