Solutions Chemistry - Class 12 Bihar Board Chemistry

Solutions and Colligative Properties

Definition and Nature of Solutions

A solution is a homogeneous mixture of two or more non-reacting substances. The composition and properties of a homogeneous mixture remain uniform throughout. Homogeneous mixtures differ from heterogeneous mixtures, where the composition is not uniform and different phases can be observed.

• Homogeneous mixture: Uniform composition throughout (e.g., salt in water, sugar in water).
• Heterogeneous mixture: Non-uniform composition, multiple layers or phases (e.g., oil and water, sand and water).
• Solute: Component present in lesser amount.
• Solvent: Component present in greater amount.
• In a solution with…

Solutions and Colligative Properties

Definition and Nature of Solutions

A solution is a homogeneous mixture of two or more non-reacting substances. The composition and properties of a homogeneous mixture remain uniform throughout. Homogeneous mixtures differ from heterogeneous mixtures, where the composition is not uniform and different phases can be observed.

• Homogeneous mixture: Uniform composition throughout (e.g., salt in water, sugar in water).
• Heterogeneous mixture: Non-uniform composition, multiple layers or phases (e.g., oil and water, sand and water).
• Solute: Component present in lesser amount.
• Solvent: Component present in greater amount.
• In a solution with more than two components, the one in largest amount is the solvent; all others are solutes.

Types of Solutions and Classification

Solutions are classified based on the number of components and the physical state of the solvent. The physical state of the solvent determines the state of the solution.

• By number of components:
  • Binary solution: Two components.
  • Ternary solution: Three components.
  • Quaternary solution: Four components.
• By physical state of solvent:
  • Liquid solution: Solvent is liquid (e.g., salt in water).
  • Gaseous solution: Solvent is gas (e.g., air).
  • Solid solution: Solvent is solid (e.g., alloys).
• The solvent decides the physical state of the solution.

Concentration Terms and Calculations

Concentration expresses the amount of solute dissolved in a specific amount of solvent or solution. Several terms are used to express concentration, each with its own formula and unit.

• Mass percentage: $\text{Mass \%} = \frac{\text{Mass of solute}}{\text{Total mass of solution}} \times 100$
• Volume percentage: $\text{Volume \%} = \frac{\text{Volume of solute}}{\text{Total volume of solution}} \times 100$
• Mass by volume percentage: $\frac{\text{Mass of solute}}{100\,\text{ml solution}} \times 100$
• Parts per million (ppm): $\text{ppm} = \frac{\text{Mass of solute}}{\text{Mass of solution}} \times 10^6$
• Parts per billion (ppb): $\text{ppb} = \frac{\text{Mass of solute}}{\text{Mass of solution}} \times 10^9$
• Mole fraction ($X$): $X_A = \frac{\text{Moles of }A}{\text{Total moles of all components}}$
  • The sum of mole fractions of all components in a solution is always 1.
  • Mole fraction is unitless and temperature independent.
• Molarity ($M$): $M = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}}$
  • Unit: mol/L
  • Molarity depends on temperature (volume changes with temperature).
• Molality ($m$): $m = \frac{\text{Moles of solute}}{\text{Mass of solvent in kg}}$
  • Unit: mol/kg
  • Molality is temperature independent (mass does not change with temperature).

Solubility and Its Factors

Solubility is the maximum amount of a substance that can be dissolved in a fixed amount of solvent at a fixed temperature. It depends on the nature of solute and solvent, temperature, and pressure (for gases).

• Solubility of solids in liquids: Depends on nature and temperature, not on pressure (solids and liquids are incompressible).
• "Like dissolves like": Polar solutes dissolve in polar solvents; non-polar solutes dissolve in non-polar solvents.
• Effect of temperature:
  • If dissolution is endothermic ($\Delta H > 0$), solubility increases with temperature.
  • If dissolution is exothermic ($\Delta H < 0$), solubility decreases with temperature.
• Effect of pressure: Significant only for gases in liquids; solubility increases with pressure.

Henry’s Law and Its Applications

Henry’s Law states that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.

• Mathematical form: $P = K_H \cdot X_{\text{gas}}$
  • $P$: Partial pressure of gas
  • $K_H$: Henry’s law constant (different for different gases)
  • $X_{\text{gas}}$: Mole fraction of gas in solution
• Higher $K_H$ value means lower solubility.
• Applications:
  • Bottling of soft drinks: CO$_2$ is dissolved under high pressure.
  • Deep-sea diving: Gas mixtures are adjusted to avoid excessive solubility of gases in blood.
  • High altitudes: Lower atmospheric pressure leads to lower oxygen solubility in blood.

Vapour Pressure and Raoult’s Law

Vapour pressure is the pressure exerted by vapour in equilibrium with its liquid in a closed container at a given temperature. Raoult’s Law relates the partial vapour pressure of each component in a solution to its mole fraction.

