Freezing point depression = K_f * m = 1.86 * 0.1 = 0.186 °C

Molality = ΔT_b / (i * K_b) = 1.024 / (2 * 0.512) = 1 mol/kg

Vapor pressure lowering = (n_solute / n_solvent) * P°_solvent = (0.5 / 55.5) * 23.76 = 1.88 mmHg

NaCl dissociates into 2 ions (Na+ and Cl-), so 1 mol of NaCl produces 2 mol of particles in solution.

NaCl dissociates into 2 ions (Na+ and Cl-), so the van 't Hoff factor i = 2.

NaCl dissociates into 2 ions (Na+ and Cl-), so 1 mol of NaCl results in 2 mol of particles.

The freezing point depression is calculated using the formula ΔTf = Kf * m, where Kf for water is 1.86 °C kg/mol.

The freezing point depression is calculated using the formula ΔTf = i * Kf * m. For a non-electrolyte, i = 1, Kf for water = 1.86 °C kg/mol, and m = 1 mol/kg gives ΔTf = 1.86 °C.

The freezing point depression for 1 mole of a non-electrolyte solute in 1 kg of water is -1.86 °C.

NaCl dissociates into 2 ions (Na+ and Cl-), so the van 't Hoff factor (i) is 2.

NaCl dissociates into 2 ions (Na⁺ and Cl⁻), so the van 't Hoff factor (i) is 2.

Molarity = π / (RT) = 3.0 / (0.0821 * 298) = 0.12 M

Molarity = π / (RT) = 3.0 / (0.0821 * 298) = 0.12 M

The freezing point of a solvent decreases when a non-volatile solute is added, a phenomenon known as freezing point depression.

The vapor pressure of a solvent decreases when a non-volatile solute is added due to the solute particles occupying space at the surface.

Boiling point elevation = i * K_b * m = 2 * 0.512 * 1 = 1.024 °C (i = 2 for NaCl)

Boiling point elevation = i * K_b * m = 2 * 0.512 * 0.5 = 0.512 °C; Boiling point = 100 + 0.512 = 100.512 °C

The addition of a non-volatile solute raises the boiling point of the solvent, a phenomenon known as boiling point elevation.

Osmotic pressure (π) can be calculated using the formula π = iCRT. For NaCl, i = 2, C = 0.5 M, R = 0.0821 L·atm/(K·mol), and T = 298 K, resulting in approximately 24.6 atm.

The boiling point elevation is calculated using the formula ΔT_b = i * K_b * m, where i is the van 't Hoff factor.

The depression of freezing point is calculated using the formula ΔTf = Kf * m, where Kf is the freezing point depression constant and m is the molality of the solution.

The freezing point depression constant (Kf) for water is 1.86 °C kg/mol.

Freezing point depression is directly proportional to the number of solute particles in the solution.

Freezing point depression = Kf * molality = 1.86 * 0.5 = 0.93 °C.

Freezing point depression = K_f * m = 1.86 * 0.3 = 0.558 °C; Freezing point = 0 - 0.558 = -0.558 °C

Osmotic pressure = iCRT = 2 * 0.2 * 0.0821 * 298 = 4.92 atm (i = 2 for NaCl)

Osmotic pressure = (n/V)RT = (0.2/1) * 0.0821 * 298 = 4.92 atm.

Osmotic pressure is directly proportional to both the temperature and the concentration of solute.

Colligative properties depend primarily on the concentration of solute particles in a solution.

The elevation of boiling point occurs because the presence of solute lowers the vapor pressure of the solvent, requiring a higher temperature to reach boiling.