Freezing Point Depression - Online Tutor, Practice Problems & Exam Prep

Freezing point depression occurs when a solute is added to a pure solvent, lowering its freezing point. The change in freezing point (ΔT_f) can be calculated using the formula: ΔT_f = I × k_f × m, where I is the van't Hoff factor, k_f is the freezing point constant, and m is the molality (moles of solute per kg of solvent). The freezing point of the solution is then found by subtracting ΔT_f from the normal freezing point of the pure solvent. More solute results in a greater decrease in freezing point.

Freezing Point Depression Concept 1

The phenomenon when adding a solute to a pure solvent results in the decreasing of the freezing point of the solvent. Now with this whole idea of freezing point depression, we have what are called the normal freezing point and the freezing point of the solution. Now the normal freezing point, which I'm going to abbreviate as FP, has to do with our pure solvent. We're going to say this is the freezing point of the solvent before the addition of the solute. And the freezing point of the solution, which we're going to say is FP solution, this is the freezing point of the solvent after the addition of solute. Remember, once you add solute to solvent, it becomes a solution.

Now if we take a look at freezing point depression, let's look at some important areas. First, we have the freezing point depression formula, which is Δt_f = I × k_f × molality where Δt_f stands for our change in freezing point, I is your van't Hoff factor, k_f is your freezing point constant of the solvent in degrees Celsius over molality, and molality is just moles of solute over kilograms of solvent. Now that we know the components of the freezing point depression formula, realize how does it relate to the freezing point of a solution? Well, we're going to say freezing point of a solution equals freezing point of the pure solvent minus Δt_f.

And we take a look here, we can see that we have some common types of solvents. We have water, benzene, chloroform, and ethanol, each with their own normal freezing point before the addition of any solute. Each of them also has their own unique freezing point constant value. No, you don't need to memorize these. This is just for reference of some of the most common types of solvents you may see. So, just remember, when it comes to freezing point depression, our freezing point decreases the more solute we add to our solvent.

Freezing Point Depression Example 1

Calculate the freezing point of a solution containing 110.7 grams of glucose, which is C₆H₁₂O₆, dissolved in 302.6 grams of water. Alright. So we're going to say here that our freezing point of our solution equals the freezing point of our solvent minus ΔT_f. Our solvent here is water, pure water freezes at 0 degrees Celsius. So, what we need to do here is figure out what ΔT_f is. We're going to say ΔT_f equals i ⋅ k f ⋅ m . Glucose here is our solute. It is not ionic, it's covalent, so it doesn't break up into ions. So i is 1. k f , we're dealing with water as a solvent. Its freezing point constant is 1.86 degrees Celsius over molality. Then all we have to do now is find the moles of glucose and convert grams of water into kilograms of water. Kilograms, we just move the decimal over 3, so there goes our kilograms of our solvent water. And here we're going to find out the moles of our glucose. So we have this many grams of glucose, We're going to say here for every 1 mole of glucose its mass is 180.156 grams. And that's the weight of the 6 carbons, 12 hydrogens, and 6 oxygens together. Grams cancel out, and now I'm going to have moles which comes up to 0.614467 moles of glucose. So we plug that here. So here, these cancel out and this molality here. What I get at the end is -3.78 degrees Celsius, which is what I plug over here. So the new freezing point after the addition of glucose is negative 3.78 degrees Celsius. So, that will be our final answer.

How many moles of ethylene glycol, C₂H₆O₂, must be added to 1,000 g of water to form a solution that has a freezing point of – 10ºC?

• A. 334 moles
• B. 5.4 moles
• C. 3.2 moles
• D. 200 moles

An ethylene glycol solution contains 28.3 g of ethylene glycol, C₂H₆O₂ in 97.2 mL of water. Calculate the freezing point of the solution. The density of water 1.00 g/mL.

• A. –8.72°C
• B. –0.848°C
• C. –0.541°C
• D. –17.4°C

When 825 g of an unknown is dissolved in 3.45 L of water, the freezing point of the solution is decreased by 2.89ºC. Assuming that the unknown compound is a non-electrolyte, calculate its molar mass.

• A. 154 g/mol
• B. 42.4 g/mol
• C. 44.5 g/mol
• D. 159 g/mol

Here’s what students ask on this topic:

What is freezing point depression and how is it calculated?

Freezing point depression occurs when a solute is added to a pure solvent, causing the freezing point of the solvent to decrease. The change in freezing point (ΔTf) can be calculated using the formula:

$\mathrm{\Delta T}f=I\times kf\times m$

where I is the van't Hoff factor, kf is the freezing point constant of the solvent, and m is the molality (moles of solute per kg of solvent). The freezing point of the solution is then found by subtracting ΔTf from the normal freezing point of the pure solvent.

What is the van't Hoff factor and how does it affect freezing point depression?

The van't Hoff factor (I) represents the number of particles into which a solute dissociates in solution. For example, NaCl dissociates into two ions (Na⁺ and Cl^-), so its van't Hoff factor is 2. The van't Hoff factor affects freezing point depression because the more particles a solute dissociates into, the greater the decrease in the freezing point. This is reflected in the formula:

$\mathrm{\Delta T}f=I\times kf\times m$

where a higher I results in a larger ΔTf, leading to a lower freezing point for the solution.

How does molality affect freezing point depression?

Molality (m) is a measure of the concentration of a solute in a solvent, defined as moles of solute per kilogram of solvent. It directly affects freezing point depression because the higher the molality, the greater the number of solute particles in the solution, which leads to a larger decrease in the freezing point. This relationship is expressed in the formula:

$\mathrm{\Delta T}f=I\times kf\times m$

Thus, increasing the molality increases ΔTf, resulting in a lower freezing point for the solution.

What is the freezing point constant (kf) and how is it used in calculations?

The freezing point constant (kf) is a property of the solvent that indicates how much the freezing point decreases per molal concentration of solute. It is specific to each solvent and is used in the formula for freezing point depression:

$\mathrm{\Delta T}f=I\times kf\times m$

where ΔTf is the change in freezing point, I is the van't Hoff factor, kf is the freezing point constant, and m is the molality. The kf value allows us to quantify the effect of adding a solute to a specific solvent.

Why does adding a solute to a solvent lower its freezing point?

Adding a solute to a solvent lowers its freezing point because the solute particles disrupt the formation of the solid structure of the solvent. This disruption requires a lower temperature to achieve the same solid structure, thus lowering the freezing point. The extent of this decrease is quantified by the formula:

$\mathrm{\Delta T}f=I\times kf\times m$

where ΔTf is the change in freezing point, I is the van't Hoff factor, kf is the freezing point constant, and m is the molality. More solute results in a greater decrease in the freezing point.