Freezing Point Depression: Ordering Solutions By Temperature

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Hey guys! Ever wondered why putting salt on icy roads helps melt the ice? It all boils down to a colligative property called freezing point depression, or cryoscopy. In this article, we're going to dive deep into this fascinating concept and tackle a question that involves ordering solutions by their freezing temperatures. We'll break down the principles behind it, walk through the calculations, and make sure you're a pro at solving these types of problems. Let's get started!

Understanding Freezing Point Depression

Freezing point depression is one of those cool colligative properties in chemistry. Colligative properties are properties of solutions that depend on the concentration of solute particles, rather than the identity of the solute itself. Think of it this way: it's not what you dissolve, but how much you dissolve that matters. Other colligative properties include boiling point elevation, osmotic pressure, and vapor pressure lowering, but we're zoning in on freezing point depression today.

So, what exactly is freezing point depression? Simply put, when you add a solute to a solvent (like water), the freezing point of the solvent decreases. Pure water freezes at 0°C (32°F), but if you dissolve salt in it, the freezing point drops below 0°C. This is why we use salt on icy roads—it helps prevent the water from freezing, making the roads safer. The more solute you add, the lower the freezing point gets, up to a certain point.

But why does this happen? It's all about the disruption of the solvent's crystal structure. When a solvent freezes, its molecules arrange themselves in an orderly crystal lattice. The presence of solute particles interferes with this process, making it harder for the solvent molecules to come together and form a solid. This means you need to lower the temperature even further to freeze the solution. The extent of the freezing point depression is directly proportional to the molality (moles of solute per kilogram of solvent) of the solution and the van't Hoff factor (i), which represents the number of particles a solute dissociates into in solution.

Mathematically, we can express freezing point depression using the following equation:

ΔTf = i * Kf * m

Where:

  • ΔTf is the freezing point depression (the change in freezing point)
  • i is the van't Hoff factor
  • Kf is the cryoscopic constant (freezing point depression constant) of the solvent (for water, Kf = 1.86 °C kg/mol)
  • m is the molality of the solution

Now that we've got a solid grasp of the theory, let's move on to applying it to a specific problem.

Applying the Concept: Ordering Solutions by Freezing Temperature

Okay, let's tackle the question at hand! We need to figure out the increasing order of freezing temperatures for the following solutions:

I. CaBr2: 0.1 mol/L II. NaOH: 0.2 mol/L III. Na2SO4: 0.2 mol/L IV. Sucrose: 0.5 mol/L

To solve this, we'll use the freezing point depression equation we just discussed: ΔTf = i * Kf * m. Remember, the lower the freezing point, the greater the freezing point depression (ΔTf). So, the solution with the smallest ΔTf will have the highest freezing point, and vice-versa.

Here’s the breakdown, step by step:

  1. Identify the van't Hoff factor (i) for each solute. This is crucial because it tells us how many particles each solute dissociates into when dissolved in water:

    • CaBr2: Calcium bromide (CaBr2) dissociates into one calcium ion (Ca2+) and two bromide ions (Br-), so i = 3.
    • NaOH: Sodium hydroxide (NaOH) dissociates into one sodium ion (Na+) and one hydroxide ion (OH-), so i = 2.
    • Na2SO4: Sodium sulfate (Na2SO4) dissociates into two sodium ions (Na+) and one sulfate ion (SO42-), so i = 3.
    • Sucrose: Sucrose is a non-electrolyte, meaning it doesn't dissociate into ions in solution, so i = 1.

  2. Calculate the effective molality for each solution. Since the freezing point depression depends on the total number of solute particles, we need to consider both the concentration and the van't Hoff factor. We'll multiply the given concentration (mol/L) by the van't Hoff factor (i) to get the effective molality.

    • CaBr2: 0.1 mol/L * 3 = 0.3
    • NaOH: 0.2 mol/L * 2 = 0.4
    • Na2SO4: 0.2 mol/L * 3 = 0.6
    • Sucrose: 0.5 mol/L * 1 = 0.5

  3. Determine the relative freezing point depression (ΔTf) for each solution. We don't need to calculate the exact ΔTf values, as we're only interested in the order. Since Kf (1.86 °C kg/mol for water) is constant for all solutions, and we're assuming the solutions are dilute enough that molality is approximately equal to molarity, we can compare the effective molalities directly. The solution with the highest effective molality will have the largest ΔTf (greatest freezing point depression), and thus the lowest freezing point.

  4. Order the solutions based on their freezing points. Remember, the higher the effective molality, the lower the freezing point. So, we arrange them in increasing order of freezing temperature (which means decreasing order of effective molality):

    • CaBr2 (0.3)
    • NaOH (0.4)
    • Sucrose (0.5)
    • Na2SO4 (0.6)

The Final Answer and Why It Matters

So, the increasing order of freezing temperatures for the given solutions is:

CaBr2 < NaOH < Sucrose < Na2SO4

This means that CaBr2 will have the lowest freezing point, while Na2SO4 will have the highest freezing point among these solutions.

You might be thinking,