Overview of Solutions

A homogeneous mixture of two or more substances is called a solution.

The solutions consisting of two components are called binary solutions.

The component present in excess and whose physical state is the same as that of the solution is called the solvent.

The other component present in the smaller amount is called solute.

The amount of solute dissolved in a particular amount of solvent is known as composition or concentration of a solution.

Mass percentage is defined as the mass of the solute in grams dissolved per 100 g of the solution.

Volume percentage is defined as the volume of a solute (in a particular unit) present in the 100 units of the volume of the solution.

The concentration of a solution in grams per litre refers to the amount of solute in grams present in one litre of the solution.

The number of moles of solute dissolved per litre of the solution at a particular temperature is called the molarity of the solution.

The number of gram formula mass of an ionic solute dissolved per litre of the solution at a particular temperature is called formality of the solution.

Molality of a solution is defined as the number of moles of solute dissolved per 1000 g (1 kg) of the solvent.

\[\text{Mass percentage of solute}=\frac{\text{Mass of solute}}{\text{Mass of solution}}\times100\]

\[\text{Volume percentage of solute}=\frac{\text{Volume of solute}}{\text{Volume of solution}}\times100\]

\[\text{Concentration}=\frac{w\mathrm{~(in~grams)}}{V\text{ (in litres)}}\]

\[\text{Molarity (M)}=\frac{\text{Number of moles of solute}}{\text{Volume of solution in litres}}\]

or

\[M=\frac{n}{V}\]

\[\text{Formality of solution}=\frac{\text{Number of gram formula mass of the solute}}{\text{Volume of the solution in litres}}\]

\[\mathrm{Molality}=\frac{\text{Number of moles of solute}}{\text{Mass of the solvent in kg}}\]

or

\[m=\frac{n}{w^{\prime}\mathrm{(in~kg)}}\]

The number of gram equivalents of the solute dissolved per litre of a solution at a particular temperature is called the normality of the solution.

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.

ppm is equal to the number of milligrams of the solute present in one litre of the solution.

The homogeneous mixture of two or more solids is termed as a solid solution.

Solubility is equal to the amount of solute (in gram) dissolved in 100 g of the solvent to form saturated solution at a given temperature.

\[\mathrm{Normality}=\frac{\text{Number of gram equivalents of solute}}{\text{Volume of solution in litres}}\]

\[N=\frac{w\times1000}{E\times v}\]

or

\[w=\frac{N\times E\times v}{1000}\]

\[\text{Mole fraction}=\frac{\text{Number of moles of the given component}}{\text{Total number of moles in the solution}}\]

\[\text{ppm of a solute}=\frac{\text{Mass of solute}}{\text{Mass of solution}}\times10^6\]

A solution of two (or more) completely miscible liquids is termed as an ideal solution when it obeys Raoult's law at all concentrations and at all temperatures.

• Statement of Henry’s Law: At constant temperature, the solubility of a gas in a liquid is directly proportional to the pressure of the gas.
• Mathematical Expression: p = K_H​ × χ
• Henry’s Constant (K_H): Henry’s constant depends on the nature of the gas, solvent, and temperature; it is not a universal constant.
• Applications of Henry’s Law: Used in carbonation of soft drinks, explaining bends in deep-sea divers, oxygen availability at high altitudes, and oxygen transport in blood.
• Limitations of Henry’s Law: Not applicable to gases that react with the solvent, ionize in solution, or show non-ideal behavior at high pressure.

• Nature of solute and solvent:
  A solid dissolves in a liquid when their intermolecular forces are similar; hence, “like dissolves like” (polar solutes dissolve in polar solvents and non-polar in non-polar).
• Dissolution process:
  When a solid is added to a solvent, it dissolves continuously and increases the concentration of the solution until a limiting stage is reached.
• Saturated solution:
  A solution in which no more solute can dissolve at a given temperature and pressure is called a saturated solution.
• Solubility:
  The amount of solute (in grams) dissolved in 100 g of solvent to form a saturated solution at a given temperature is called solubility.
• Effect of temperature:
  Solubility increases with temperature for endothermic dissolution and decreases with temperature for exothermic dissolution.

Raoult’s Law (Statement):
At a given temperature, the partial vapour pressure of a volatile component of a solution is directly proportional to its mole fraction in the solution.

Vapour Pressure: 

Vapour pressure of a liquid = pressure exerted by its vapour in equilibrium with the liquid at a given temperature.

Raoult’s Law (Volatile Liquids)

The partial vapour pressure of each volatile component in a solution is equal to the product of its vapour pressure in the pure state and its mole fraction in the solution.

Formula:

p_i​ = p_i⁰ ​x_i

Where:

• pⁱ = partial vapour pressure of component i

• p_i⁰​ = vapour pressure of pure component i

• x_i​ = mole fraction of component i

Total Vapour Pressure (Binary Solution)

Formula:

 p = p_A​ + p_B​

p = p⁰_A x_A + p⁰_B x_B

​Raoult’s Law for Non-Volatile Solute

For a solution containing a non-volatile solute, the vapour pressure of the solution is directly proportional to the mole fraction of the solvent, and the relative lowering of vapour pressure equals the mole fraction of the solute.

