Problem 9 - Chemistry An Atoms First Approach

Question

Is molality or molarity dependent on temperature? Explain your answer. Why is molality, and not molarity, used in the equations describing freezing-point depression and boiling point elevation?

Step-by-Step Solution

Answer

Molality is independent of temperature because it is based on the mass of solvent, which does not change with temperature. Molarity is dependent on temperature because it is based on the volume of the solution, which can change with temperature. Molality is used in equations describing freezing-point depression and boiling point elevation because it remains constant with temperature, providing a more accurate measurement of solute particle concentration. This ensures that calculated values for these colligative properties are consistent and accurate.

Step 1: Understand Molality and Molarity

Molality is the number of moles of solute per kilogram of solvent, and molarity is the number of moles of solute per liter of solution. We need to determine if either of these measurements is affected by temperature in order to answer the question.

Step 2: Identify the Temperature Dependence

Molarity is dependent on temperature because it is based on the volume of the solution, and the volume can change with temperature. On the other hand, molality is not dependent on temperature because it is based on the mass of solvent, which does not change with temperature. Therefore, molality is independent of temperature.

Step 3: Use of Molality in Freezing Point Depression and Boiling Point Elevation Equations

Molality is used in the equations describing freezing-point depression and boiling point elevation because it is not affected by temperature. These properties are colligative properties, which depend on the concentration of solute particles in the solution. Since molality remains constant with temperature, it provides a more accurate measurement of the concentration of solute particles in the solution, ensuring that the calculated values for freezing point depression and boiling point elevation are consistent and accurate. In summary, molality is temperature-independent, making it a more reliable measurement to use in equations describing freezing-point depression and boiling-point elevation. Molarity, on the other hand, can be affected by changes in temperature due to its dependence on the volume of the solution.

Key Concepts

Colligative Properties

Colligative properties are fascinating because they depend solely on the number of solute particles in a solution and not on the nature of these particles. This means that colligative properties are influenced by the concentration of solute molecules or ions rather than their identity. This unique characteristic makes colligative properties quite universal. Examples of these properties include:

• Freezing Point Depression
• Boiling Point Elevation
• Vapor Pressure Lowering
• Osmotic Pressure

Understanding these properties can help us predict how a solute will impact the behavior of a solvent. This predictability stems from the fact that by adding solute particles, we alter the physical properties of the solution in a manner consistent with thermodynamic principles.

Temperature Dependence

The distinction between molality and molarity becomes particularly interesting when considering their temperature dependencies. Molarity refers to the number of moles of solute per liter of solution. Because it relies on volume, and volume can change with temperature, molarity is temperature-dependent. As the solution heats or cools, its volume will expand or contract respectively, altering the molarity.

In contrast, molality is calculated as the moles of solute per kilogram of solvent. Since mass does not change with temperature, molality remains constant, making it temperature-independent. This independence from temperature makes molality a more stable measure for calculations that involve temperature changes, such as those found in colligative properties.

Freezing Point Depression

Freezing point depression is a colligative property that describes how the freezing point of a solvent decreases when a solute is added. This allows solutions to freeze at lower temperatures compared to the pure solvent. When a solute is dissolved, the solute particles disrupt the formation of solid crystalline structures, requiring a lower temperature to achieve the solid state.

The formula for freezing point depression involves molality (\[ \Delta T_f = i imes K_f imes m \]where \( \Delta T_f \) is the change in the freezing point, \( i \) is the van’t Hoff factor, \( K_f \) is the freezing point depression constant, and \( m \) is the molality. Using molality ensures that temperature fluctuations do not introduce inaccuracies in the calculation, providing a reliable and consistent method for determining the new freezing point.

Boiling Point Elevation

Boiling point elevation refers to the increase in the boiling point of a solvent when a solute is added. Much like freezing point depression, it is a colligative property that depends on the number of solute particles present in the solution, rather than their nature. Adding a solute causes the liquid's vapor pressure to decrease, thus requiring a higher temperature to reach the point where the vapor pressure equals atmospheric pressure.

The equation for boiling point elevation is similar to that of freezing point depression:\[ \Delta T_b = i imes K_b imes m \]where \( \Delta T_b \) is the boiling point elevation, \( i \) is the van’t Hoff factor, \( K_b \) is the ebullioscopic constant, and \( m \) is the molality. By using molality, which is unaffected by temperature changes, the boiling point elevation remains predictable and precise, making it the preferred measure for these calculations.