Colligative Properties: Relative Lowering of Vapour Pressure, Raoult’s Law Ideal Solution and Deviations, Determination of Molecular Mass

Let's pretend it's a hot summer day. What is your first thought about beating the heat?

I can hear you screaming "Ice cream!"

On a hot summer day, who wouldn't want ice cream?

Have you ever wondered why an ice cube is rock solid but ice cream, which is mostly water, is not?

The presence of air due to the use of whipped cream is one of the reasons for the liquid texture of ice creams. However, freezing whipped cream also creates a solid icy texture.

So, how come ice cream isn't solid ice?

In comes the important ingredient, sugar!

Water is the main component of most ice cream because it is majorly present in the milk or cream used. The addition of sugar lowers the freezing point significantly. Sugar dissolves in water, interfering with the formation of crystals. As a result, the freezing point of the water in the ice cream is altered. The phenomenon observed above is called depression in freezing point, which is one of the colligative properties.

TABLE OF CONTENTS:

• Colligative Properties
• Relative Lowering of Vapour Pressure
• Elevation in Boiling Point
• Depression in Freezing Point
• Osmotic Pressure
• Applications of Colligative Properties
• Practice Problems
• Frequently Asked Questions - FAQ

Colligative Properties

According to Raoult’s law, the vapour pressure of a solution decreases when a non-volatile solute is added to a volatile solvent. This decrease in the vapour pressure of the solution is associated with many properties of solutions namely, 

1. Relative lowering of vapour pressure of the solvent
2. Depression in freezing point of the solvent
3. Elevation in boiling point of the solvent
4. Osmotic pressure of the solution

The aforementioned properties of solutions are those that are entirely determined by the ratio of the number of solute particles to the number of solvent molecules in a given solution and are entirely independent of the nature of the chemical species present. These properties are called the ‘colligative properties’, which are derived from the Latin words ‘co’ meaning ‘together’ and ‘ligare’ meaning ‘to bind’.

Relative Lowering of Vapour Pressure

Vapour pressure is the pressure exerted by the vapours over the liquid under the equilibrium conditions at a given temperature. 

Let us take an example of a pure liquid. The surface of the liquid is occupied by the molecules of the pure liquid. The vapour above the liquid consists of only the pure liquid (solvent) particles. Suppose a non-volatile solute is added to this pure liquid, since the solute molecules are non-volatile, the vapour pressure of the solution is found to be lower than that of the pure liquid at a given temperature. 

This decrease in vapour pressure is due to the fact that after the solute was added to the pure liquid (solvent), the surface of the liquid contained both pure liquid and solute molecules. The number of solvent molecules escaping into the gas phase is reduced, which in turn reduces the pressure exerted by the solvent molecules in the gaseous phase. This is known as the relative lowering of vapour pressure. This decrease in vapour pressure is one of the colligative properties because it depends on the amount of the non-volatile solute added to the solution, regardless of the type of solution.

For a solution of a non-volatile solute in a volatile solvent,

P_A = 𝜒_A P⁰_A … … … … … (1)

P_A is the vapour pressure of the solution.

𝜒_A is the mole fraction of the solvent

P⁰_A is the vapour pressure of the pure solvent

The decrease in vapour pressure of the solvent (△P_A) is expressed as,

△P_A=P⁰_A - P_A … … … … … (2)

We know that P_A = 𝜒_A P⁰_A … … … … … (3)

Substituting (3) in (2),

△P_A = P⁰_A - 𝜒_A P⁰_A

△P_A = P⁰_A (1 - 𝜒_A) … … … … … (4)

Since the total mole fraction is 1, 

1-𝜒_A = 𝜒_B … … … … … (5)

Substituting (5) in (4),

△P_A = P⁰_A  𝜒_B … … … … … (6)

The lowering of vapour pressure in a solution containing many non-volatile solutes depends on the sum of the mole fractions of the different solutes.

Equation (6) can be written as,

Equation (7) is called the relative lowering of vapour pressure and is equal to the mole fraction of the solute.

Determining the molar mass of the solute from the relative lowering of vapour pressure

From equation (7), 

Where W_A and W_B are the weights of the solvent and the solute, respectively 

Mw_A and Mw_B are the molar mass of the solvent and the solute, respectively.

