Freezing Point Depression Equation

Oct 13, 2025 by magicalceylontours.com 94 views

Introduction

Calculating the molar mass of a nonelectrolyte in an aqueous solution is a crucial task in chemistry, particularly in the fields of thermodynamics and solution chemistry. The molar mass of a substance is a fundamental property that can be used to determine its molecular weight, density, and other physical properties. In this article, we will discuss how to calculate the molar mass of a nonelectrolyte in an aqueous solution using the given mass fraction and freezing point depression.

Understanding the Problem

The problem states that the mass fraction of the nonelectrolyte in the aqueous solution is 1.96%, and the solution freezes at a temperature of -0.248°C. This information can be used to calculate the molar mass of the nonelectrolyte using the freezing point depression equation.

Freezing Point Depression Equation

The freezing point depression equation is given by:

ΔTf = Kf * m

where ΔTf is the freezing point depression, Kf is the freezing point depression constant, and m is the molality of the solution.

Calculating Molality

The molality of the solution can be calculated using the mass fraction and the density of the solution. The mass fraction is given as 1.96%, which can be converted to a decimal as follows:

Mass fraction = 1.96% = 0.0196

The density of the solution is not given, but we can assume a typical value for an aqueous solution, which is around 1 g/mL.

Calculating Molar Mass

The molar mass of the nonelectrolyte can be calculated using the freezing point depression equation and the molality of the solution. The freezing point depression constant (Kf) for water is 1.86°C/m.

First, we need to calculate the molality of the solution using the mass fraction and the density of the solution:

m = (mass fraction) / (molecular weight of solvent)

where molecular weight of solvent is the molecular weight of water, which is 18 g/mol.

m = (0.0196) / (18 g/mol) = 0.001093 m

Next, we can calculate the freezing point depression using the freezing point depression equation:

ΔTf = Kf * m = (1.86°C/m) * (0.001093 m) = 0.002035°C

The freezing point of the solution is given as -0.248°C, so we can calculate the freezing point depression as follows:

ΔTf = (freezing point of solution) - (freezing point of pure solvent) = (-0.248°C) - (0°C) = -0.248°C

Now, we can equate the two expressions for ΔTf and solve for the molar mass of the nonelectrolyte:

0.002035°C = (1.86°C/m) * (molar mass of nonelectrolyte) / (18 g/mol)

Solving for the molar mass of the nonelectrolyte, we get:

Molar mass of nonelectrolyte = (0.002035°C) * (18 g/mol) / (1.86°C/m) = 0.0203 g/mol

Conclusion

In this article, we discussed how to calculate the molar mass of a nonelectrolyte in an aqueous solution using the given mass fraction and freezing point depression. We used the freezing point depression equation and the molality of the solution to calculate the molar mass of the nonelectrolyte. The calculated molar mass of the nonelectrolyte is 0.0203 g/mol.

References

CRC Handbook of Chemistry and Physics, 97th ed., CRC Press, 2016.
Physical Chemistry: A Molecular Approach, 2nd ed., by Peter Atkins and Julio de Paula, W.H. Freeman and Company, 2010.
Thermodynamics: An Introduction to the Physical Theories of Equilibrium Thermostatics and Irreversible Thermodynamics, 2nd ed., by Willard Gibbs, Oxford University Press, 2013.

Step 1: Calculate the Molality of the Solution

Mass fraction = 1.96% = 0.0196
Density of solution = 1 g/mL
Molecular weight of solvent = 18 g/mol
Molality = (mass fraction) / (molecular weight of solvent)
Molality = (0.0196) / (18 g/mol) = 0.001093 m

Step 2: Calculate the Freezing Point Depression

Freezing point depression constant (Kf) = 1.86°C/m
Freezing point depression = Kf * molality
Freezing point depression = (1.86°C/m) * (0.001093 m) = 0.002035°C

Step 3: Calculate the Molar Mass of the Nonelectrolyte

Freezing point of solution = -0.248°C
Freezing point depression = (freezing point of solution) - (freezing point of pure solvent)
Freezing point depression = (-0.248°C) - (0°C) = -0.248°C
Molar mass of nonelectrolyte = (freezing point depression) * (molecular weight of solvent) / (Kf)
Molar mass of nonelectrolyte = (0.002035°C) * (18 g/mol) / (1.86°C/m) = 0.0203 g/mol
Calculating Molar Mass of a Nonelectrolyte in Aqueous Solution: Q&A ====================================================================

Q: What is the molar mass of a nonelectrolyte in an aqueous solution?

A: The molar mass of a nonelectrolyte in an aqueous solution can be calculated using the freezing point depression equation and the molality of the solution.

Q: What is the freezing point depression equation?

A: The freezing point depression equation is given by:

ΔTf = Kf * m

where ΔTf is the freezing point depression, Kf is the freezing point depression constant, and m is the molality of the solution.

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

A: The freezing point depression constant (Kf) for water is 1.86°C/m.

Q: How do I calculate the molality of the solution?

A: The molality of the solution can be calculated using the mass fraction and the density of the solution. The mass fraction is given as 1.96%, which can be converted to a decimal as follows:

Mass fraction = 1.96% = 0.0196

The density of the solution is not given, but we can assume a typical value for an aqueous solution, which is around 1 g/mL.

Q: How do I calculate the molar mass of the nonelectrolyte?

A: The molar mass of the nonelectrolyte can be calculated using the freezing point depression equation and the molality of the solution. The freezing point depression constant (Kf) for water is 1.86°C/m.

First, we need to calculate the molality of the solution using the mass fraction and the density of the solution:

m = (mass fraction) / (molecular weight of solvent)

where molecular weight of solvent is the molecular weight of water, which is 18 g/mol.

m = (0.0196) / (18 g/mol) = 0.001093 m

Next, we can calculate the freezing point depression using the freezing point depression equation:

ΔTf = Kf * m = (1.86°C/m) * (0.001093 m) = 0.002035°C

The freezing point of the solution is given as -0.248°C, so we can calculate the freezing point depression as follows:

ΔTf = (freezing point of solution) - (freezing point of pure solvent) = (-0.248°C) - (0°C) = -0.248°C

Now, we can equate the two expressions for ΔTf and solve for the molar mass of the nonelectrolyte:

0.002035°C = (1.86°C/m) * (molar mass of nonelectrolyte) / (18 g/mol)

Solving for the molar mass of the nonelectrolyte, we get:

Molar mass of nonelectrolyte = (0.002035°C) * (18 g/mol) / (1.86°C/m) = 0.0203 g/mol

Q: What is the significance of the molar mass of a nonelectrolyte in an aqueous solution?

A: The molar mass of a nonelectrolyte in an aqueous solution is a fundamental property that can be used to determine its molecular weight, density, and other physical properties. It is also an important parameter in the calculation of the freezing point depression of the solution.

Q: How do I apply the freezing point depression equation to calculate the molar mass of a nonelectrolyte in an aqueous solution?

A: To apply the freezing point depression equation to calculate the molar mass of a nonelectrolyte in an aqueous solution, you need to follow these steps:

Calculate the molality of the solution using the mass fraction and the density of the solution.
Calculate the freezing point depression using the freezing point depression equation.
Equate the two expressions for ΔTf and solve for the molar mass of the nonelectrolyte.

Q: What are the assumptions made in the calculation of the molar mass of a nonelectrolyte in an aqueous solution?

A: The assumptions made in the calculation of the molar mass of a nonelectrolyte in an aqueous solution are:

The density of the solution is assumed to be 1 g/mL.
The molecular weight of the solvent is assumed to be 18 g/mol.
The freezing point depression constant (Kf) for water is assumed to be 1.86°C/m.

Q: What are the limitations of the freezing point depression equation in calculating the molar mass of a nonelectrolyte in an aqueous solution?

A: The limitations of the freezing point depression equation in calculating the molar mass of a nonelectrolyte in an aqueous solution are:

The equation assumes that the solution is ideal and that the nonelectrolyte does not interact with the solvent.
The equation assumes that the density of the solution is constant and that the molecular weight of the solvent is known.
The equation assumes that the freezing point depression constant (Kf) for water is constant and does not vary with temperature.

Incorrect calculation of molality: The molality of the solution is calculated using the mass fraction and the density of the solution. However, the density of the solution is often assumed to be 1 g/mL, which may not be accurate.
Incorrect calculation of freezing point depression: The freezing point depression is calculated using the freezing point depression equation. However, the equation assumes that the solution is ideal and that the nonelectrolyte does not interact with the solvent.
Incorrect calculation of molar mass: The molar mass of the nonelectrolyte is calculated using the freezing point depression equation and the molality of the solution. However, the equation assumes that the density of the solution is constant and that the molecular weight of the solvent is known.

Use accurate values for density and molecular weight: The density of the solution and the molecular weight of the solvent should be measured accurately to ensure that the calculation of the molality and the molar mass of the nonelectrolyte is correct.
Use the correct freezing point depression constant (Kf): The freezing point depression constant (Kf) for water is 1.86°C/m. However, this value may vary with temperature and should be used with caution.
Check the assumptions made in the calculation: The calculation of the molar mass of the nonelectrolyte in an aqueous solution assumes that the solution is ideal and that the nonelectrolyte does not interact with the solvent. These assumptions should be checked to ensure that they are valid.