Which Of The Following Has The Lowest Freezing Point

Which of the Following Has the Lowest Freezing Point? A Deep Dive into Freezing Point Depression

Determining which substance among a given set possesses the lowest freezing point requires understanding the fundamental principles governing freezing point depression. This phenomenon, a colligative property, depends not on the identity of the solute but on its concentration. This article will explore the science behind freezing point depression, providing a comprehensive guide to understanding how different solutions compare and offering tools to predict the lowest freezing point among several options. We'll delve into the intricacies of molarity, molality, and the cryoscopic constant, ultimately equipping you with the knowledge to confidently answer this question for various scenarios.

Introduction: Understanding Freezing Point Depression

The freezing point of a pure substance, like water, is the temperature at which it transitions from a liquid to a solid state. Adding a solute to a solvent, however, lowers this freezing point. This lowering, known as freezing point depression, is a colligative property, meaning it depends on the number of solute particles, not their identity. The more solute particles present, the greater the depression of the freezing point. This is why saltwater freezes at a lower temperature than pure water.

Several factors contribute to the magnitude of freezing point depression:

• The nature of the solute: Electrolytes (substances that dissociate into ions in solution, like salts) cause a greater freezing point depression than non-electrolytes (substances that do not dissociate, like sugars) because they produce more particles in solution. For example, NaCl (sodium chloride) dissociates into two ions (Na⁺ and Cl⁻), leading to a greater depression than a non-electrolyte like glucose.

• The concentration of the solute: A higher concentration of solute particles results in a greater freezing point depression. This is directly proportional – doubling the concentration roughly doubles the depression (assuming ideal conditions). This concentration is usually expressed in terms of molality (moles of solute per kilogram of solvent).

• The nature of the solvent: The solvent itself also plays a crucial role. The cryoscopic constant (Kf), a characteristic property of the solvent, quantifies how much the freezing point decreases for a 1 molal solution. Water has a Kf of 1.86 °C/m. Other solvents have different Kf values.

The Formula: Calculating Freezing Point Depression

The freezing point depression (ΔTf) can be calculated using the following formula:

ΔTf = Kf * m * i

Where:

• ΔTf is the change in freezing point (in °C).
• Kf is the cryoscopic constant of the solvent (in °C/m).
• m is the molality of the solution (moles of solute per kilogram of solvent).
• i is the van't Hoff factor, representing the number of particles a solute dissociates into in solution. For non-electrolytes, i = 1. For NaCl, i = 2; for MgCl₂, i = 3, and so on. It's important to note that the van't Hoff factor is an ideal value; in reality, it can be slightly lower due to ion pairing.

Step-by-Step Guide to Determining the Lowest Freezing Point

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

1. Identify the solvent: All solutions must have the same solvent for a fair comparison. If the solutions have different solvents, you'll need to use the appropriate Kf value for each solvent in your calculations.

2. Calculate the molality (m) for each solution: This requires knowing the number of moles of solute and the mass of the solvent (in kilograms).

3. Determine the van't Hoff factor (i) for each solute: Consider whether the solute is an electrolyte or a non-electrolyte. For electrolytes, account for the number of ions produced upon dissociation.

4. Calculate the freezing point depression (ΔTf) for each solution: Use the formula ΔTf = Kf * m * i.

5. Calculate the new freezing point: Subtract the calculated ΔTf from the freezing point of the pure solvent. The solution with the largest ΔTf will have the lowest freezing point.

Illustrative Examples

Let's consider some examples to solidify our understanding. Assume all solutions are aqueous (water is the solvent, Kf = 1.86 °C/m).

Example 1:

• Solution A: 0.5 molal glucose (non-electrolyte, i = 1)
• Solution B: 0.25 molal NaCl (electrolyte, i = 2)

Calculations:

• Solution A: ΔTf = 1.86 °C/m * 0.5 m * 1 = 0.93 °C. Freezing point = 0 °C - 0.93 °C = -0.93 °C
• Solution B: ΔTf = 1.86 °C/m * 0.25 m * 2 = 0.93 °C. Freezing point = 0 °C - 0.93 °C = -0.93 °C

In this case, both solutions have the same freezing point.

Example 2:

• Solution C: 0.1 molal sucrose (non-electrolyte, i = 1)
• Solution D: 0.1 molal MgCl₂ (electrolyte, i = 3)

Calculations:

• Solution C: ΔTf = 1.86 °C/m * 0.1 m * 1 = 0.186 °C. Freezing point = 0 °C - 0.186 °C = -0.186 °C
• Solution D: ΔTf = 1.86 °C/m * 0.1 m * 3 = 0.558 °C. Freezing point = 0 °C - 0.558 °C = -0.558 °C

Here, Solution D (MgCl₂) has a lower freezing point than Solution C (sucrose).

Advanced Considerations: Non-Ideal Solutions and Ion Pairing

The formula ΔTf = Kf * m * i assumes ideal behavior, where solute particles interact minimally with each other and the solvent. In reality, especially at higher concentrations, deviations from ideality occur. Ion pairing, where oppositely charged ions associate in solution, reduces the effective number of particles, leading to a smaller freezing point depression than predicted by the ideal formula. Therefore, the van't Hoff factor (i) is often less than the theoretically expected value for electrolytes at higher concentrations.

Frequently Asked Questions (FAQ)

Q1: Can freezing point depression be used to purify substances?

A1: Yes, a technique called fractional freezing utilizes freezing point depression to separate components of a mixture. As a solution freezes, the pure solvent crystallizes, leaving behind a more concentrated solution of impurities. This process can be repeated to increase the purity of the solvent.

Q2: What is the role of the cryoscopic constant (Kf)?

A2: The cryoscopic constant (Kf) is a solvent-specific constant that reflects the solvent's sensitivity to the presence of solutes. A higher Kf value indicates a greater freezing point depression for a given molality of solute.

Q3: How does freezing point depression affect the environment?

A3: Freezing point depression plays a role in various environmental processes. For example, the salt used to de-ice roads in winter lowers the freezing point of water, preventing ice formation. However, this can have negative environmental consequences, impacting aquatic life and soil chemistry.

Q4: Why is molality used instead of molarity in freezing point depression calculations?

A4: Molality (moles of solute per kilogram of solvent) is preferred over molarity (moles of solute per liter of solution) because molality is independent of temperature. The volume of a solution changes with temperature, affecting molarity, whereas the mass of the solvent remains constant.

Conclusion: Mastering Freezing Point Depression

Understanding freezing point depression is crucial for various scientific and practical applications. By applying the formula ΔTf = Kf * m * i, considering the nature of the solute and solvent, and accounting for deviations from ideality, one can accurately predict which solution will exhibit the lowest freezing point. Remember that the higher the concentration of solute particles, and the stronger the electrolyte, the greater the depression, leading to a lower freezing point. This knowledge empowers you to confidently analyze and compare the freezing points of different solutions and appreciate the subtle yet powerful effects of colligative properties.