Thus, if the other quantities such as the weight of the solute (W_B), weight of the solvent (W_A), molar mass of the solvent (Mw_A), and the relative lowering of vapour pressure in equation (9) are known, the molar mass of the solute can be calculated.

Elevation in Boiling Point

A liquid's boiling point is the temperature at which its vapour pressure is equal to the external pressure.

Boiling points are related to liquids and gases. When a liquid is heated, its average kinetic energy increases and its evaporation rate increases as the liquid molecules escape from the surface to the gas phase. Eventually, all molecules in the liquid reach a point (temperature) with sufficient kinetic energy to vapourise. This is the point where the liquid begins to boil and the vapour pressure equals the atmospheric pressure. The temperature at which this phenomenon occurs is the liquid's boiling point.

Generally, boiling point elevation is directly proportional to the molality of the added solutes. The elevation in the boiling point of the solution can be described by the following formula,

For the pure solvent, its vapour pressure at boiling point (P⁰_A) and its molar mass (Mw_A) are constant.

Where K_b is the molal elevation constant. It is the elevation in boiling point when 1 mole of the solute is dissolved in 1000 g of the solvent.

Therefore, K=1000 K_b … … … … … (15)

Substituting (15) in (14),

The boiling point elevation of a solution of a nonelectrolyte is proportional to its molality. 

Equimolal solutions of all substances in the same solvent will show an equal elevation in boiling points. This is known as Raoult’s law of elevation in boiling point.

Depression in Freezing Point

A solution will freeze only when its vapour pressure equals that of the pure solid solvent. Therefore, freezing point is the temperature at which the vapour pressures of both the solid and the liquid substance are the same. The temperature at which a liquid changes state from liquid to solid at atmospheric pressure is called the freezing point. 

The factors affecting the freezing point are:

• If the intramolecular force between liquid molecules is strong, their freezing points will be high. 
• If the intramolecular force between liquid molecules is weak, their freezing points will be relatively low.

Generally, the depression in freezing point is directly proportional to the molality of the added solutes. The depression in the freezing point of the solution can be expressed as, 

For the pure solvent, its vapour pressure at boiling point (P⁰_A) and its molar mass (Mw_A) are constant.

Where K is the depression constant.

Osmotic pressure

The flow of solvent molecules from the high solvent concentration region to the low solvent concentration region through a semipermeable membrane is called osmosis.

Semi-permeable membrane seems to be a continuous sheet but they have microscopic pores that allow the small solvent molecules to pass through but not the big solute molecules. Semi-permeable membranes are of two types.

1. Natural semi-permeable membrane: Animal and plant membranes that are found under the outer skin of the animals and plants respectively constitute the natural semi-permeable membrane.

• Artificial or Synthetic semi-permeable membrane: Parchment paper, cellophane and freshly prepared inorganic substances like copper ferrocyanide that are supported by the walls of a porous pot are some of the examples of artificial or synthetic semi-permeable membranes.

By applying additional pressure to the solution side, the flow of solvent molecules through the semipermeable membrane from the solvent side to the solution side can be stopped. This extra pressure that just stops the flow of solvent is called the osmotic pressure of the solution. A solution's osmotic pressure is directly proportional to its concentration.

For dilute solutions, Van’t Hoff observed that osmotic pressure is proportional to the molarity C of the solution at a given temperature T. Thus,

Thus, if other quantities like W_B, T, and V are known, we can calculate the molar mass of the solute.

Types of solutions based on osmotic pressure

1. Isotonic solution: Two solutions having the same osmotic pressure are termed isotonic solutions.
2. Hypertonic solution: A solution having a higher osmotic pressure relative to some other solution is called a hypertonic solution.
3. Hypotonic solution: A solution having a lower osmotic pressure relative to some other solution is called a hypotonic solution.

Applications of Colligative Properties

Some of the applications of colligative properties are given below.

1. Sugar Solution (Relative lowering of vapour pressure)

The exposed surface of a cup of pure water is entirely made up of water molecules. If a solute, such as sugar, is mixed with water, a few of the particles on the surface will be sugar. This effectively reduces the water's exposed surface area, making it less evaporable and, as a result, lowering the vapour pressure.

