CBSE Class 12, Unit-1:Solutions Notes
Raoult's Law for Volatile and Non-Volatile Solutes
Colligative Properties
Those properties which depend on the number of solute particles (molecules, atoms or ions) but not upon their nature are called colligative properties. The following are the colligative properties:
1. Relative lowering of vapour pressure of the solvent
2. Elevation of boiling point of the solvent
3. Depression of freezing point of the solvent
4. Osmotic pressure of the solution
Relative Lowering of Vapour Pressure
When a non-volatile solute is dissolved in a pure solvent, the vapour pressure of the solvent decreases because the presence of solute molecules reduces the number of solvent molecules that can escape into the vapor phase. Consequently, the vapor pressure of the solution becomes lower than that of the pure solvent at the same temperature.
The relative lowering of vapour pressure can be mathematically expressed as:
Relative Lowering of Vapour Pressure = (po − p)/po
where po is the vapour pressure of the pure solvent, and p is the vapour pressure of the solution, (po − p) is lowering of vapour pressure.
We can also say that the relative loweing of vapour pressure is the ratio of lowering of vapour pressure to the vapour pressure of the pure solvent.
Elevation in Boiling Point
We know that the vapour pressure of solution is always lower than that of the solvent. Therefore, the boiling point of solution is always higher than that of solvent. In other words, when a non-volatile solute is dissolved in the pure solvent, the boiling point increases or elevated. This phenomenon is known as elevation in boiling point.
T2 > T1
and T2 − T1 = ΔTb (Elevation in Boiling Point).
The elevation in boiling point (ΔTb) is proportional to the concentration of the solute in the solution. It can be calculated as-
ΔTb = i × Kb × m
Where, i is the Van't Hoff factor, Kb is the ebullioscopic constant and m is the molality of the solute.
For dilute solution, elevation in boiling point can be calculated by using the given formula-
Where, W is the weight of the solvent, w is the weight of the solute and m is the mass of the solute.
Depression in Freezing Point
When a non-volatile solute is dissolved in the pure solvent, the freezing point decreases. This phenomenon is known as depression in freezing point. When a liquid is cooled by dropping the temperature, the vapour pressure decreases as the quantity of vapour molecules decreases on the surface of the liquid. Unless supercooling occurs, the temperature finally stops decreasing and at the same time a few crystals of crystalline solids are formed and the liquid starts to freeze. At this temperature, both liquid and solid forms have the same vapour pressure. This temperature is called freezing point of liquid.
T2 < T1
and T2 − T1 = ΔT (Depression in Freezing Point).
The depression in freezing point is proportional to the molality of the added solute. The depression in the freezing point of a solution can be described by the following formula.
ΔTf = i × Kf × m
Where, ΔTf is the freezing point depression, i is the Van't Hoff factor, Kf is the cryoscopic constant, and m is the molality.
For dilute solution, depression in freezing point can be calculated by using the given formula-
Where, W is the weight of the solvent, w is the weight of the solute and m is the mass of the solute.
Osmotic Pressure
When two solutions are separated by a semipermeable membrane, then there is a spontaneous flow of the solvent from lower to higher concentration due to osmosis. The pressure that must be applied on the solution of higher concentration to prevent the flow of the solvent from the solution of lower concentration is called osmotic pressure of the solution. It is denoted by π
Osmotic pressure (π), can be expressed mathematically using the van't Hoff equation:
π= i C S T
where, i is the van't Hoff factor, C is the molar concentration of the solute, S is the solution constant (0.082 ltr.atm.K−mol−) and T is the absolute temperature in kelvins
Measurement of Molecular weight of Solute by Osmotic Pressure
We know that PV = nRT for n mole of gas,
Similarly, for n molecules of a solution,
πV = nST
or, πV = (w/m)ST
or, m = wST/πV
where, m is the molecular mass of the solute, w is weight of the solute, V is volume of the solution having w gm of solute, R is solution constant, T is absolute temperature and π is the osmotic pressure.
Abnormal Molecular Weight
Colligative properties are the properties of dilute solutions which depend upon the number of solute particles. Abnormal molecular weight refers to the condition where the molecular mass of a solute, calculated from colligative properties deviates from its expected value. This abnormality arises due to the association or dissociation of solute particles in solution.