Formula:

p = p⁰ x_solvent

Where:

• p = vapour pressure of solution

• p⁰ = vapour pressure of pure solvent

Relative Lowering of Vapour Pressure

Formula:

\[\frac{p^0-p}{p^0}=x_\mathrm{solute}\]

(Relative lowering of vapour pressure = mole fraction of solute)

The solutions which do not obey Raoult's law are called non ideal solutions.

The solution of completely miscible liquids, which boils at a constant temperature like a pure liquid and distils over without any change in composition, is called an azeotropic mixture or constant boiling mixture.

Meaning:
When a non-volatile solute is dissolved in a volatile solvent, the vapour pressure of the solvent decreases.
Lowering of vapour pressure = p⁰−p

Relative Lowering Formula:
Relative lowering of vapour pressure is given by:

\[\frac{p^0-p}{p^0}\]

where p⁰ = vapour pressure of pure solvent and
p = vapour pressure of solution.

Colligative Nature:
Relative lowering of vapour pressure is a colligative property as it depends only on the number of solute particles and not on their nature.

Relation with Mole Fraction:
According to Raoult’s law:

\[\frac{p^0-p}{p^0}=x_\mathrm{solute}\]

Thus, relative lowering of vapour pressure is equal to the mole fraction of the solute.

Meaning of Boiling Point:
The boiling point of a liquid is the temperature at which its equilibrium vapour pressure becomes equal to atmospheric pressure.

Effect of Solute:
When a non-volatile solute is dissolved in a solvent, the vapour pressure of the solvent decreases, hence the boiling point of the solution increases.

Elevation of Boiling Point:
The increase in boiling point of a solvent on addition of a non-volatile solute is called elevation of boiling point. It is a colligative property.

Mathematical Expression:
Elevation of boiling point is directly proportional to molality:

ΔT_b = K_b m

where K_b​ is the molal elevation constant of the solvent.

Molal Elevation Constant:
K_b​ is defined as the elevation of boiling point produced when one mole of solute is dissolved in 1000 g (1 kg) of solvent.
Its value depends only on the solvent, not on the solute.

Freezing Point:
The freezing point of a substance is the temperature at which its liquid and solid forms coexist in equilibrium, and the vapour pressure of liquid equals that of the solid.

Effect of Solute:
When a non-volatile solute is dissolved in a solvent, the vapour pressure of the solvent decreases, causing the freezing point of the solution to be lower than that of the pure solvent.

Depression of Freezing Point:
The decrease in freezing point of a solvent on addition of a non-volatile solute is called depression of freezing point. It is a colligative property.

Mathematical Expression
Depression of freezing point is directly proportional to molality:

ΔT_f = K_f m

where K_f is the molal depression constant (cryoscopic constant) of the solvent.

Molal Depression Constant:
K_f​ is defined as the depression of freezing point produced when one mole of solute is dissolved in 1000 g (1 kg) of solvent.
Its value depends only on the solvent, not on the solute.

The spontaneous flow of the solvent through a semipermeable membranefrom a pure solvent to a solution or from a dilute solution to a concentrated solution is called osmosis.

The osmotic pressure of a solution at a particular temperature may be defined as the hydrostatic pressure which builds up when the solution is separated from the solvent by a semipermeable membrane and which is just sufficient to stop the phenomenon of osmosis.

or

Osmotic pressure may also 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.

Degree of association is defined as the fraction of the total number of moles of solute which undergoes association in the solution.

At constant temperature, the osmotic pressure of a dilute solution is directly proportional to its concentration.
Since concentration is inversely proportional to volume, osmotic pressure is inversely proportional to volume.

\[\pi\propto\frac{1}{V}\quad\text{(at constant temperature)}\]

At constant concentration, the osmotic pressure of a dilute solution is directly proportional to absolute temperature.
An increase in temperature results in an increase in osmotic pressure.

π ∝ T (at constant concentration)

Equal volumes of solutions containing equal number of moles of solute exert equal osmotic pressure, provided temperature is the same.
Osmotic pressure depends only on the number of solute particles present.
This law is analogous to Avogadro’s law for gases.

Meaning:
van’t Hoff factor (i) represents the extent of association or dissociation of a solute in solution.

It is defined as the ratio of the observed value of a colligative property to the calculated (normal) value of the same property.

\[i=\frac{\Delta_{\mathrm{obs}}}{\Delta_{\mathrm{cal}}}\]

Importance:
Since colligative properties depend on the number of solute particles, the value of i indicates whether particles associate (i < 1) or dissociate (i > 1) in solution.

Degree of dissociation is defined as the fraction of the total
number of moles of solute which undergoes dissociation in the
solution.