2. Cooking with salt (Elevation in boiling point)

In our kitchen, salt is a fantastic ingredient. It not only adds flavour to our food but also raises the boiling point of water. This is an illustration of boiling point elevation. When salt, i.e., sodium chloride, is added to water, it dissociates into sodium and chloride ions. These ions change the intermolecular forces that exist between water molecules. Furthermore, even when no charged solute is present, adding any solute to water raises its temperature due to boiling point elevation. The boiling point rises with the amount of salt added because it is a colligative property that depends on the number of particles formed in the solution.

3. Antifreeze in automobiles (Depression in freezing point)

Depression in freezing point is a colligative property in day-to-day life. In the automobile industry, most antifreeze has a lower freezing point than usual, allowing automobile engines to operate in subfreezing temperatures. 

4. Salting of icy roads (Depression in freezing point)

You may have noticed that applying salt to ice causes it to melt, and this is a popular process for de-icing snow-covered roads. The most popular salts used to de-ice roadways are sodium chloride (NaCl) and calcium chloride (CaCl2). The fundamental rationale for sprinkling salt on an ice road is that a solution of water containing dissolved salts has a lower freezing point than pure water due to the solution's lower freezing point. Water generally freezes at 273 K (0oC), but when salt is added, the temperature reduces. The overall freezing point is lower when the salt concentration is higher.

5. Killing snails! (Osmosis and osmotic pressure)

You've probably heard that slugs and snails can be killed by sprinkling salt on them. It's simply the process of osmosis that kills them. The liquid inside them leaks out in an attempt to dilute the salt concentration and maintain the mucus layer, and as a result, they shed water. Slugs and snails will die if they are exposed to too much salt!

Practice Problems

Q1. Calculate the lowering in vapour pressure induced by adding 34.2 g of sucrose (molar mass of sucrose = 342) to 500 g of water if the vapour pressure of pure water at 20^o C is 20 mm Hg.

Q3. How much of ethyl alcohol must be added to 1 L of water so that the solution will not freeze at

-20o C? Given Kf of water =1.86 K Kg mol-1.

Amount of ethyl alcohol added = m ✕ molar mass of ethyl alcohol
                                                         = 10.7 ✕ 46
                                                         =495 g

Q4. Two solutions of glucose have osmotic pressures 1.5 and 2.5 atm respectively. 1 L of the first solution is mixed with 2 L the second solution. The osmotic pressure of the resultant solution is: 

Frequently Asked Questions - FAQ

Question 1. When a cell is placed in an isotonic solution, what happens?
Answer: When the cell is placed in an isotonic liquid, water does not enter or leave the cell and the volume of the cell stabilises. If the concentration of solute on the outside of the cell is the same as on the inside of the cell and the solute cannot pass through the membrane, the solution is isotonic to the cell.

Question 2. What is the desalination of water?
Answer: Desalination is the process of removing excess salt or minerals from water, such as seawater, in order to produce fresh water that is fit for agriculture or human consumption. The desalination process includes many stages of reverse osmosis (RO). ROs are now installed in almost every home. Osmosis occurs naturally without the use of energy, but in order to reverse the process, energy must be added to the saline solution. Reverse osmosis membranes are semipermeable membranes that allow water molecules but not most dissolved salts, organics, bacteria, or pyrogens to pass through. However, in order to desalinate (desalt or deionize) water during the process, a pressure greater than the naturally occurring osmotic pressure must be applied to the reverse osmosis membrane. This process allows pure water to pass through while retaining the majority of the contaminants. Reverse osmosis is also used for large-scale seawater desalination.

Question 3. Are colligative properties physical or chemical in nature?
Answer: Colligative properties are the physical changes that occur when a solute is added to a solvent. Colligative Properties are affected by the number of solute particles present as well as the amount of solvent present, but not by the type of solute particles, though they are affected by the type of solvent.

Question 4. Why is molality used in colligative properties?
Answer: Physical properties of solutions such as boiling point elevation and freezing point depression are examples of colligative properties. In these calculations, the temperature of the solution changes as more solute is added to the solvent, implying that the volume of the solution changes. We cannot use molarity as our concentration unit because it is expressed as moles of solute per litre of solution. This is why we use molality (moles solute per kg of solvent) since the kg of solvent does not change with temperature.

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