Solutions Karnataka - Class 12 Karnataka Board Accountancy

Solutions: Properties, Types, and Quantitative Aspects

Definition and Core Concepts

A solution is a homogeneous mixture composed of two or more substances. The substance present in the largest amount is called the solvent, while the other components are called solutes. Solutions can exist in different physical states depending on the nature of the solvent and solute, such as solid, liquid, or gas. The composition of a solution is described by the amount of solute dissolved in a given quantity of solvent or solution.

• Homogeneous mixture: Uniform composition throughout.
• Solvent: Component present in greater quantity.
• Solute:…

Solutions: Properties, Types, and Quantitative Aspects

Definition and Core Concepts

A solution is a homogeneous mixture composed of two or more substances. The substance present in the largest amount is called the solvent, while the other components are called solutes. Solutions can exist in different physical states depending on the nature of the solvent and solute, such as solid, liquid, or gas. The composition of a solution is described by the amount of solute dissolved in a given quantity of solvent or solution.

• Homogeneous mixture: Uniform composition throughout.
• Solvent: Component present in greater quantity.
• Solute: Component present in lesser quantity.
• Physical states: Solutions can be solid-solid, solid-liquid, solid-gas, liquid-liquid, liquid-gas, gas-gas, etc.

Types of Solutions

Solutions are classified based on the physical state of the solute and solvent. The transcript explicitly mentions several types and provides examples for each.

• Solid in solid: Alloys, e.g., brass.
• Solid in liquid: Sugar in water, salt in water.
• Gas in liquid: Carbon dioxide in soft drinks.
• Liquid in liquid: Alcohol in water.
• Gas in gas: Air (mixture of gases).
• Solid in gas: Not commonly found.

The nature of the solute and solvent (polar or non-polar) affects the formation and properties of the solution.

Concentration Terms and Formulas

Concentration expresses the amount of solute present in a given quantity of solvent or solution. Several terms and formulas are explicitly stated:

• Molarity (M): Number of moles of solute per liter of solution.$$M = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}}$$
• Normality (N): Number of equivalents of solute per liter of solution.$$N = \frac{\text{Number of equivalents of solute}}{\text{Volume of solution in liters}}$$
• Molality (m): Number of moles of solute per kilogram of solvent.$$m = \frac{\text{Number of moles of solute}}{\text{Mass of solvent in kg}}$$
• Percentage by mass: $$\% \text{ by mass} = \frac{\text{Mass of solute}}{\text{Mass of solution}} \times 100$$
• Percentage by volume: $$\% \text{ by volume} = \frac{\text{Volume of solute}}{\text{Volume of solution}} \times 100$$
• Mole fraction (X): Ratio of moles of one component to total moles in solution.$$X_A = \frac{n_A}{n_A + n_B}$$

Preparation and Calculation Methods

To prepare a solution of known concentration, the transcript describes the following steps:

1. Calculate the required mass or volume of solute using the desired concentration formula.
2. Dissolve the solute in a portion of solvent.
3. Transfer the solution to a volumetric flask and dilute to the mark with solvent to achieve the desired volume.

For calculations:

• Use the molarity, normality, or molality formulas as per the requirement.
• For dilution, use the relationship $M_1V_1 = M_2V_2$ (if stated).
• For percentage solutions, calculate the mass or volume of solute needed for a given total mass or volume.

Properties Dependent and Independent of Temperature

Some properties of solutions depend on temperature, while others do not.

• Molarity changes with temperature because volume expands or contracts.
• Molality and mole fraction are independent of temperature as they depend on mass, not volume.
• Normality may change with temperature if the volume changes.

Vapour Pressure and Raoult’s Law

The vapour pressure of a solution is influenced by the presence of solute particles. The transcript states:

• The vapour pressure of a solution is lower than that of the pure solvent.
• Raoult’s Law: The partial vapour pressure of each component in an ideal solution is directly proportional to its mole fraction.$$P_A = X_A P_A^0$$$$P_B = X_B P_B^0$$$$P_{total} = P_A + P_B$$
• For non-volatile solute, the vapour pressure of the solution is due only to the solvent.

Colligative Properties

Colligative properties depend on the number of solute particles, not their nature. The transcript mentions:

• Relative lowering of vapour pressure
• Elevation of boiling point
• Depression of freezing point
• Osmotic pressure

Key relationships:

• The depression in freezing point and elevation in boiling point are directly proportional to the number of solute particles.
• The formulas for these properties are not fully stated, but the proportionality is emphasized.

Effect of Temperature and Pressure

Temperature and pressure affect the solubility and properties of solutions.

• Solubility of solids in liquids generally increases with temperature.
• Solubility of gases in liquids decreases with increase in temperature and increases with pressure.
• Boiling point elevation and freezing point depression are affected by the addition of solute and are related to the number of particles.

Electrolytes and Non-Electrolytes

The transcript distinguishes between electrolytes and non-electrolytes:

• Electrolytes dissociate into ions in solution and conduct electricity (e.g., NaCl).
• Non-electrolytes do not dissociate and do not conduct electricity (e.g., sugar).
• The van’t Hoff factor ($i$) accounts for the number of particles produced by dissociation or association.

Osmosis and Osmotic Pressure

Osmosis is the movement of solvent molecules through a semi-permeable membrane from a region of lower solute concentration to higher solute concentration.

• Osmotic pressure ($\pi$): The pressure required to stop osmosis.
• The transcript gives the formula:$$\pi = CRT$$where $C$ is concentration, $R$ is the gas constant, and $T$ is temperature.
• Isotonic solutions: Solutions with equal osmotic pressure.
• Hypotonic solution: Lower osmotic pressure compared to another.
• Hypertonic solution: Higher osmotic pressure compared to another.

Special Cases and Examples

Several examples and special cases are mentioned:

• Carbonated drinks: Example of gas dissolved in liquid under pressure.
• Scuba diving: Increased solubility of gases in blood under high pressure.
• Blood and saline: Isotonic solutions for medical use.
• Soft drinks: Carbon dioxide dissolved in water under pressure.

Limitations and Validity of Laws

Raoult’s Law and colligative property relationships are valid for ideal solutions and dilute solutions. The transcript notes:

• Ideal solutions: Intermolecular interactions between solute and solvent are similar to those in pure components.
• Non-ideal solutions: Deviations occur due to differences in interactions.
• Raoult’s Law is strictly applicable only to ideal solutions.

Quantitative Problem-Solving

The transcript provides steps and formulas for solving quantitative problems:

• Calculate the number of moles, mass, or volume as required.
• Use the appropriate formula for molarity, normality, or molality.
• For colligative properties, relate the change in boiling/freezing point or osmotic pressure to the number of solute particles.
• For vapour pressure, use the mole fraction and vapour pressure of pure components.

Key Exam Points and Pitfalls

• Always check whether the property is dependent on temperature or not.

• Use the correct formula for the type of concentration required.

• For solutions involving electrolytes, account for dissociation using the van’t Hoff factor.

• In calculations involving dilution, ensure volumes are additive only for ideal solutions.

• For colligative properties, only the number of particles matters, not their nature.

• Common mistakes: Confusing molarity and molality, ignoring temperature dependence, not accounting for dissociation in electrolytes, and misapplying Raoult’s Law to non-ideal solutions.

• Important relationships: Boiling point is inversely proportional to vapour pressure; as solute is added, vapour pressure decreases, boiling point increases, and freezing point decreases.

• Units: Always use consistent units (e.g., liters for volume, kilograms for mass) in calculations.

• Application: Understanding solution properties is essential for practical applications such as medical saline preparation, beverage carbonation, and industrial chemical processes.