Revision: Solutions and Colligative Properties Chemistry HSC Science (General) 12th Standard Board Exam Maharashtra State Board

It is characterised as a solution that adheres to Raoult's Law, with no interactions between the molecules and no volume or heat change during mixing.

For an ideal solution, Enthalpy of mixing of the pure components to form the solution is Δ_mix H = 0 and the volume of mixing is Δ_mix V = 0.

Two or more solutions exerting the same osmotic pressure are called isotonic solutions.

When two solutions are separated by a semipermeable membrane and no osmosis occurs, i.e., there is no net flow of water on either side through the membrane, the solutions are said to be isotonic solutions. If the membrane is perfectly semipermeable, the two solutions possess the same osmotic pressure and are also referred to as iso-osmotic solutions.

Normality (N) of a solution is defined as the number of gram equivalents of the solute present in one liter of the solution. Normality is used in acid-based redox titrations.

Normality (N) = `"Number of gram equivalents of solute"/"Volume of solution in litre"`

Molality (m) is defined as the number of moles of the solute dissolved in one kilogram (Kg) of the solvent. The units of molality are moles per kilogram, i.e., mole kg⁻¹. The molality is preferred over molarity if the volume of the solution is either expanding or contracting with temperature.

molality (m) = `"Number of mole of solute"/"mass of solvent (in kg)"`

The mass percentage of a component of a solution is defined as the mass of the solute in grammes present in 100 g of the solution. It is expressed as:

Mass % of a component = `"Mass of the component in the solution"/"Total mass of solution"xx100`

For example, if a solution is described as 10% glucose in water by mass, it means that 10 g of glucose is dissolved in 90 g of water, resulting in a 100 g solution. Concentration, described by mass percentage, is commonly used in industrial chemical applications. For example, a commercial bleaching solution contains a 3.62 mass percentage of sodium hypochlorite in water.

Molality (m) is defined as the number of moles of the solute per kilogram (kg) of the solvent. It is expressed as:

Molality (m) = `"Moles of solute"/"Mass of solvent in Kg"`

Therefore, the unit of molality is mole per kg (mol kg⁻¹).

If n_B moles of solute are dissolved in W grams of solvent, then

Molality = `"n"_"B"/"W" xx 1000`

Molarity (M) is defined as the number of moles of the solute dissolved in one Litre (or one cubic decimetre) of solution.

It is expressed as:

Molarity (M) = `"Moles of solute"/"Volume of Solution in Litre"`

For example, a 0.25 mol L⁻¹ (or 0.25 M) solution of NaOH means that 0.25 mol of NaOH has been dissolved in one litre (or one cubic decimetre).

It is defined as the number of moles of solute present in 1000 mL of the solution. Molarity is represented by M.

Molarity (M)  = `"Number of moles of solute"/"Volume of solution in mL" xx 1000`

or

M = `"Weight of solute"/"Molar mass of solute × Volume of solution in mL" xx 1000`

The mole fraction of a particular component in a solution is the ratio of the number of moles of that component to the total number of moles of all the components present in the solution.

Cryoscopic constant:
Molal depression constant or cryoscopic constant is the depression in the freezing point of a solution containing one mole of the non - volatile solute in one kilogram of solvent.

Resistivity or specific resistance:
Resistivity is defined as the resistance of the conductor that is 1 m long and 1 m² in cross-sectional area.

Cryoscopic constant or the Molal depression constant is defined as the depression in freezing point when one mole of non-volatile solute is dissolved in one kilogram of solvent. Its unit is K Kg mol⁻¹.

The temperature at which the liquid and solid forms of a substance can exist together in equilibrium is called the freezing point of that substance.

The net spontaneous flow of solvent molecules into the solution or from more dilute solution to more concentrated solution through a semipermeable membrane is called osmosis.

The solution having lower osmotic pressure as compared to some other solution is referred to as a hypotonic solution.

Osmotic pressure may be defined as the external pressure which should be applied to the solution in order to stop the phenomenon of osmosis, i.e., to stop the flow of solvent into the solution when the two are separated by a semipermeable membrane.

Semipermeable membrane: It is a membrane which allows the solvent molecules, but not the solute molecules, to pass through it.

Semipermeable membrane is a film such as cellophane which has pores large enough to allow the solvent molecules to pass through them.

Two or more solutions exerting the same osmotic pressure are called an isotonic solution.

The process of moving a solvent from a solution to a pure solvent through a semipermeable membrane while applying excessive pressure on the solution side is known as reverse osmosis.

The ratio of the observed (experimental) value of a colligative property to the normal (calculated) value of the same property is termed as van’t Hoff factor, i.

Molal elevation constant (K_b) is defined as the elevation in boiling point of a solution when one mole of a non-volatile solute is dissolved in one kilogram of a volatile solvent.

Henry’s law: The mass of a gas dissolved in a given volume of the liquid at constant temperature is directly proportional to the pressure of the gas present in equilibrium with the liquid.

Henry’s law relates solubility of a gas with external pressure. The law states that, “the
solubility of a gas in liquid at constant temperature is proportional to the pressure of
the gas above the solution”.

If S is the solubility of the gas in mol dm⁻³, then according to Henry’s law,

S ∝ P i.e. S = KP

where, P is the pressure of the gas in atmosphere, K is constant of proportionality and
has the unit of mol dm⁻³ atm⁻¹.

Henry’s law states that the partial pressure of a gas in the vapour phase is proportional to the mole fraction of the gas in the solution.

1. Henry was the first to give a quantitative relationship between the pressure and solubility of a gas in a solvent, which is known as Henry’s law. The law states that at a constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas present above the surface of the liquid or solution.
2. Dalton, a contemporary of Henry, also concluded independently that the solubility of a gas in a liquid solution is a function of the partial pressure of the gas. If we use the mole fraction of a gas in the solution as a measure of its solubility, then it can be said that the mole fraction of gas in the solution is proportional to the partial pressure of the gas over the solution.
3. The most commonly used form of Henry’s law states that “the partial pressure of the gas in the vapour phase (p) is proportional to the mole fraction of the gas (x) in the solution” and is expressed as:
   p ∝ x
   p = K_H . x
4. Here, K_H is Henry’s law constant. When a mixture of more than one gas is brought into contact with a solvent, each gaseous component dissolves in proportion to its partial pressure. That is why Henry’s law is applied to every gas, independent of the presence of other gases.