The colligative properties, also called collective properties of solutions, are a group of four properties that depend only on the number of particles in the solution, but the nature of these particles.
In other words, these properties arise from the presence of particles other than the solvent, that is, particles of the solute, but they do not depend on who the solute is. Any type of particle can give rise to colligative properties, no matter if it is atoms, ions, or molecules. The only thing that matters is your concentration.
The colligative properties are four:
- Drop-in solvent vapor pressure
- Boiling elevation
- Cryoscopic descent
- Osmotic pressure
All are characterized by being proportional to the solute concentration in the case of relatively dilute solutions (concentration <0.2 M). For more concentrated solutions, the behavior becomes more complex and difficult to analyze.
Let’s look at each of these four properties in detail:
1. Drop in solvent vapor pressure (colligative properties)
When preparing a solution of a non-volatile solute, the vapor pressure of the resulting solution is always less than the vapor pressure of the pure solvent. In other words, dissolving a non-volatile solute in a solvent causes a decrease in the vapor pressure of that solvent, compared to the pure solvent.
Vapor pressure drop formula
Like all colligative properties, the decrease in vapor pressure (DP) is proportional to the concentration of the solute. By combining Raoult’s law with the mole fraction equations, it can be shown that DP is given by:
where P ° solvent represents the vapor pressure of the pure solvent at a given temperature, P solution corresponds to the vapor pressure of the solution and X solute represents the concentration of the solute expressed as a mole fraction.
Why does the vapor pressure decrease with the solute?
The driving force behind most natural processes, such as the evaporation of a solvent, is the increase in entropy or the level of disorder. When a liquid evaporates, it goes from a very orderly state (in the liquid) to a very disorderly one (in the gas), since in the gas phase there is much more freedom of movement.
However, in a solution, the presence of the solute adds disorder to the liquid phase while it does not affect the gas phase (since the solute does not evaporate).
For this reason, the difference in the level of disorder between the solution and the gas phase is less than between the pure solvent and the gas phase, so the solvent has less tendency to evaporate in the second case.
Problem: knowing that the vapor pressure of water at a certain temperature is 30.55 mmHg, determine the vapor pressure of a solution prepared by dissolving 7.20 grams of glucose (molar mass or MM = 180g / mol) in 360 g of water (MM = 18.0 g / mol) at the same temperature.
Solution: in this case, the mole fraction of the solute must first be calculated. We already have all the necessary data for this:
Then the equation for the decrease in vapor pressure is applied.
Now we determine the new vapor pressure of the solvent:
2. Boiling elevation or boiling point increase (colligative properties)
Boiling elevation refers to the increase in the boiling point of a solution compared to the boiling point of the pure solvent. To understand why this happens, let’s remember that the boiling point is defined as the temperature at which the vapor pressure of a liquid becomes equal to atmospheric pressure.
As solutions have a lower vapor pressure than pure solvent (as we have just seen in the previous section), it is necessary to heat it more in order to reach atmospheric pressure and thus reach its boiling point. For this reason, the boiling point of solutions (with non-volatile solutes) is always higher than that of the pure solvent.
Boiling elevation formula of Colligative Properties
The increase in the boiling point (DT b ) is proportional to the concentration of the solute expressed in molality, as indicated by the following equation:
Where T b is the boiling point of the solution, T b ° is the boiling point of the pure solvent, K b is the boiling constant of the solvent and m is the molality of the solute.
Problem: Knowing that the boiling constant of water is 0.52 ° C. Kg/mol, determine the boiling point of the glucose solution prepared in the previous example.
Solution: To determine the ebullioscopy elevation we only need the molality.
Now we apply the formula of DT b :
3. Cryoscopic descent
Cryoscopic descent is the decrease in the freezing point of a solution compared to the freezing point of the pure solvent as colligative properties. The reason why this happens is similar to the boiling increase and has its origin in the decrease in vapor pressure.
This property is widely used in cold climate countries where it snows in winter. In these countries, it is very common to see trucks spreading salts such as NaCl or CaCl 2 on the roads or on public benches, after which the snow melts. The reason it melts is that the salt lowers the freezing point of water.
Cryoscopic descent formula
The equation for the cryoscopic decline is very similar to that for ebullioscopic increase. It is also proportional to the molal concentration and depends, in this case, on a cryoscopic constant of the solvent.
where T f is the freezing point of the solution, T f ° is the freezing point of the pure solvent, K f is the cryoscopic constant of the solvent and m is the molality of the solute.
Problem: Knowing that the cryoscopic constant of water is 1.86 ° C. Kg/mol, determine the freezing point of the glucose solution prepared in the previous example.
Solution: The molality of the solution has already been determined, so we can proceed directly to determining DT f, using the above formula:
4. Osmotic pressure (colligative properties)
With colligative properties, Osmosis is a process of great importance on a chemical and biological level. This consists of the flow of solvent molecules (for example, water) from a dilute solution to another more concentrated solution when they are separated by means of a semi-permeable membrane (which only allows the solvent to pass, but not the solute).
This tendency to “absorb” solvent through a semi-permeable membrane is a property that depends solely on the total concentration of solute particles present in the solution, no matter what solute it is. For this reason, this tendency is a colligative property and is measured through osmotic pressure.
Osmotic pressure (π) is the pressure that must be applied to a solution to stop osmosis. The higher the osmotic pressure, the more tendency the solution has to absorb solvent (or, more precisely, the more tendency the solvent has to diffuse into said solution).
Why does osmosis occur?
The explanation behind the osmosis process is very simple. All substances tend to diffuse from where they are most concentrated to where they are most dilute. This is told to follow your concentration gradient.
When a solution is more concentrated in solute, at the same time it is more diluted insolvent and vice versa. For this reason, the solvent has a natural tendency to go from the most dilute solution (where the solvent is most concentrated) to the most concentrated solution (where it is most dilute).
Osmotic pressure formula
Osmotic pressure can be calculated with a formula very similar to the ideal gas equation:
In this equation, π is the osmotic pressure, M is the molar concentration of the solute, R is the universal ideal gas constant (0.0821 atm. L / mol.K) and T is the absolute temperature in K.
Osmotic pressure and tonicity
in colligative properties, Osmotic pressure is very important for the functioning of the human body. In fact, saline solutions that are injected intravenously are classified according to whether their osmotic pressure is greater, equal to, or less than that of blood plasma, which is called tonicity.
- A solution less concentrated than plasma has a lower osmotic pressure and is called a hypotonic solution.
- If it has the same total concentration of solutes, it is called an isotonic solution.
- If it has a higher osmotic pressure (or concentration), it is called a hypertonic solution.
Problem: Calculate the osmotic pressure at 310 K of a 0.9% (m / V) saline solution, which is isotonic with blood plasma.
Solution: we already have the temperature, so the only thing left is to determine the molar concentration of the salt particles (NaCl) in the solution. For this, the fact that sodium chloride, when dissolved in water, separates into two ions, must be taken into account, so that the total concentration of particles will be twice the total concentration of salt.
Each 100 mL of solution contains 0.9 g of NaCl, so:
This is the total concentration of solute particles in the solution, so now we can calculate the osmotic pressure as colligative properties: