Unit 1: Solutions

Homogeneous mixtures of two or more components — the basis for many biological and industrial processes

1.1 Types of Solutions

Solutions are homogeneous mixtures where composition and properties are uniform throughout. The component present in largest quantity is the solvent, and others are solutes.

Concentration Units

Unit	Formula	Temperature Dependent?
Mass % (w/w)	(Mass of component / Total mass) × 100	No
Volume % (V/V)	(Volume of component / Total volume) × 100	No
Parts per million (ppm)	(Parts of component / Total parts) × 10⁶	No
Mole fraction (x)	xₐ = nₐ / (nₐ + nᵦ)	No
Molarity (M)	Moles of solute / Volume of solution (L)	Yes
Molality (m)	Moles of solute / Mass of solvent (kg)	No

Mole fractions sum to unity: x₁ + x₂ + ... + xᵢ = 1. Molarity is temperature-dependent because volume changes with temperature.

1.2 Solubility

Solubility is the maximum amount of solute that can dissolve in a given amount of solvent at a given temperature and pressure.

Solubility of Solids in Liquids

Polar solutes dissolve in polar solvents ("like dissolves like")
If dissolution is endothermic (ΔₛₒₗH > 0), solubility ↑ with ↑ temperature
If dissolution is exothermic (ΔₛₒₗH < 0), solubility ↓ with ↑ temperature
Pressure has negligible effect on solid solubility

Solubility of Gases in Liquids — Henry's Law

Gas solubility increases with pressure and decreases with temperature.

        Henry's Law: p = Kₕ · x, where p is partial pressure, x is mole fraction in solution, and Kₕ is the Henry's law constant.

        Applications: Soft drinks (CO₂ sealed under pressure), scuba diving (He-N₂-O₂ mix to avoid bends), aquatic life in cold water.

1.3 Raoult's Law

For solutions of volatile liquids, the partial vapor pressure of each component is proportional to its mole fraction in solution.

        Raoult's Law: pᵢ = xᵢ · pᵢ⁰ for each component.

        Total pressure: p_total = x₁p₁⁰ + x₂p₂⁰

        Raoult's law is a special case of Henry's law when Kₕ = p₁⁰.

Ideal vs Non-Ideal Solutions

Property	Ideal Solution	Non-Ideal Solution
Raoult's Law	Obeys over entire range	Deviation from Raoult's law
ΔₘᵢₓH	= 0	≠ 0
ΔₘᵢₓV	= 0	≠ 0
Interactions	A-A ≈ B-B ≈ A-B	A-B ≠ A-A or B-B
Examples	n-Hexane + n-Heptane, Benzene + Toluene	Ethanol + Acetone (+), CHCl₃ + Acetone (−)

Azeotropes

Minimum boiling azeotrope: Large + deviation (e.g., 95% ethanol + 5% water)
Maximum boiling azeotrope: Large − deviation (e.g., 68% HNO₃ + 32% water)
Cannot be separated by fractional distillation

1.4 Colligative Properties

Properties that depend on the number of solute particles, not their identity. There are four colligative properties.

1. Relative Lowering of Vapor Pressure

(p₁⁰ − p₁) / p₁⁰ = x₂ = n₂ / (n₁ + n₂)

2. Elevation of Boiling Point

ΔTᵦ = Kᵦ · m

Where Kᵦ = molal elevation constant (K kg mol⁻¹), m = molality. For water, Kᵦ = 0.52 K kg mol⁻¹.

3. Depression of Freezing Point

ΔT𝒻 = K𝒻 · m

Where K𝒻 = molal depression constant. For water, K𝒻 = 1.86 K kg mol⁻¹.

4. Osmotic Pressure

        Π = CRT — Widely used for determining molar masses of proteins, polymers, and biomolecules because:
        Measured at room temperature (unlike boiling/freezing methods)
Large magnitude even for very dilute solutions
Biomolecules are stable at room temperature

    

Isotonic, Hypertonic, Hypotonic Solutions

Isotonic: Same osmotic pressure (e.g., 0.9% NaCl = blood plasma → safe for IV)
Hypertonic: Higher solute outside → water flows OUT → cells shrink
Hypotonic: Lower solute outside → water flows IN → cells swell

1.5 Abnormal Molar Masses — Van't Hoff Factor

Electrolytes dissociate into ions, increasing the number of particles. Some molecules associate (dimers), decreasing particles. This causes abnormal molar masses.

        Van't Hoff factor (i):

        i = Normal molar mass / Abnormal molar mass = Observed colligative prop. / Calculated colligative prop.

        Modified equations:

        ΔTᵦ = i · Kᵦ · m   |   ΔT𝒻 = i · K𝒻 · m   |   Π = i · n₂RT / V

        i > 1 for dissociation (e.g., NaCl → i ≈ 2)   |   i < 1 for association (e.g., acetic acid dimer → i ≈ 0.5)

Salt	i (0.001 m)	Complete Dissociation i
NaCl	1.97	2
KCl	1.98	2
MgSO₄	1.82	2
K₂SO₄	2.84	3

Summary

Solutions are classified by physical state of solute and solvent. Concentration is expressed in multiple units. Henry's law relates gas solubility to pressure. Raoult's law gives vapor pressure of ideal solutions. Colligative properties (vapor pressure lowering, boiling point elevation, freezing point depression, osmotic pressure) depend on number of solute particles. Van't Hoff factor accounts for dissociation/association of electrolytes.