Ability of a solute to dissolve in a solvent

How can you distinguish between solute and solvent in a solution?

Solute is present in lesser quantity, solvent in greater quantity

State Henry's Law and provide its equation.

Henry's Law states that the solubility ($S$) of a gas in a liquid is directly proportional to the partial pressure ($P$) of the gas above the liquid at a constant temperature. The equation is $S = K_H P$, where $K_H$ is Henry's Law constant.

What is Raoult's Law for a volatile component in a solution?

Raoult's Law states that the partial vapor pressure ($P_1$) of any volatile component in a solution is equal to the vapor pressure of the pure component ($P_1^0$) multiplied by its mole fraction ($X_1$). The equation is $P_1 = P_1^0 X_1$.

Solution One Shot | Class 12 Maharashtra Board Chemistry

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Solutions and Colligative Properties

Nature of Solutions and Components

A solution is a homogeneous mixture where the solute and solvent are uniformly mixed at the molecular level. The solute is present in lesser quantity, while the solvent is present in greater quantity. The physical state of solute or solvent is not fixed; both can be solid, liquid, or gas.

Solute: Present in lesser quantity.
Solvent: Present in greater quantity.
The distinction between solute and solvent is based solely on their relative amounts, not their physical state.

Types of Solutions: Saturation Concepts

Solutions are classified…

Solutions and Colligative Properties

Nature of Solutions and Components

A solution is a homogeneous mixture where the solute and solvent are uniformly mixed at the molecular level. The solute is present in lesser quantity, while the solvent is present in greater quantity. The physical state of solute or solvent is not fixed; both can be solid, liquid, or gas.

Solute: Present in lesser quantity.
Solvent: Present in greater quantity.
The distinction between solute and solvent is based solely on their relative amounts, not their physical state.

Types of Solutions: Saturation Concepts

Solutions are classified based on the amount of solute dissolved relative to the solvent's capacity. The three main types are unsaturated, saturated, and supersaturated solutions.

Unsaturated Solution: All added solute dissolves completely in the solvent.
Saturated Solution: No more solute dissolves; excess solute settles at the bottom.
Supersaturated Solution: Excess solute settles down in large amounts, indicating the solution holds more solute than its normal capacity.

Solubility and Its Factors

Solubility is the amount of solute that dissolves in a given volume of solvent (usually 1 L). Its unit is mol per liter. Solubility varies with the nature of solute and solvent, temperature, and pressure.

Definition: Amount of solute dissolved per unit volume of solvent (1 L).
Unit: mol/L.
Key Factors Affecting Solubility:
- Nature of Solute and Solvent: "Like dissolves like"—polar solutes dissolve in polar solvents, non-polar in non-polar.
- Temperature: For endothermic processes, solubility increases with temperature; for exothermic, it decreases.
- Pressure: For gases, solubility increases with pressure (directly proportional).

Henry’s Law

Henry’s Law states that the solubility of a gas in a liquid is directly proportional to the pressure of the gas above the solution. The proportionality constant is called Henry’s Law constant ( $K_H$ ).

Statement: Solubility of a gas is directly proportional to pressure.
Formula: $S = K_H \cdot P$ $S = K_{H} \cdot P$
- $S$ = solubility, $K_H$ = Henry’s Law constant, $P$ = pressure.
Unit of Solubility: mol/L.
Exceptions: Ammonia ( $NH_3$ ) and carbon dioxide ( $CO_2$ ) do not obey Henry’s Law.
Exam Points: Statement, formula, and exceptions are frequently asked.

Raoult’s Law

Raoult’s Law relates the vapor pressure of a solution to the mole fraction of the solvent. The partial vapor pressure of each volatile component is equal to the vapor pressure of the pure component multiplied by its mole fraction.

Statement: Partial vapor pressure of a component in solution equals the vapor pressure of pure component times its mole fraction.
Formula: $P_1 = P_1^0 \cdot x_1$ $P_{1} = P_{1}^{0} \cdot x_{1}$
- $P_1$ = vapor pressure of solution, $P_1^0$ = vapor pressure of pure solvent, $x_1$ = mole fraction of solvent.
Dalton’s Law Connection: Total vapor pressure $P_T = P_1 + P_2$ , with $P_1 = x_1 P_1^0$ , $P_2 = x_2 P_2^0$ , and $x_1 + x_2 = 1$ .
Deviation: Positive deviation if solute-solute and solvent-solvent attractions are stronger; negative deviation if solute-solvent attractions are stronger.

Colligative Properties

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

Relative Lowering of Vapor Pressure
Elevation in Boiling Point
Depression in Freezing Point
Osmotic Pressure

1. Relative Lowering of Vapor Pressure

Adding a non-volatile solute lowers the vapor pressure of the solvent.

Formula: $\Delta P = P_1^0 - P_1 = P_1^0 x_2$ $Δ P = P_{1}^{0} - P_{1} = P_{1}^{0} x_{2}$
- $\Delta P$ = lowering of vapor pressure, $x_2$ = mole fraction of solute.
In terms of molar mass: $\frac{\Delta P}{P_1^0} = \frac{w_2 M_1}{w_1 M_2}$
- $w_2$ = mass of solute, $M_1$ = molar mass of solvent, $w_1$ = mass of solvent, $M_2$ = molar mass of solute.

2. Elevation in Boiling Point

The boiling point of a solution is higher than that of the pure solvent.

