Problem 48 - Chemistry The Science in Context

Question

What is the definition of the concentration scale called molality that is used to determine the molar mass of a nonvolatile solute by measuring the solute's effect on the freezing and boiling points of the solvent? Why must a mass- based concentration scale and not molarity be used?

Step-by-Step Solution

Answer

Define molality and explain why it is advantageous to use a mass-based concentration scale instead of molarity for determining the molar mass of a nonvolatile solute through boiling and freezing point measurements. Molality (m) is the number of moles of solute per kilogram of solvent and is calculated using the formula: m = \(\frac{n_{solute}}{m_{solvent}}\). A mass-based concentration scale (molality) is advantageous over molarity for determining the molar mass of a nonvolatile solute because it is less sensitive to changes in temperature and pressure. Molarity depends on the volume of the solution, which can change with temperature and pressure, making it temperature-dependent. In contrast, molality is based on the mass of the solvent, which does not change with temperature or pressure, providing a more reliable and temperature-independent concentration scale for various applications where temperature and pressure fluctuations are common.

Step 1: Define Molality

Molality (m) is defined as the number of moles of solute per kilogram of solvent. The equation for calculating molality is given by the formula: m = \(\frac{n_{solute}}{m_{solvent}}\) Here, \(n_{solute}\) is the number of moles of the solute and \(m_{solvent}\) is the mass of the solvent in kilograms.

Step 2: Explain the use of molality for boiling and freezing point measurements

Molality is used to determine the molar mass of nonvolatile solutes through boiling and freezing point measurements of the solvent because it is a temperature-independent concentration measurement. The relationship between boiling point elevation or freezing point depression and molality allows us to directly determine the molar mass of the solute: ΔTb = Kb × m ΔTf = Kf × m Here, ΔTb and ΔTf are the changes in boiling and freezing points respectively, Kb and Kf are the boiling and freezing point constants for the solvent, and m is the molality of the solution.

Step 3: Explain why a mass-based concentration scale is used instead of molarity

A mass-based concentration scale (molality) is used instead of molarity because it is less sensitive to changes in temperature and pressure. Molarity is defined as the number of moles of solute per liter of solution, which depends on the volume of the solution. The volume of a solution, and hence its molarity, can change with temperature and pressure, which makes molarity temperature-dependent. In contrast, molality is based on the mass of the solvent, which does not change with temperature or pressure. This makes molality a reliable and temperature-independent concentration scale for determining the molar mass of a nonvolatile solute in colloids, atmospheric chemistry, and other applications where temperature and pressure fluctuations are common.

Key Concepts

Temperature Independence

Molality is a concentration measure that is independent of temperature. This is because it depends on the mass of the solvent rather than its volume. Since mass remains constant regardless of changes in environmental conditions, molality provides a stable and reliable measure. In contrast, other concentration measures such as molarity change with temperature because they are volume-dependent.

• Mass remains unchanged despite temperature variations
• Reliable for precise scientific calculations and experiments

The temperature independence of molality is especially applicable in scenarios where temperature fluctuations are unavoidable, such as in outdoor and industrial settings. By offering a concentration measure based on mass, molality ensures accurate and consistent results when dealing with properties like boiling and freezing points of solutions.

Molar Mass Determination

Molality plays an essential role in determining the molar mass of a nonvolatile solute. This is achieved through the solute's effect on the solvent's boiling and freezing points. By calculating how much the boiling point elevates or the freezing point drops, chemists can find the molar mass of the solute.

• Use the equations: ΔTb = Kb × m and ΔTf = Kf × m
• ΔTb = Boiling point elevation; ΔTf = Freezing point depression
• Kb and Kf = Constants for a given solvent

These relationships help identify the molar mass by using measured changes in temperature, giving insights into the solute's identity and properties. Because these changes rely on the number of moles of solute per mass of solvent (molality), the calculations remain unaffected by temperature and pressure changes.

Boiling Point Elevation

Boiling point elevation is a phenomenon where the boiling point of a solvent increases when a solute is added. The relationship between boiling point elevation and molality is direct, as shown by the equation: ΔTb = Kb × m. This indicates that the extent of the temperature increase depends on the molality of the solution as well as a specific consistency constant, Kb, for that solvent.
Important aspects include:

• It is a colligative property; depends on the number of solute particles
• An increase in boiling points helps to analyze and determine molar mass
• Useful in practical applications like antifreeze solutions

The boiling point elevation allows chemists to deduce essential characteristics of the solute, making it a valuable tool in thermodynamics and molecular discovery.

Freezing Point Depression

Freezing point depression occurs when the addition of a solute to a solvent causes the solvent's freezing point to drop. Similar to boiling point elevation, the relationship is expressed by: ΔTf = Kf × m. This equation demonstrates that the degree of freezing point decrease is proportional to the molality of the solution and the solvent constant, Kf.
Key points include:

• Another colligative property; depends on solute particle quantity
• Utilized in real-world situations like road de-icing
• Helps ascertain molar mass of unknown solutes

Understanding freezing point depression is essential for analyzing solution behavior under varying conditions, helping in fields ranging from chemistry lab experiments to industrial freezing processes.