Problem 75 - Chemistry The Central Science In Si Units

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 \(\mathrm{A}\) must consist of nonpolar molecules with lower molecular weight than B. \((\mathbf{c})\) Both liquids \(A\) and \(B\) have higher total intermolecular forces than water. (d) Liquid \(A\) is more volatile than liquid B because it has a lower boiling point. (e) At \(112^{\circ} \mathrm{C}\) both liquids have a vapor pressure of 1 atm.

Step-by-Step Solution

Answer

(d) is correct; all other statements need modification as discussed.

Step 1: Understand Boiling Point Concept

Boiling point of a liquid is the temperature at which its vapor pressure equals the external pressure. Since atmospheric pressure is 1 atm, the liquids A and B will have vapor pressures equal to 1 atm at their respective boiling points (78°C for A and 112°C for B).

Step 2: Analyze Statement (a)

Statement (a) claims both A and B have identical vapor pressures at 25°C. This is incorrect; vapor pressure decreases with an increase in boiling point. Modify the statement: 'Liquid A has a higher vapor pressure than liquid B at 25°C.'

Step 3: Analyze Statement (b)

Statement (b) says liquid A must consist of nonpolar molecules with a lower molecular weight than B. This is partly incorrect; lower molecular weight can influence the boiling point, but nonpolarity isn't a necessity. Modify the statement: 'Liquid A likely has a lower molecular weight than B but may or may not be nonpolar.'

Step 4: Analyze Statement (c)

Statement (c) asserts both A and B have higher intermolecular forces than water. This is incorrect; since both have lower boiling points than water (100°C), their intermolecular forces are likely weaker. Modify the statement: 'Both liquids A and B may have weaker intermolecular forces compared to water.'

Step 5: Analyze Statement (d)

Statement (d) indicates liquid A is more volatile due to its lower boiling point. This is correct because volatility is inversely related to boiling point; the lower the boiling point, the higher the volatility.

Step 6: Analyze Statement (e)

Statement (e) suggests at 112°C both liquids have a vapor pressure of 1 atm. This is incorrect for liquid A because it's already boiling at 78°C. Modify the statement: 'At 112°C, liquid B has a vapor pressure of 1 atm, while liquid A's vapor pressure would exceed 1 atm.'

Key Concepts

Vapor Pressure

Vapor pressure is a crucial concept when studying the boiling points of liquids. It refers to the pressure exerted by a vapor in equilibrium with its liquid phase. When the vapor pressure equals the external atmospheric pressure, the liquid boils. The notion of vapor pressure explains why different substances have different boiling points.

For instance, liquid A with a boiling point of 78°C reaches an atmospheric pressure of 1 atm at that temperature, indicating a higher vapor pressure at lower temperatures compared to liquid B, which boils at 112°C. As a result, at any temperature below their boiling points, liquid A typically has a higher vapor pressure than liquid B, making it crucial in determining their relative volatilities. This discrepancy arises due to differences in molecular interactions within the liquids.

Intermolecular Forces

Intermolecular forces determine much about a liquid's properties, including its boiling point. These forces are the attractions between molecules. The stronger the intermolecular forces, the more energy is needed to separate the molecules and, thus, the higher the boiling point.

Both liquids A and B have lower boiling points than water (100°C), suggesting they have weaker intermolecular forces compared to water. Intermolecular forces include various types such as hydrogen bonding, dipole-dipole interactions, and London dispersion forces. For example, if one of the liquids exhibits hydrogen bonding, it would generally have a higher boiling point compared to another liquid with only London dispersion forces, assuming all else is equal.

• Hydrogen bonding is the strongest among these and often leads to higher boiling points.
• London dispersion forces are the weakest, influenced strongly by molecular weight and shape.
• Dipole-dipole interactions fall intermediate in strength.

These forces play a vital role in determining the thermal behavior of substances.

Volatility

Volatility describes a liquid's tendency to evaporate. It's closely related to vapor pressure—a higher vapor pressure at a given temperature means a substance is more volatile. Therefore, volatility is inversely related to boiling point: the lower the boiling point, the higher the volatility.

Liquid A, with a boiling point of 78°C, is more volatile than liquid B, which boils at 112°C. As liquid A requires less heat to reach its vapor pressure equivalent to atmospheric pressure, it tends to evaporate more readily than liquid B. This explains why volatile liquids are often associated with high vapor pressures, as they can turn into vapor under less intense thermal conditions.

Molecular Weight

Molecular weight plays a significant role in determining physical properties such as boiling points and vapor pressures. It refers to the mass of a molecule, and generally, lighter molecules with lower molecular weights tend to have lower boiling points.

In the case of liquids A and B, liquid A having a lower boiling point implies it might have a lower molecular weight compared to B. This is because lighter molecules can generate greater kinetic energy at lower temperatures, increasing their vapor pressure, hence boiling earlier. However, the impact of molecular weight is not universal; structural aspects and intermolecular forces also significantly influence these properties. Thus, while liquid A may likely be lighter, its exact nature depends on the interplay of all these factors together.