Overview of Solutions

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

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

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.

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

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

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.

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

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

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

For binary solution:

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

x_A ​+ x_B​ = 1

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

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

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):

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

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:

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

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

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.

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 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