Question

Describe how you would use freezing-point depression and osmotic pressure measurements to determine the molar mass of a compound. Why are boiling-point elevation and vapor-pressure lowering normally not used for this purpose?

Short answer

Use freezing-point depression or osmotic pressure to find molar mass. Boiling-point elevation and vapor-pressure lowering are less sensitive.

Step-by-step solution

Understanding Freezing-Point Depression

Freezing-point depression occurs when a solute is dissolved in a solvent, which lowers the freezing point of the solution compared to the pure solvent. The change in freezing point, \( \Delta T_f \), is given by the equation: \[ \Delta T_f = i \cdot K_f \cdot m \] where \( i \) is the van't Hoff factor, \( K_f \) is the freezing-point depression constant of the solvent, and \( m \) is the molality of the solution.

Calculate Molality and Molar Mass From Freezing-Point Data

Using the measured freezing-point depression, calculate the molality of the solution: \[ m = \frac{\Delta T_f}{i \cdot K_f} \] Once the molality is known, the molar mass of the solute can be found using the equation relating moles of solute to mass and molality. Since molality is moles of solute per kilogram of solvent, rearrange the definition of molality to solve for moles, and then divide the mass of solute by this value to find molar mass.

Understanding Osmotic Pressure

Osmotic pressure \( \Pi \) is the pressure required to prevent the flow of solvent into the solution through a semipermeable membrane. The equation for osmotic pressure is: \[ \Pi = i \cdot M \cdot R \cdot T \] where \( M \) is the molarity of the solution, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.

Calculate Molar Mass From Osmotic Pressure Data

Given the osmotic pressure, determine the molarity using: \[ M = \frac{\Pi}{i \cdot R \cdot T} \] From the molarity and the volume of the solution, calculate the number of moles. Then, determine the molar mass by dividing the mass of the solute by the number of moles obtained.

Limitations of Boiling-Point Elevation and Vapor-Pressure Lowering

Boiling-point elevation and vapor-pressure lowering are generally less sensitive to the presence of solutes compared to freezing-point depression and osmotic pressure, making them less accurate for determining molar mass. Additionally, boiling-point measurements can be affected by solvent evaporation and require precise temperature control, whereas freezing-point depression and osmotic pressure offer more accurate and reliable data.

Key concepts

Freezing-Point Depression

When a non-volatile solute is added to a pure solvent, the freezing point of the resulting solution is lower than that of the pure solvent. This phenomenon is known as freezing-point depression. It occurs because the solute disrupts the formation of a solid crystalline structure, thus requiring a lower temperature to freeze.

The key to using freezing-point depression to determine molar mass is the equation:

1. \[ \Delta T_f = i \cdot K_f \cdot m \]
2. where \( \Delta T_f \) is the change in freezing point, \( i \) is the van’t Hoff factor, \( K_f \) is the freezing-point depression constant, and \( m \) is the molality of the solution.

By measuring how much the freezing point lowers, we can calculate the molality of the solution. This helps determine the number of moles of solute per kilogram of solvent.

Once the molality is known, the molar mass of the solute can be determined by dividing the mass of the solute by the number of moles. Freezing-point depression is a very sensitive method, making it particularly useful for solutions with lower concentrations of solute.

Osmotic Pressure

Osmotic pressure is the pressure required to stop the natural flow of solvent molecules across a semipermeable membrane from pure solvent to the solution. It is a unique property because it only depends on the number of solute particles, not their identity—this makes it a colligative property.

The osmotic pressure \( \Pi \) can be used to find the molar mass of a solute using the equation:

1. \[ \Pi = i \cdot M \cdot R \cdot T \]
2. Where \( M \) is the molarity of the solution, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.

By measuring the osmotic pressure of a solution, we can compute the molarity. Combining the known mass of the solute and the solution volume gives the moles of solute. The molar mass is then calculated by dividing the mass of the solute by the amount of substance in moles.

Osmotic pressure measurements are particularly advantageous because they can be applied at lower concentrations and are less influenced by temperature or other conditions compared to boiling-point elevation and vapor-pressure lowering.

Colligative Properties

Colligative properties are properties of solutions that depend on the number of solute particles rather than their chemical identity. Examples include freezing-point depression, osmotic pressure, boiling-point elevation, and vapor-pressure lowering.

These properties occur because the addition of solute particles affects the physical interactions amongst solvent molecules. For instance:

• Freezing-point depression decreases the temperature at which a solution freezes.
• Osmotic pressure measures how strong solvent molecules are drawn into a solution.

Both freezing-point depression and osmotic pressure are highly sensitive to solute concentrations and can therefore accurately help in molar mass determination.

While boiling-point elevation and vapor-pressure lowering are also colligative properties, they are less commonly used for molar mass determination. This is due to their less pronounced changes, making accuracy a challenge. Additionally, external factors such as evaporative losses and precise temperature regulation make them less reliable compared to freezing-point depression and osmotic pressure.