Calculating Freezing Point Depression

Oct 13, 2025 by wbrum.org 54 views

Introduction

Freezing point depression (FPD) is a fundamental concept in chemistry that describes the decrease in the freezing point of a solvent when a solute is dissolved in it. This phenomenon is a result of the solute particles disrupting the formation of a crystal lattice in the solvent, making it more difficult for the solvent to freeze. In this article, we will explore the concept of freezing point depression and how it can be used to determine the molar mass of an organic compound.

Calculating Freezing Point Depression

To calculate the freezing point depression, we need to know the freezing point of the pure solvent and the freezing point of the solution. The formula for calculating FPD is:

ΔTf = Tf - Ts

where ΔTf is the freezing point depression, Tf is the freezing point of the solution, and Ts is the freezing point of the pure solvent.

Example 1: Freezing Point Depression of an Organic Compound

An organic compound is dissolved in nitrobenzene. The freezing point of the solution is 4.754°C. What is the freezing point depression (FPD) for this solution?

To solve this problem, we need to know the freezing point of pure nitrobenzene. The freezing point of nitrobenzene is 5.71°C. Using the formula above, we can calculate the FPD as follows:

ΔTf = Tf - Ts = 4.754°C - 5.71°C = -0.956°C

Therefore, the freezing point depression of the organic compound in nitrobenzene is 0.956°C.

Calculating Molar Mass from Freezing Point Depression

The freezing point depression can also be used to calculate the molar mass of a solute. The formula for calculating molar mass from FPD is:

M = (RT^2 * Kf) / (ΔTf * 1000)

where M is the molar mass of the solute, R is the gas constant, T is the temperature in Kelvin, Kf is the freezing point depression constant, and ΔTf is the freezing point depression.

Example 2: Molar Mass of Sodium Chloride in Acetic Acid

What is the freezing point of sodium chloride dissolved in acetic acid with an FPD of 0.5°C?

To solve this problem, we need to know the freezing point of pure acetic acid. The freezing point of acetic acid is 16.6°C. Using the formula above, we can calculate the freezing point of the solution as follows:

Tf = Ts + ΔTf = 16.6°C + 0.5°C = 17.1°C

Therefore, the freezing point of sodium chloride dissolved in acetic acid with an FPD of 0.5°C is 17.1°C.

Calculating Molar Mass of Sodium Chloride

To calculate the molar mass of sodium chloride, we need to know the freezing point depression constant (Kf) of acetic acid. The Kf value for acetic acid is 3.9°C/m. Using the formula above, we can calculate the molar mass of sodium chloride as follows:

M = (RT^2 * Kf) / (ΔTf * 1000) = (8.314 * (273.15 + 17.1)^2 * 3.9) / (0.5 * 1000) = 58.44 g/mol

Therefore, the molar mass of sodium chloride is 58.44 g/mol.

Conclusion

In conclusion, freezing point depression is a fundamental concept in chemistry that describes the decrease in the freezing point of a solvent when a solute is dissolved in it. By calculating the freezing point depression, we can determine the molar mass of a solute. In this article, we have explored the concept of freezing point depression and how it can be used to calculate the molar mass of an organic compound and a salt.

References

CRC Handbook of Chemistry and Physics, 97th Edition
Atkins, P. W., & De Paula, J. (2010). Physical Chemistry. Oxford University Press.
Chang, R. (2010). Physical Chemistry for the Biosciences. University Science Books.

Q: What is freezing point depression?

A: Freezing point depression is the decrease in the freezing point of a solvent when a solute is dissolved in it. This phenomenon occurs because the solute particles disrupt the formation of a crystal lattice in the solvent, making it more difficult for the solvent to freeze.

Q: How is freezing point depression calculated?

A: The freezing point depression is calculated using the formula:

ΔTf = Tf - Ts

where ΔTf is the freezing point depression, Tf is the freezing point of the solution, and Ts is the freezing point of the pure solvent.

Q: What is the freezing point depression constant (Kf)?

A: The freezing point depression constant (Kf) is a value that depends on the solvent and is used to calculate the molar mass of a solute. The Kf value is typically expressed in units of °C/m.

Q: How is the molar mass of a solute calculated from freezing point depression?

A: The molar mass of a solute can be calculated from freezing point depression using the formula:

M = (RT^2 * Kf) / (ΔTf * 1000)

where M is the molar mass of the solute, R is the gas constant, T is the temperature in Kelvin, Kf is the freezing point depression constant, and ΔTf is the freezing point depression.

Q: What are some common applications of freezing point depression?

A: Freezing point depression has several applications in chemistry, including:

Determining the molar mass of a solute
Identifying the presence of a solute in a solution
Measuring the concentration of a solute in a solution
Studying the properties of solutions

Q: Can freezing point depression be used to determine the purity of a solvent?

A: Yes, freezing point depression can be used to determine the purity of a solvent. If the freezing point of a solvent is lower than expected, it may indicate the presence of impurities.

Q: What are some common solvents used in freezing point depression experiments?

A: Some common solvents used in freezing point depression experiments include:

Water
Ethanol
Acetic acid
Nitrobenzene

Q: What are some common solutes used in freezing point depression experiments?

A: Some common solutes used in freezing point depression experiments include:

Sodium chloride
Sucrose
Glucose
Urea

Q: How can freezing point depression be used in real-world applications?

A: Freezing point depression has several real-world applications, including:

Developing new pharmaceuticals
Improving the efficiency of industrial processes
Studying the properties of biological systems
Developing new materials with unique properties

Conclusion

In conclusion, freezing point depression is a fundamental concept in chemistry that has several practical applications. By understanding how to calculate freezing point depression and how to use it to determine the molar mass of a solute, you can gain a deeper understanding of the properties of solutions and how they can be used in real-world applications.

References

CRC Handbook of Chemistry and Physics, 97th Edition
Atkins, P. W., & De Paula, J. (2010). Physical Chemistry. Oxford University Press.
Chang, R. (2010). Physical Chemistry for the Biosciences. University Science Books.