colligiative+properties

A **//colligiative//** property is a physical property, such as freezing point or boiling point, of a solution that is affected by the concentration of its solute.

Some examples of colligiative properties include:
 * solubility
 * freezing point
 * boiling point
 * vapor pressure
 * osmotic pressure

When dealing with colligiative properties, we usually work with the unit //molality// (//m//), because it is measured in moles of solute per kilogram of solvent. The kilogram part of this unit is the important part - as temperature changes, the mass of the solution remains constant (unlike its volume, which will expand or contract).

For information regarding solubility, please visit this page.

**Modeling a Solution**
The best way to understand how solute concentration affects these physical properties is by visualization. **//Particle-level diagrams//** are very useful in terms of modeling solutions, as they show how the solute is "carried" by the solvent.

First, watch this animation or this one on how solid sodium chloride is dissolved by water. Note that the polarity of water is the driving force behind the dissolution of the salt.

Now, once a solute is dissolved, it may look something like this:

The solute ions or molecules are dispersed amongst the water molecules. This is an important concept to hold on to. Here is another animation of this concept.

Note that for ionic compounds, the positive and negative ions are physically separated by the water molecules. This does not occur when a molecular solid, such as sucrose, dissolves in water.

The sucrose molecule is capable of dissolving in water (due to the hydrogen-bonding capability of its "O-H" groups):



So when it dissolves in water, it remains intact, and is surrounded by water molecules:

In the lab, the difference between a solution made from an ionic compound, and one made from a molecule, is easily determined if you can measure the solution's conductivity. An ionic solute will conduct (called an electrolyte), whereas a molecular solute will not (a non-electrolyte).

Freezing Point Depression
Have you ever wondered why we spread salt on icy or snowy sidewalks in the winter?

The result is usually that the salt melts the ice or snow. This is a perfect example of taking advantage of a colligiative property, one called //freezing point depression//.

First, take a look at what happens to water at the molecular level when it freezes (solidifies):



The water molecules arrange into a uniform, crystalline pattern. See this page for a 3D model.

Imagine taking a bucket of golf balls ('liquid' form, randomly arranged) and stacking them up in a pyramid ('solidifying' them). This is relatively easy to do, right?

Now imagine the bucket of golf balls, but with a number of tennis balls mixed in (a solution). Try stacking the golf balls - freezing them - but having to randomly insert tennis balls in the stack. This will not be as easy.

The tennis balls (solute) will interfere with crystal formation of the golf balls (solvent). See the following diagram:



As you can see, the solute molecules are dispersed in the solvent molecules.

When crystal growth is interfered with, it stays liquid longer, at lower temperatures. Hence the freezing point is "depressed".

So, when salt is spread on an icy sidewalk, it is disrupting the crystal structure of the ice, and dropping its freezing point, causing it to liquefy. (There is also some heat of solvation occurring).

The freezing point depression temperature can be calculated. The equation looks like this:


 * ΔT f = i x K** f **x //m//**

Where ΔT f is the change in freezing point temperature, K f is the molal freezing point depression constant (or **cryoscopic** constant) for the solvent, and //m// is the solution concentration in molality. The letter "i" is the //van't Hoff factor//.

The **van't Hoff factor** is simply the number of ions or particles per molecule of solute; for example, NaCl would have two ions, and i = 2; FeCl 3 would have four ions, so i = 4. If a solute is not ionic, like sugar, its i = 1.

__Example:__

Calculate the new freezing point of a solution of 2.0 //m// sodium chloride. The value of K f for water is 1.86 K kg/mol.

First, NaCl has an i = 2, because there are two ions in the salt.

Next, set up the math:


 * ΔT f = i x K** f **x //m//**


 * ΔT f = 2 x 1.86** **x 2.0**


 * ΔT f =** **7.44 K**

In order to answer the question, realize that it was asking for the new freezing point. A freezing point depression of 7.44 K means that the solution will now freeze 7.4 K //below// the original freezing point temperature of the solvent (hence "depression").

Water freezes at 273.16 K, so the new freezing point of the solution is:


 * 273.16 - 7.44 = 265.72 K, or -7.44** o **C**

**Boiling Point Elevation**
Recall that at the surface of a solution, solute particles are mingling with solvent molecules (see the images above). This means the solute is 'blocking' the solvent from evaporating. There are also intermolecular forces holding the solvent molecules to the solute particles. Overall, it takes more energy to evaporate the solvent, hence the boiling point gets elevated.

The math is very similar to that of calculating freezing point depression:


 * ΔT b = i x K b x //m//**

Where ΔT b is the change in boiling point temperature, K b is the molal boiling point elevation constant (or **ebullioscopic** constant) for the solvent, and //m// is the solution concentration in molality. Again, the letter "i" is the //van't Hoff factor//.

__Example:__

Calculate the new boiling point of a solution of 2.0 //m// sodium chloride. The value of K b for water is 0.512 K kg/mol.

First, NaCl has an i = 2, because there are two ions in the salt.

Next, set up the math:


 * ΔT b = i x K** b **x //m//**


 * ΔT f = 2 x 0.512** **x 2.0**


 * ΔT f =** **2.05 K**

In order to answer the question, realize that it was asking for the new boiling point. A boiling point elevation of 2.05 K means that the solution will now boil 2.05 K //above// the original boiling point temperature of the solvent (hence "elevation").

Water boils at 372.16 K, so the new boiling point is 374.21 K, or 102.05 o C.

Try this online colligiative properties simulator.



Vapor Pressure

 * //Vapor pressure//** is the pressure exerted by a gas over a solution in equilibrium with its liquid phase. In other words, when a liquid evaporates, its resulting gas creates pressure.

The lower the boiling point for a liquid, the more readily it evaporates, meaning it will have a higher vapor pressure. Liquids with high vapor pressures are considered **//volatile//**.

So, when a non-volatile solute interacts with the evaporating solvent, and reduces its ability to evaporate, it causes a drop in the vapor pressure.

In order to calculate vapor pressure depression, first understand the **mole fraction (X)** concept.

In a mixture of A and B, the **mole fraction** is the ratio of moles of substance A to the sum of the moles of A and B:


 * X A = n** ​**A** **/ (n A + n B )**

Then, by multiplying the mole fraction of the solvent (X solvent ) by the partial pressure of the pure solvent (P o solvent ), you calculate the new vapor pressure of the solution (P solution ).


 * P solution = (X solvent ) x (P o solvent )**

Try this online vapor pressure lab.

Follow this link for an animation of osmotic pressure. **ΔT f =**