Revision: Solutions Chemistry Science (English Medium) Class 12 CBSE

Homogeneous mixtures of two or more than two components are known as solutions.

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.

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`

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`

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"`

Azeotropes are the binary mixtures of solutions that have the same composition in liquid and vapour phases and that have constant boiling points.

The elevation in boiling point of a solution is directly proportional to the molal concentration (molality) of the solute in the solution.

ΔT_b = K_b m

Where

ΔT_b = Elevation in boiling point

K_b = Molal elevation constant (ebullioscopic constant)

m = Molality of 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.

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.

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.

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.

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.

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.

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.

The increase in boiling point of a solvent on addition of a non-volatile solute is called elevation of boiling point.

\[\Delta T_b=iK_bm\]

A membrane which allows only solvent molecules to pass through it but not solute molecules is called a semipermeable membrane.

The flow of solvent molecules through a semipermeable membrane from lower concentration to higher concentration is called osmosis.

The excess pressure that must be applied to a solution to stop the flow of solvent through a semipermeable membrane is called osmotic pressure.

It states that at infinite dilution, the molar conductance of an electrolyte is the sum of molar conductances of its ions with molar conductance of each ion multiplied with the number of ions present in the formula of the electrolyte.

A solution in which more solute can be dissolved at the same temperature is called an unsaturated solution.

The maximum amount of a solute that can be dissolved in a given amount of solvent at a specified temperature is called solubility.

The pressure exerted by vapours of a liquid over the liquid surface in equilibrium at a given temperature is called vapour pressure.

A solution is a homogeneous mixture of two or more components whose composition and properties are uniform throughout.

The component present in larger quantity in a solution is called the solvent.

The component present in smaller quantity in a solution is called the solute.

A solution which contains the maximum amount of solute dissolved at a given temperature and pressure is called a saturated solution.

Two solutions having the same osmotic pressure at a given temperature are called isotonic solutions.

A solution having higher osmotic pressure than another solution is called hypertonic solution.

A solution having lower osmotic pressure than another solution is called hypotonic solution.

The flow of solvent from solution to pure solvent through a semipermeable membrane when pressure greater than osmotic pressure is applied is called reverse osmosis.

The experimentally determined molar mass of a solute which is different from its expected (normal) molar mass is called abnormal molar mass.

The composition of a solution expressed quantitatively is called its concentration.

A solution which obeys Raoult’s law over the entire range of concentration is called an ideal solution.

For an ideal solution:

ΔH_mix = 0

$\Delta Vmix=0$

A solution which does not obey Raoult’s law over the entire range of concentration is called a non-ideal solution.

A binary liquid mixture which boils at a constant temperature with fixed composition is called an azeotrope.

• Large positive deviation → Minimum boiling azeotrope
• Large negative deviation → Maximum boiling azeotrope

 The properties of solutions which depend only on the number of solute particles present and not on their nature are called colligative properties.

The decrease in vapour pressure of a solvent on adding a non-volatile solute is called lowering of vapour pressure.

\[\Delta p=p_1^0-p_1\]

Relative lowering:

\[\frac{p_1^0-p_1}{p_1^0}=x_2\]

For dilute solution:

\[\frac{p_1^0-p_1}{p_1^0}=\frac{n_2}{n_1}\]

\[=\frac{w_2M_1}{w_1M_2}\]

\[\mathrm{Volume}\%=\frac{\text{Volume of component}}{\text{Total volume of solution}}\times100\]

\[x_i=\frac{n_i}{n_1+n_2+\cdots+n_i}\]

For binary solution:

\[x_A=\frac{n_A}{n_A+n_B}\]

x_A ​+ x_B​ = 1

\[m=\frac{\text{Moles of solute}}{\text{Mass of solvent in kg}}\]

\[M=\frac{\text{Moles of solute}}{\text{Volume of solution in litre}}\]

\[\mathrm{Mass}\%=\frac{\text{Mass of component in solution}}{\text{Total mass of solution}}\times100\]

\[\mathrm{ppm}=\frac{\text{Number of parts of component}}{\text{Total number of parts of all components}}\times10^6\]

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.

Statement:

At 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.

Mathematical Form:

p = K_H x

Where
p = partial pressure of gas
x = mole fraction of gas
K_H = Henry’s law constant

Raoult’s Law (For Volatile Liquids):

Statement:

For a solution of volatile liquids, the partial vapour pressure of each component is directly proportional to its mole fraction in the solution.

Mathematical Form:

\[p_1=p_1^0x_1\]

\[p_2=p_2^0x_2\]

Total Vapour Pressure (Dalton’s Law):

\[P_{total}=p_1+p_2\]

\[P_{total}=p_1^0x_1+p_2^0x_2\]

Raoult’s Law (For Non-Volatile Solute):

\[p=p^0x_{solvent}\]

The factor used to account for the extent of association or dissociation of solute particles in solution is called van’t Hoff factor.

\[i=\frac{\text{Normal molar mass}}{\text{Abnormal molar mass}}\]

\[i=\frac{\text{Observed colligative property}}{\text{Calculated colligative property}}\]

\[i=\frac{\text{Total moles of particles after dissociation/association}}{\text{Total moles of particles before dissociation/association}}\]

Value of i

• For dissociation → i > 1
• For association → i < 1
• For no association/dissociation → i = 1