We know that elevation in boiling point and depression in freezing point is given by the formula-
ΔT = (1000 x K X w)/m x W
or, ΔT ∝ 1/m
The osmotic pressure (π) is-
π = (w x S X T)/Mm x V
π ∝ 1/m
and the lowering of vapour pressure (ΔP) is-
ΔP/P = wM/mW
or, ΔP ∝ 1/m
Overall we can write as-
Colligative properties ∝ 1/m
or, Number of Solute Particles ∝ 1/Molecular Weight.
Therefore, compounds undergo association or dissociation in solution show abnormal molecular weight.
Solubility of Gas in Liquid
The solubility of gases in liquid is the maximum amount of gas that can dissolve in a given volume of liquid at a particular temperature and pressure. Gases dissolve in liquids to form homogeneous solutions. The solubility of gas in a liquid depends upon the following factors-
1. The nature of the substance (solute)
2. The nature of the solvent
3. Temperature of the solution
4. Pressure
Some gases like N2, H2, O2 etc. dissolve in water to very small extent whereas the gases like NH3, HCl etc. are highly soluble in water. The most soluble gases are those which chemically react with the liquid solvent.
The solubility of a gases in liquids is greatly influenced by pressure and temperature
1. Effect of temperature: The solubility of a gases decreases with increase in temperature because gases dissolve in a liquid with the evolution of heat (i.e. exothermic process).
2. Effect of pressure: The solubility of gases increases with increase in pressure. This is also in accordance with Le-Chatelier's principle.
Solubility of gas in liquid was explained by Henry's law which stated taht the solubilty of gas increases with incresing the pressure at constant temperature.
Henry's law also stated taht the partial pressure of a gas in vapour phase (p) is proportional to the mole fraction of the gas (X) in a solution.
p ∝ X
or, p = KH X
Where KH = Henry's law constant which depend on the nature of gas and temperature.
KH has constant value but different for different gas. KH value increases with increasing the temperature. So, the value of KH is inversely proportional to solubility of gas in liquid.
How does temperature and pressure affect solubility?
Types of Solution
On the basis of physical state of solute and solvent, there are nine types of solutions.
| Type of Solution | Solute | Solvent | Examples |
|---|---|---|---|
| Gas | Gas | Mixture of oxygen and nitrogen gases | |
| Gaseous Solutions | Liquid | Gas | Chloroform mixed with nitrogen gas |
| Solid | Gas | Camphor in nitrogen gas | |
| Gas | Liquid | Oxygen dissolved in water | |
| Liquid Solutions | Liquid | Liquid | Ethanol dissolved in water |
| Solid | Liquid | Glucose dissolved in water | |
| Gas | Solid | Solution of hydrogen in palladium | |
| Solid Solutions | Liquid | Solid | Amalgam of mercury with sodium |
| Solid | Solid | Copper dissolved in gold |
Amongst the nine types of solutions, the widely studied ones are:
A. Solid–liquid
B. Liquid–liquid
C. Gas–liquid solutions.
A. Solid–Liquid Solutions: A small amount of solute (usually ionic solids) is dissolved in a large quantity of solvent. If the amount of solvent is large as compared to the solute, the solution is referred to as a dilute solution.
Saturated solution: A solution is said to be saturated if it holds the maximum amount of solute at a given temperature in a given quantity of the solvent.
Solubility: It may be defined as the maximum amount of solute that can be dissolved in 100 g of solvent at a specified temperature. The solubility of solid into liquid depends upon the following factors:
a. Nature of solute
b. Nature of solvent
c. Temperature
Causes of Solubility:
The following types of forces of attraction are operated when a solute is mixed with a solvent:
A. Inter-ionic attraction in the solute molecules: Ions are held together in the lattice due to electrostatic forces. Due to these forces molecules are stabilised and the energy released is called lattice energy. This is defined as the energy released when 1 g mole of the compound is formed due to electrostatic attraction between the ions.
B. Inter-molecular attraction between solvent molecules: Water is a polar solvent because of the difference in electronegativity between hydrogen and oxygen atoms constituting water molecule. This difference gives rise to the development of a slight negative charge on oxygen and equal positive charge on hydrogen. A dipole is thus created giving rise to dipole–dipole attraction between water molecules.
C. Solvation: It represents force of attraction between solute and solvent molecules. If the solvent is water then the energy released is called hydration energy.
If hydration energy > lattice energy, then solution is easily formed. Both the ions of the solute get hydrated to overcome the lattice energy of the solute.