Formula: $\Delta T_b = K_b \cdot m$ $Δ T_{b} = K_{b} \cdot m$
- $\Delta T_b = T_b - T_b^0$ , $K_b$ = ebullioscopic constant, $m$ = molality.
- $K_b$ unit: K kg/mol.
In terms of molar mass: $\Delta T_b = \frac{K_b \cdot w_2 \cdot 1000}{M_2 \cdot w_1}$
- $w_2$ = mass of solute, $M_2$ = molar mass of solute, $w_1$ = mass of solvent (g).

3. Depression in Freezing Point

The freezing point of a solution is lower than that of the pure solvent.

Formula: $\Delta T_f = K_f \cdot m$ $Δ T_{f} = K_{f} \cdot m$
- $\Delta T_f = T_f^0 - T_f$ , $K_f$ = cryoscopic constant, $m$ = molality.
- $K_f$ unit: K kg/mol.
In terms of molar mass: $\Delta T_f = \frac{K_f \cdot w_2 \cdot 1000}{M_2 \cdot w_1}$

4. Osmotic Pressure

Osmotic pressure is the minimum pressure required to stop the flow of solvent molecules through a semipermeable membrane from a dilute to a concentrated solution.

Definition: Minimum force applied to stop the flow of solvent molecules through a semipermeable membrane.
Formula: $\pi = MRT$ $π = M R T$
- $\pi$ = osmotic pressure, $M$ = molarity, $R$ = gas constant, $T$ = temperature (K).
In terms of molar mass: $\pi = \frac{w_2 R T}{M_2 V}$
- $w_2$ = mass of solute, $M_2$ = molar mass of solute, $V$ = volume of solution (L).

Special Terms: Isotonic, Hypertonic, Hypotonic Solutions

These terms describe solutions based on their osmotic pressure relative to each other.

Isotonic Solutions: Two or more solutions with the same osmotic pressure.
Hypertonic Solution: Solution with higher osmotic pressure compared to another.
Hypotonic Solution: Solution with lower osmotic pressure compared to another.

Reverse Osmosis

Reverse osmosis occurs when pressure greater than the osmotic pressure is applied, causing solvent molecules to move from the concentrated to the dilute side, reversing the natural direction of osmosis.

Condition: Applied pressure must be greater than osmotic pressure.
Application: Used in water purification.

Ideal and Non-Ideal Solutions

Ideal solutions obey Raoult’s Law at all concentrations and show no enthalpy or volume change upon mixing. Non-ideal solutions deviate from Raoult’s Law and may show positive or negative deviations.

Ideal Solution:
- Obeys Raoult’s Law.
- No heat absorbed or evolved ( $\Delta H_{mix} = 0$ ).
- No volume change on mixing.
Non-Ideal Solution:
- Does not obey Raoult’s Law.
- Vapor pressure may be higher or lower than predicted.
- May absorb or evolve heat on mixing.

Van’t Hoff Factor

The van’t Hoff factor ( $i$ ) accounts for the effect of solute dissociation or association on colligative properties.

Formula for colligative property with $i$ :
- For vapor pressure lowering: $\Delta P = i \cdot P_1^0 x_2$
- For boiling point elevation: $\Delta T_b = i \cdot K_b m$
- For freezing point depression: $\Delta T_f = i \cdot K_f m$
- For osmotic pressure: $\pi = i \cdot MRT$
Degree of dissociation ( $\alpha$ ): $\alpha = \frac{i - 1}{n - 1}$
- $n$ = number of ions formed per formula unit.

Key Exam Points and Formula List

Several formulas and definitions are repeatedly emphasized for exams. Focus on the following:

Henry’s Law: $S = K_H \cdot P$
Raoult’s Law: $P_1 = P_1^0 x_1$
Relative Lowering of Vapor Pressure: $\frac{\Delta P}{P_1^0} = \frac{w_2 M_1}{w_1 M_2}$
Elevation in Boiling Point: $\Delta T_b = K_b m$
Depression in Freezing Point: $\Delta T_f = K_f m$
Osmotic Pressure: $\pi = MRT$
Van’t Hoff Factor: Multiply $i$ in all colligative property formulas.
Degree of Dissociation: $\alpha = \frac{i - 1}{n - 1}$

Definitions to memorize:

Osmosis
Osmotic Pressure
Reverse Osmosis
Isotonic, Hypertonic, Hypotonic Solutions

Common Calculation Strategies

When solving numericals:

Identify given values: mass (g) is $w$ , molar mass (g/mol) is $M$ .
For vapor pressures, the higher value is $P_1^0$ (solvent), the lower is $P_1$ (solution).
For freezing point depression, if only one negative temperature is given, take its positive value as $\Delta T_f$ .
For colligative property numericals, use the formula with $i$ if dissociation/association is involved.

Table: Key Formula Mapping

Property	Basic Formula	With van’t Hoff Factor ( $i$ )
Relative Lowering of Vapor Pressure	$\Delta P = P_1^0 x_2$	$\Delta P = i P_1^0 x_2$
Elevation in Boiling Point	$\Delta T_b = K_b m$	$\Delta T_b = i K_b m$
Depression in Freezing Point	$\Delta T_f = K_f m$	$\Delta T_f = i K_f m$
Osmotic Pressure	$\pi = MRT$	$\pi = i MRT$

All formulas and definitions above are directly stated or derived in the transcript and are essential for board exam preparation.

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What is solubility?

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What is a solution?

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A solution is defined as a homogeneous mixture where solute and solvent are completely intermixed. The solute is present in a lesser quantity, while the solvent is in a greater quantity, and their phases are not fixed.