Colligative Properties

Colligative Properties: Definition

To start, let's look at the definition of colligative properties.

For example, if we added radiator antifreeze (solute) to the water (solvent) in a car, the freezing point of the car's cooling system would become lower, keeping the car's system from freezing and becoming damaged when the temperature falls.

Colligative properties are considered to be Physical Properties since they are dependent on the quantity but not on the chemical identity of the solute. So, it doesn't matter what kind of solute you are adding to a solvent, just how much of it you are adding!

When more solute particles are added to the solvent, the Intermolecular Forces present in the solvent are disrupted, changing the solution's colligative properties.

Types of Colligative: Properties

There are different types of colligative properties you should know about. These are boiling point elevation, freezing point depression, vapor pressure depression and osmotic pressure. The magnitude of the changes in most of these properties depends on the molality of the solute particles.

The formula for determining molality is as follows:

$$ \text{m = }\frac{\text{mol of solute}}{\text{kg of solvent}} $$

Now, let's look at the effects of a solute in each of these colligative properties. The effect that the addition of solutes to a particular solution has on boiling point (T_b) is that as more solute gets added, the higher the boiling point of a solution becomes. In other words, the addition of a nonvolatile solute will result in a solution with a higher boiling point than the pure solvent.

The freezing point (T_f) of a solution decreases with the addition of more and more solute to a solution. Think of it this way: when more solute is added to a solution, the boiling point increases and the freezing point decreases, basically expanding the limits at which that solution is in a liquid state!

The third colligative property is Vapor Pressure (V_A). When solute is added, the Vapor Pressure of the solvent decreases because the solute molecules get attached to the solvent molecules and prevent them from escaping into the gas phase.

Lastly, we have osmotic pressure (π), and yes, it has something to do with osmosis.

Now, in terms of solute concentration, we say that there will be a high concentration of water where the solute concentration is lower. Basically, water will travel from where there is lower solute concentration to where there is higher solute concentration.

For example, let's say that you have a container separated in the middle by a semi-permeable membrane. On one side of the container you have a solution, and on the other side of the container you have a pure solvent. Since this semi-permeable membrane allows the passage of some particles, you will start seeing that the level of the pure solvent side will start decreasing, whereas the solution side level would increase. This difference in levels that is seen when the system reaches equilibrium is the osmotic pressure.

Colligative Properties: Formula

When dealing with solutions and colligative properties, the van't Hoff factor becomes important. This factor takes into account that Electrolytes tend to dissociate into ions when dissolved in water.

Let's look at some examples. Sodium chloride (NaCl) is a strong electrolyte that completely dissociates into one sodium ion (Na⁺) and one chlorine ion (Cl^-). Therefore, the van't Hoff factor in this case would be equal to 2. Methanol, CH₃OH, on the other hand, is a non-electrolyte. For non-electrolytes, the van hoff factor is always equal to 1.

Knowing how to figure out the van't Hoff factor of Electrolytes and non-electrolyte will be very important when talking about the different formulas involved in the calculation of different colligative properties!

Freezing Point Depression

Let's start with freezing point depression. Since the lowering of the freezing point is proportional to the solute's molality, we can determine the change in freezing point by using the formula below:

$$ \Delta \text{T}_{f} = i\times \text{K}_{f}\times \text{m} $$

Where:

• \( \Delta \text{T}_{f} \) is the number of degrees that the freezing point has been lowered to (i.e. the difference in the pure solven't freezing point and the freezing point of the solution).
• \( i \) is the van't Hoff factor
• \( \text{K}_{f} \) is the freezing-point depression constant related to the solvent.
• m is the molality of the solute

Let's put this formula into use and solve a problem.

Boiling Point Elevation

The formula for boiling point elevation looks similar to the formula used to calculate freezing point depression.

• Keep in mind that, by adding solute to a solution, the boiling point of the solution increases and becomes higher than that of the pure solvent.

$$ \Delta \text{T}_{b} = i\times \text{K}_{b}\times \text{m} $$

Where:

• \( \Delta \text{T}_{b} \) is the number of degrees that the boiling point has been increased to (i.e. the difference in the boiling pt. of the pure solvent and the boiling point of the solution).
• \( i \) is the van't Hoff factor
• \( \text{K}_{b} \) is the boiling-point elevation constant related to the solvent.
• m is the molality of the solute

Let's look at an example.

Vapor Pressure Depression

Vapor pressure is related to Raoult's Law, which states that the higher the solute concentration, the lower the vapor pressure will be.

The formula for vapor pressure is given below:

$$ P_{A} = \chi_{A}\text{ }\times \text{ }P_{A}^{*} $$

Where:

• \( P_{A} \) is the vapor pressure contributed by liquid, A, in the solution.
• \( \chi_{A} \), is the mole fraction of that particular liquid. The mole fraction is calculated by using the following equation: \( \chi_{A}= \frac{\text{moles of A}}{\text{moles of A + moles of B + ....}} \)
• \( P_{A}^{*} \), is the vapor pressure of liquid, A, when pure.

Osmotic Pressure

The last formula we will be looking at is the formula for osmotic pressure, which is the following:

$$ \Pi = i\times \text{M}\times \text{R}\times \text{T} $$

Where:

• \( \Pi \) is the osmotic pressure.
• \( i \) is the van't Hoff factor
• M is the Molarity
• R is the Gas Constant (0.08206 L·atm/mol·K)
• T is the temperature in K

Colligative Properties Examples

Now, let's talk about examples of colligative properties in a chemistry lab. Probably the most common experiment you will encounter in a laboratory to learn about colligative properties involves determining a compound's molar mass by freezing point depression.

For example, if we know the mass of the unknown compound that has been added to a known mass of solvent, and if we are able to find the freezing point change of the solution relative to the pure solvent, then we can calculate the molar mass of the unknown compound by using the equation below!

$$ \text{Molar mass of unknown compound} = \frac{\text{(K}_{f} \times \text{ g})}{ \text {(ΔT}_{f} \times \text{kg of solvent}) } $$

Application of colligative properties

To finish off, let's talk about another daily application of colligative properties. In areas where the temperature falls below freezing point, salt gets added to the icy roads and sidewalks in order to lower the freezing point and cause the ice to melt!

Now, I hope that you feel more confident in your understanding of colligative properties!