Mole, Molarity & Solutions
The mole is chemistry's counting unit — it links the microscopic world of atoms to measurable quantities in the lab. Molarity connects moles to solution volumes.
A. The Mole Concept
What is a Mole?
- 1 mole = 6.022 × 10²³ particles (Avogadro's Number, Nₐ)
- Particles can be atoms, molecules, ions, or formula units
- Molar mass = mass of 1 mole in grams = numerically equal to relative atomic/molecular mass (from periodic table)
- Molar volume of any gas at STP = 22.4 L/mol (at 0°C, 1 atm)
n = m / M
Moles = Mass (g) ÷ Molar Mass (g/mol)
m = n × M
Mass = Moles × Molar Mass
N = n × Nₐ
Particles = moles × 6.022×10²³
V = n × 22.4
Volume at STP (L) = moles × 22.4
⚡ Common molar masses: H₂O = 18 g/mol · NaCl = 58.5 g/mol · CO₂ = 44 g/mol · H₂SO₄ = 98 g/mol · NaOH = 40 g/mol · HCl = 36.5 g/mol
B. Molarity (Molar Concentration)
Molarity & Concentration Expressions
Molarity (M)
M = n / V(L)
Molarity = moles of solute ÷ volume of solution in litres. Unit: mol/L or M
% Composition by Mass
% = (mass of element / molar mass of compound) × 100
| Expression | Formula | Unit |
|---|---|---|
| Molarity (M) | mol solute / L solution | mol/L or M |
| Molality (m) | mol solute / kg solvent | mol/kg |
| Mass percent | (mass solute / mass solution) × 100 | % (w/w) |
| Volume percent | (volume solute / volume solution) × 100 | % (v/v) |
| ppm | (mass solute / mass solution) × 10⁶ | ppm |
⚡ Worked Example Dissolve 5.85 g NaCl (M = 58.5 g/mol) in water to make 500 mL solution. What is the molarity?
n = 5.85/58.5 = 0.1 mol · V = 0.5 L · M = 0.1/0.5 = 0.2 mol/L
n = 5.85/58.5 = 0.1 mol · V = 0.5 L · M = 0.1/0.5 = 0.2 mol/L
C. Empirical & Molecular Formulae
Formula Types & Stoichiometry
| Term | Definition | Example (Glucose) |
|---|---|---|
| Empirical Formula | Simplest whole-number ratio of atoms in a compound | CH₂O |
| Molecular Formula | Actual number of each atom in one molecule | C₆H₁₂O₆ |
- Limiting reagent: the reactant completely used up first — determines the maximum product yield
- Excess reagent: the reactant that remains after the reaction is complete
- Stoichiometry: uses mole ratios from balanced equations to calculate amounts of reactants and products
- The mole ratio from the balanced equation is the key to all stoichiometric calculations
D. Solutions
Solution Types & Solubility
| Type | Definition | Example |
|---|---|---|
| Unsaturated | Can still dissolve more solute at the given temperature | Dilute sugar water |
| Saturated | Cannot dissolve any more solute at a given temperature — at maximum capacity | Salt solution at saturation point |
| Supersaturated | Contains MORE solute than normally possible — unstable, crystallises suddenly if disturbed | Honey, rock candy, sodium acetate hand warmers |
- Solubility of solids: generally increases with temperature
- Solubility of gases: decreases with increasing temperature (explains why fizzy drinks go flat when warm)
- "Like dissolves like": polar solvents (e.g. water) dissolve polar/ionic solutes; non-polar solvents (e.g. hexane) dissolve non-polar solutes
E. Colligative Properties
Properties That Depend on Solute Particle Number
Colligative properties depend only on the number of solute particles dissolved, not on their identity or nature.
| Property | Effect | Practical Example |
|---|---|---|
| Boiling Point Elevation | Adding solute raises the boiling point of the solvent | Salt water boils above 100°C; antifreeze raises car coolant BP |
| Freezing Point Depression | Adding solute lowers the freezing point of the solvent | Salt on icy roads; antifreeze in car radiators; seawater freezes below 0°C |
| Osmotic Pressure | Pressure needed to stop osmosis across a semipermeable membrane | Red blood cells in salt water — water leaves cell (crenation) |
| Vapour Pressure Lowering | Solute particles reduce the vapour pressure of the solvent | Salt water evaporates more slowly than pure water |
⚡ MCQ Tip More solute = higher BP, lower FP. "Like dissolves like." Solubility of gases ↓ with heat. Tyndall effect = colloids only. Solution → Colloid → Suspension (increasing particle size: <1nm → 1-1000nm → >1000nm).
Quick MCQ Revision
| Fact | Answer |
|---|---|
| Avogadro's Number | 6.022 × 10²³ particles per mole |
| Moles formula | n = m / M (mass ÷ molar mass) |
| Molarity formula | M = n / V(L) — moles per litre |
| Molar volume at STP | 22.4 L/mol |
| Molar mass of H₂O | 18 g/mol |
| Molar mass of NaCl | 58.5 g/mol |
| Solubility of gas with temperature | Decreases (gases less soluble when hot) |
| Adding solute to solvent | Raises BP, lowers FP (colligative properties) |
| "Like dissolves like" | Polar solvents dissolve polar solutes; non-polar dissolves non-polar |
| Limiting reagent | Reactant completely used up first — limits product yield |