Which Of The Following Has The Lowest Freezing Point

Which of the Following Has the Lowest Freezing Point? Understanding Freezing Point Depression

Determining which substance among a group possesses the lowest freezing point requires understanding the concept of freezing point depression. This phenomenon, a colligative property, depends not on the identity of the solute but on its concentration. This article will delve into the science behind freezing point depression, exploring the factors that influence it and providing a framework for accurately predicting which solution will freeze last. We will then tackle various scenarios and provide examples to solidify this understanding.

Understanding Freezing Point Depression

Freezing point depression refers to the decrease in the freezing point of a solvent when a solute is added. This is a crucial concept in many fields, from chemistry and physics to engineering and everyday life. Think about how salt is used to de-ice roads in winter – this is a direct application of freezing point depression.

The key factor governing the extent of freezing point depression is the concentration of solute particles in the solution. More solute particles mean a greater decrease in the freezing point. This is because the solute particles interfere with the solvent molecules' ability to form a regular crystalline structure, the defining characteristic of a solid. The presence of solute particles disrupts the intermolecular forces holding the solvent molecules together, requiring a lower temperature to achieve the solid state.

Factors Affecting Freezing Point Depression

Several factors contribute to the magnitude of freezing point depression:

• Molality (m): This is the most crucial factor. Molality is defined as the number of moles of solute per kilogram of solvent. A higher molality directly translates to a greater depression of the freezing point. This is because a higher molality means a higher concentration of solute particles interfering with the solvent's crystallization.

• Van't Hoff Factor (i): This factor accounts for the dissociation of solutes in solution. Electrolytes, such as salts, dissociate into ions in solution. For example, NaCl dissociates into Na⁺ and Cl⁻ ions. The Van't Hoff factor represents the number of particles produced per formula unit of solute. For NaCl, i is approximately 2. Non-electrolytes, like sugar, do not dissociate, and their i value is 1. A higher Van't Hoff factor signifies more particles in solution, leading to a greater freezing point depression.

• Cryoscopic Constant (Kf): This is a property of the solvent itself. It represents the extent to which the freezing point of the solvent is lowered by a 1 molal solution of a non-volatile, non-electrolyte solute. Each solvent has a unique cryoscopic constant. Water, for example, has a Kf of 1.86 °C/m. A solvent with a larger Kf value experiences a greater freezing point depression for the same molality.

The Formula for Freezing Point Depression

The relationship between these factors is mathematically expressed as:

ΔTf = i * Kf * m

Where:

• ΔTf is the freezing point depression (the difference between the freezing point of the pure solvent and the freezing point of the solution).
• i is the Van't Hoff factor.
• Kf is the cryoscopic constant of the solvent.
• m is the molality of the solution.

Using this formula, we can quantitatively compare the freezing points of different solutions and determine which one will have the lowest freezing point.

Comparing Solutions: A Step-by-Step Approach

To determine which of several solutions has the lowest freezing point, follow these steps:

1. Identify the Solvent: All solutions being compared must have the same solvent. If they don't, you cannot directly compare them using this method.

2. Calculate the Molality (m): Determine the molality of each solution using the formula: moles of solute / kilograms of solvent. Remember to convert grams of solute to moles using its molar mass.

3. Determine the Van't Hoff Factor (i): Assess whether the solute is an electrolyte or a non-electrolyte. For electrolytes, estimate the Van't Hoff factor based on the number of ions produced upon dissociation (remember, this is an approximation, as ion pairing can reduce the effective i). For non-electrolytes, i = 1.

4. Find the Cryoscopic Constant (Kf): Obtain the cryoscopic constant for the solvent from a reference table.

5. Calculate ΔTf for Each Solution: Use the formula ΔTf = i * Kf * m to calculate the freezing point depression for each solution.

6. Determine the Lowest Freezing Point: The solution with the largest ΔTf will have the lowest freezing point because its freezing point is depressed the most from the pure solvent's freezing point.

Example Scenarios

Let's illustrate this with a few examples:

Scenario 1:

Compare the freezing points of the following aqueous solutions:

• Solution A: 0.1 molal sucrose (C₁₂H₂₂O₁₁)
• Solution B: 0.1 molal NaCl
• Solution C: 0.2 molal urea (CH₄N₂O)

Solution:

• Solvent: Water (Kf = 1.86 °C/m)

• Molality: Given.

• Van't Hoff Factor (i):

  • Sucrose (A): i = 1 (non-electrolyte)
  • NaCl (B): i ≈ 2 (electrolyte)
  • Urea (C): i = 1 (non-electrolyte)

• ΔTf Calculation:

  • Solution A: ΔTf = 1 * 1.86 °C/m * 0.1 m = 0.186 °C
  • Solution B: ΔTf = 2 * 1.86 °C/m * 0.1 m = 0.372 °C
  • Solution C: ΔTf = 1 * 1.86 °C/m * 0.2 m = 0.372 °C

• Conclusion: Solutions B and C have the lowest freezing points (both -0.372 °C), followed by Solution A (-0.186 °C). Note that while the molality of Solution C is double that of solution A and B, the equivalent number of particles in solution B is the same as in Solution C due to the dissociation of NaCl. Hence, they display the same freezing point depression.

Scenario 2:

Consider two solutions, both with the same concentration of solute: A 0.5 molal solution of glucose and a 0.5 molal solution of calcium chloride (CaCl₂) in water. Which one would have a lower freezing point?

Solution:

The key difference lies in the Van't Hoff factor. Glucose is a non-electrolyte (i = 1), while calcium chloride is a strong electrolyte that dissociates into three ions (Ca²⁺ and 2Cl⁻), making i ≈ 3. Therefore, the calcium chloride solution will have a significantly lower freezing point because of the greater number of solute particles disrupting the water's crystal lattice.

Beyond Simple Solutions: More Complex Scenarios

The principles outlined above apply to many scenarios. However, some situations require more nuanced considerations:

• Weak Electrolytes: Weak electrolytes do not fully dissociate, so their Van't Hoff factor is less than the theoretical value. Estimating the effective i value for weak electrolytes requires additional information or experimentation.

• Ion Pairing: At higher concentrations, ions in solution may interact and form ion pairs, effectively reducing the number of independent particles and diminishing the freezing point depression.

• Non-Ideal Solutions: The formula provided above is based on the assumption of ideal solutions, where solute-solute and solute-solvent interactions are negligible. In non-ideal solutions, these interactions can significantly affect the freezing point depression, and more advanced models are required for accurate predictions.

Conclusion

Determining which substance among a group has the lowest freezing point hinges on understanding the principles of freezing point depression. By systematically considering the molality of the solution, the Van't Hoff factor, and the cryoscopic constant of the solvent, and utilizing the formula ΔTf = i * Kf * m, one can accurately predict the relative freezing points of different solutions. Remember that the solution with the highest ΔTf value will exhibit the lowest freezing point. While simple calculations provide a good approximation, remember to consider the limitations of the ideal solution model and potential deviations in real-world scenarios. This understanding has wide-ranging practical applications, impacting various fields from road de-icing to the design of industrial cooling systems.