Freezing point depression and vapor pressure lowering are two crucial colligative properties of solutions, which are directly proportional to the concentration of the solute present in the solution. These properties play a vital role in understanding the behavior of solutions and have numerous applications in various fields of science and engineering.
Understanding Freezing Point Depression
The freezing point depression is the decrease in the freezing point of a solution compared to that of the pure solvent. This phenomenon is described by the following equation:
ΔTf = m × Kf
Where:
– ΔTf is the change in freezing point (°C)
– m is the molal concentration of the solute (mol/kg)
– Kf is the freezing point depression constant or cryoscopic constant (°C·kg/mol)
The values of Kf for various solvents are listed in the table below:
| Solvent | Kf (°C·kg/mol) |
|---|---|
| Water | 1.86 |
| Benzene | 5.12 |
| Ethanol | 1.99 |
| Acetic Acid | 3.90 |
To calculate the freezing point of a solution, you can follow these steps:
- Determine the molal concentration of the solute (m).
- Multiply the molal concentration by the freezing point depression constant (Kf) to find the change in freezing point (ΔTf).
- Subtract the change in freezing point (ΔTf) from the freezing point of the pure solvent to find the freezing point of the solution.
For example, let’s consider a 0.33 m solution of a nonvolatile, nonelectrolyte solute in benzene:
- The molal concentration (m) is 0.33 mol/kg.
- The freezing point depression constant (Kf) for benzene is 5.12 °C·kg/mol.
- The change in freezing point (ΔTf) is calculated as: ΔTf = m × Kf = 0.33 mol/kg × 5.12 °C·kg/mol = 1.69 °C.
- The freezing point of the pure benzene is 5.5 °C.
- The freezing point of the solution is 5.5 °C – 1.69 °C = 3.81 °C.
Understanding Vapor Pressure Lowering
The vapor pressure of a solution is lower than that of the pure solvent, and the decrease in vapor pressure is directly proportional to the concentration of the nonvolatile solute present in the solution. This relationship is described by the following equation:
ΔP = P0 – P = -x × K
Where:
– ΔP is the change in vapor pressure (torr)
– P0 is the vapor pressure of the pure solvent (torr)
– P is the vapor pressure of the solution (torr)
– x is the mole fraction of the solvent
– K is the vapor pressure lowering constant (torr)
To calculate the vapor pressure of a solution, you can follow these steps:
- Determine the mole fraction of the solvent (x).
- Multiply the mole fraction of the solvent by the vapor pressure lowering constant (K) to find the change in vapor pressure (ΔP).
- Subtract the change in vapor pressure (ΔP) from the vapor pressure of the pure solvent (P0) to find the vapor pressure of the solution (P).
For example, let’s consider a 0.1 m aqueous solution of glucose at 25 °C:
- The mole fraction of the solvent (water) is calculated as:
x = nH2O / (nH2O + nglucose) = 55.56 mol / (55.56 mol + 0.1 mol) = 0.998 - The vapor pressure lowering constant (K) for water at 25 °C is 1.052 × 10^3 torr·kg/mol.
- The change in vapor pressure (ΔP) is calculated as:
ΔP = -x × K = -0.998 × 1.052 × 10^3 torr·kg/mol = -1.05 torr - The vapor pressure of pure water at 25 °C is 23.75 torr.
- The vapor pressure of the solution is 23.75 torr – 1.05 torr = 22.70 torr.
Determining Molar Mass Using Freezing Point and Vapor Pressure
The freezing point and vapor pressure of a solution can also be used to determine the molar mass of an unknown solute. Let’s consider an example:
A solution of 4.00 g of a nonelectrolyte dissolved in 55.0 g of benzene is found to freeze at 2.32 °C. Determine the molar mass of the solute.
- Determine the change in freezing point:
ΔTf = 5.5 °C – 2.32 °C = 3.18 °C - Determine the molal concentration from Kf, ΔTf, and the mass of solvent:
m = ΔTf / Kf = 3.18 °C / 5.12 °C·kg/mol = 0.62 mol/kg - Determine the number of moles of solute in the solution:
n = m × mass of solvent = 0.62 mol/kg × 0.055 kg = 0.034 mol - Determine the molar mass of the solute:
M = mass of solute / number of moles = 4.00 g / 0.034 mol = 117.6 g/mol
In summary, freezing point depression and vapor pressure lowering are important colligative properties of solutions that can be used to determine the molar mass of an unknown solute. The values of Kf for various solvents are crucial in these calculations.
Additional Resources
For further information and examples on freezing point depression and vapor pressure lowering, you can refer to the following resources:
Reference:
– Freezing-Point Depression and Boiling-Point Elevation of Solutions
– Colligative Properties
– Colligative Properties- Freezing Point Depression, Boiling Point Elevation, and Osmosis
– Colligative Properties: Freezing-Point Depression and Molar Mass
I am Raghavi Acharya, I have completed my post-graduation in physics with a specialization in the field of condensed matter physics. I have always considered Physics to be a captivating area of study and I enjoy exploring the various fields of this subject. In my free time, I engage myself in digital art. My articles are aimed towards delivering the concepts of physics in a very simplified manner to the readers.