D. Temperature: Saturated solution represents equilibrium between undissolved solute and dissolved solute.
Undissolved solute + Solvent → SolutionΔsolH ± x
If Δsol H < 0, i.e., (–ve), the dissolution is exothermic. In this case, as the temperature increases, solubility decreases (Le Chatelier's principle).
If Δsol H > 0, i.e., (+ve), there is endothermic dissolution. In this case, increase in temperature increases the solubility (Le Chatelier's principle).
Liquid–Liquid Solutions: When two liquids are mixed, three different situations result:
A. Miscible Liquids: The two components are completely soluble. They are miscible only when they have similar nature or belong to the same homologous series. Example: water and alcohol (both polar), benzene–toluene (both belong to the same homologous series). There is a rule: Like dissolves like – Polar solute is soluble in polar solvent and a non-polar one in a non-polar solvent.
B. Partially Miscible Liquids: This happens only when the intermolecular forces of one liquid is greater than that of the other is. Solubility, however, increases with increasing temperature.
Examples: aniline-water, phenol-water.
Immiscible Liquids: Two components are completely immiscible. This happens when one liquid is polar and the other is non-polar.
Examples: Carbon tetrachloride-water; chloroform-water.
Gas–Liquid Solutions: The gases are generally soluble in water and to a limited extent in other solvents too. Solubility, however, depends on the following factors:
A. Nature of gas: Easily liquefiable gases are generally more soluble in common solvents.
B. Nature of liquid: Those gases which easily form ions in solution are more soluble in water than in other solvents. Ion formation in other solvents is not an easy process.
HCl(g) + H2O(l) ⇌ H3O+(aq) + Cl–(aq)
C. Pressure: Pressure is an important factor affecting the solubility of gas in liquids. This is governed by Henry's law.
D. Temperature: With rise in temperature, the solubility generally decreases because gas is expelled. Some gases, however, find their solubility increased at a higher temperature.
Henry's law:
It states that at a constant temperature, the solubility of a gas in a liquid is directly proportional to the pressure of the gas.
The most commonly used form of Henry's law states that the partial pressure (p) of a gas in vapour phase is proportional to the mole fraction of the gas (x) in the solution and is expressed as
p = KHx
Here KH is the Henry's law constant and x is the mole fraction of the gas.
Limitations of Henry's Law:
Henry's law is applicable only when
1. The pressure of the gas is not too high and temperature is not too low.
2. The gas should not undergo any chemical change.
3. The gas should not undergo association or dissociation in the solution.
Applications of Henry's Law:
1. To increase the solubility of CO2 in soda water and soft drinks, the bottle is sealed under high pressure.
2. To avoid the toxic effects of high concentration of nitrogen in the blood, the tanks used by scuba divers are filled with air diluted with helium (11.7% helium, 56.2% nitrogen and 32.1% oxygen).
3. At high altitudes, low blood oxygen causes climbers to become weak and make them unable to think clearly, which are symptoms of a condition known as anoxia.
Raoult's law as a special case of Henry's law
In the solution of a gas in a liquid, if one of the components is so volatile that it exists as a gas, then it can be said that Raoult's law becomes a special case of Henry's law in which KH becomes equal to p°A.
Vapour Pressure of Solutions of Solids in Liquids
Raoult's law for a solution containing a non-volatile solute and volatile solvent: It states that the relative lowering of vapour pressure is equal to mole fractions of solute which is non-volatile.
Mathematically,
P = PA + PB
or, P = PA (Since solute B is non-volatile)
or, P = P°AXA
or, P = P°A (1 − XB) = P°A − P°AXB
or, P°AXB = P°A − P
or, (P°A − P)/P°A = XB
or, Relative lowering of vapour pressure = Mole fraction of solute
Azeotropes or Azeotropic Mixture:
Azeotropes are binary mixtures having the same composition in liquid and vapour phase and boil at a constant temperature.
Types of Azeotropes:
Minimum Boiling Azeotropes: These are the binary mixtures whose boiling point is less than either of the two components. The non-ideal solutions which show a large positive deviation from Raoult's law form minimum boiling azeotrope at a specific composition, e.g., a mixture of 94.5% ethyl alcohol and 4.5% water by volume.
Maximum Boiling Azeotropes: These are the binary mixtures whose boiling point is more than either of the two components. The solutions that show large negative deviation from Raoults's law form maximum boiling azeotrope at a specific composition, e.g., a mixture of 68% HNO3 and H2O by mass.
