Chemistry is built on a surprisingly small set of core formulas. Master these and you can work through the vast majority of A-Level, AP, and first-year university problems. This guide covers the most important equations — what they mean, how to use them, and the mistakes students most often make.
The Mole and Molarity
Everything in quantitative chemistry starts with the mole. One mole of anything contains 6.022 × 10²³ particles (Avogadro's number). The relationship between mass, moles, and molar mass is:
n = m / M
Where n is moles, m is mass in grams, and M is molar mass in g/mol (found by summing atomic masses from the periodic table).
Molarity extends this to solutions:
M = n / V
Concentration in mol/L equals moles divided by volume in litres. A 0.1 M solution of NaCl contains 0.1 moles of sodium chloride per litre of solution.
Common mistake: Students often forget to convert volume to litres before dividing. 500 mL is 0.5 L, not 500.
The Dilution Formula
When you add solvent to a solution, the moles of solute stay constant even though concentration drops:
C₁V₁ = C₂V₂
Example: You have 50 mL of a 2 M HCl solution and need 0.5 M HCl. What final volume do you need?
2 × 50 = 0.5 × V₂
V₂ = 200 mL
Add 150 mL of water to the original 50 mL. Always add acid to water — never the reverse — to safely dissipate heat.
The Gas Laws
The three classical gas laws combine into one powerful equation:
P₁V₁ / T₁ = P₂V₂ / T₂
This is the combined gas law, and by holding one variable constant you recover each individual law:
| Law | Constant | Relationship | |-----|----------|-------------| | Boyle's | Temperature | P₁V₁ = P₂V₂ | | Charles's | Pressure | V₁/T₁ = V₂/T₂ | | Gay-Lussac's | Volume | P₁/T₁ = P₂/T₂ |
Critical rule: Temperature must always be in Kelvin. Convert using K = °C + 273.15. Using Celsius is one of the most common exam mistakes.
For the Ideal Gas Law at a single set of conditions:
PV = nRT
Where R = 8.314 J/mol·K (or 0.08206 L·atm/mol·K). Use the second value when pressure is in atmospheres and volume in litres.
Stoichiometry: The Mole Ratio Method
Stoichiometry converts between masses of reactants and products using balanced equations. The method is always the same four steps:
- Balance the equation
- Convert given mass → moles (divide by molar mass)
- Scale using the mole ratio from the equation
- Convert back → mass (multiply by molar mass)
Example: How many grams of water form when 18 g of H₂ reacts with excess O₂?
2H₂ + O₂ → 2H₂O
- 18 g H₂ ÷ 2 g/mol = 9 mol H₂
- Ratio is 2:2, so 9 mol H₂ → 9 mol H₂O
- 9 mol × 18 g/mol = 162 g H₂O
Percent Yield
Real reactions never give 100% yield due to side reactions, incomplete conversion, and handling losses:
% yield = (actual yield / theoretical yield) × 100
If your stoichiometry predicts 162 g of water but you collect 145 g:
% yield = (145 / 162) × 100 = 89.5%
Enthalpy and Hess's Law
Enthalpy change (ΔH) measures heat released or absorbed at constant pressure. For calorimetry:
q = m × c × ΔT
Where c for water = 4.18 J/g·°C.
Hess's Law states that ΔH is path-independent — you can add equations (and their ΔH values) to find the enthalpy of a reaction you can't measure directly. If you reverse an equation, change the sign of ΔH. If you multiply by a factor, multiply ΔH by the same factor.
Gibbs Free Energy
The most powerful single equation in thermodynamics:
ΔG = ΔH - TΔS
- ΔG < 0: Reaction is spontaneous (proceeds without added energy)
- ΔG > 0: Non-spontaneous (requires energy input)
- ΔG = 0: System is at equilibrium
The interplay between enthalpy and entropy means temperature determines spontaneity when ΔH and TΔS point in opposite directions.
| ΔH | ΔS | Spontaneous? | |----|-----|-------------| | − | + | Always | | + | − | Never | | − | − | Only at low T | | + | + | Only at high T |
Equilibrium Constant
For a reversible reaction aA + bB ⇌ cC + dD:
Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ
- Kc >> 1: Products favoured (reaction goes nearly to completion)
- Kc << 1: Reactants favoured (barely any product forms)
- Pure solids and liquids are excluded from the expression
The reaction quotient Q has the same form as Kc but uses any concentrations, not equilibrium values. If Q < Kc, the reaction proceeds forward; if Q > Kc, it goes backward.
Henderson-Hasselbalch for Buffers
Buffers resist pH changes by containing both a weak acid and its conjugate base:
pH = pKa + log([A⁻] / [HA])
When [A⁻] = [HA] (equal concentrations), log(1) = 0, so pH = pKa. This is the midpoint of the buffer's working range. Buffers work effectively within ±1 pH unit of the pKa.
Blood uses the carbonic acid / bicarbonate system (pKa 6.1) to maintain pH 7.4 — an example of Henderson-Hasselbalch with a specific [A⁻]/[HA] ratio of about 20:1.
The Nernst Equation
Cell voltage under non-standard conditions:
E = E° - (0.0592/n) × log Q (at 25°C)
Where n is electrons transferred and Q is the reaction quotient. As a battery discharges, Q increases and E falls — eventually reaching zero at full discharge.
Key Numbers to Memorise
| Constant | Value | |----------|-------| | Avogadro's number | 6.022 × 10²³ /mol | | Gas constant R | 8.314 J/mol·K | | Faraday constant F | 96,485 C/mol | | Speed of light c | 3.00 × 10⁸ m/s | | Kw (water, 25°C) | 1.0 × 10⁻¹⁴ |
Putting It All Together
The most important habit in chemistry is unit tracking. Write every unit in every step. When units cancel correctly, the method is almost certainly right. When they don't cancel, you'll catch the error before losing marks.
Use our Molarity Calculator, Stoichiometry Calculator, Gibbs Free Energy Calculator, and Henderson-Hasselbalch Calculator to check your working.