• Raoult’s Law for volatile liquids:
  • $P_A = P_A^0 X_A$
  • $P_B = P_B^0 X_B$
  • $P_{\text{total}} = P_A + P_B = P_A^0 X_A + P_B^0 X_B$
• For a binary solution, $X_A + X_B = 1$.
• Vapour pressure does not depend on the amount of substance or surface area, only on temperature.
• More volatile liquids have lower boiling points.

Ideal and Non-Ideal Solutions

Ideal solutions obey Raoult’s Law at all concentrations and show no enthalpy or volume change on mixing. Non-ideal solutions deviate from Raoult’s Law and show enthalpy and/or volume changes.

• Ideal solution:
  • Obeys Raoult’s Law for all concentrations.
  • $\Delta V_{\text{mix}} = 0$, $\Delta H_{\text{mix}} = 0$.
  • Intermolecular forces between A and B are approximately equal to those between A-A and B-B.
• Non-ideal solution:
  • Deviates from Raoult’s Law.
  • $\Delta V_{\text{mix}} \neq 0$, $\Delta H_{\text{mix}} \neq 0$.
  • Positive deviation: $P_{\text{total}} >$ predicted, $\Delta V_{\text{mix}} > 0$, $\Delta H_{\text{mix}} > 0$.
  • Negative deviation: $P_{\text{total}} <$ predicted, $\Delta V_{\text{mix}} < 0$, $\Delta H_{\text{mix}} < 0$.

Colligative Properties

Colligative properties depend only on the number of solute particles, not their nature. There are four main colligative properties:

• Relative lowering of vapour pressure (RLVP):
  • $\frac{P^0 - P_s}{P^0} = X_{\text{solute}}$
  • For dilute solutions, $X_{\text{solute}} \approx \frac{n_1}{n_2}$ if $n_2 \gg n_1$.
• Elevation in boiling point ($\Delta T_b$):
  • $\Delta T_b = K_b \cdot m$
  • $K_b$: Ebullioscopic constant
  • $m$: Molality
• Depression in freezing point ($\Delta T_f$):
  • $\Delta T_f = K_f \cdot m$
  • $K_f$: Cryoscopic constant
• Osmotic pressure ($\pi$):
  • $\pi = CRT$
  • $C$: Molarity, $R$: Universal gas constant, $T$: Temperature in Kelvin

Special Solution Types and Phenomena

Some mixtures and phenomena have special properties or definitions relevant to solutions.

• Azeotropic mixture: Mixture of two liquids that boils at a constant temperature and cannot be separated by fractional distillation. Types:
  • Minimum boiling azeotrope: Mixture boils at a lower temperature than either component.
  • Maximum boiling azeotrope: Mixture boils at a higher temperature than either component.
• Boiling point: Temperature at which vapour pressure of liquid equals external (atmospheric) pressure.
• Osmosis: Spontaneous flow of solvent from low to high solute concentration through a semipermeable membrane.
• Reverse osmosis: Flow of solvent from high to low solute concentration when excess pressure is applied to the higher concentration side; used in desalination.
• Isotonic solutions: Solutions with equal osmotic pressure at the same temperature.
• Hypertonic solution: Higher osmotic pressure (higher concentration) relative to another.
• Hypotonic solution: Lower osmotic pressure (lower concentration) relative to another.

Abnormal Molar Mass and van’t Hoff Factor

Abnormal molar mass arises when solute particles associate or dissociate in solution, affecting colligative properties. The van’t Hoff factor ($i$) corrects for this.

• van’t Hoff factor ($i$):
  • $i = \frac{\text{Total number of particles after association/dissociation}}{\text{Total number before}}$
  • $i = 1$ for non-electrolytes (no association/dissociation).
  • $i > 1$ for dissociation (e.g., NaCl $\rightarrow$ Na$^+$ + Cl$^-$).
  • $i < 1$ for association (e.g., dimerization).
• All colligative property formulas are multiplied by $i$ to account for abnormal molar mass.

Exam-Focused Problem Types and Pitfalls

Questions often focus on calculation of colligative properties, identification of solution types, and application of laws. Common pitfalls include unit errors and misidentification of the number of particles.

• Always convert volumes to liters and masses to kilograms as required by formulas.

• For boiling point elevation and freezing point depression, identify the number of particles produced by dissociation or association.

• For RLVP, remember only non-volatile solute is considered; its vapour pressure is zero.

• For osmotic pressure, use molarity and temperature in Kelvin.

• For ideal/non-ideal solutions, check if the solution follows Raoult’s Law and if enthalpy/volume changes are zero.

• For azeotropes, note that they cannot be separated by fractional distillation due to constant boiling point.

• Practice previous year questions on molarity, molality, mole fraction, and colligative properties for best exam performance.