Calculate enthalpy changes with calorimetry, bond enthalpies, Hess's Law, Born-Haber cycles, and Gibbs free energy. Step-by-step solutions with energy diagrams for GCSE and A-Level Chemistry.
Energy transferred = mass × specific heat capacity × temperature change
Enthalpy change = total bonds broken − total bonds formed
Using standard enthalpies of formation
Using standard enthalpies of combustion (note reversed order!)
ΔG determines spontaneity. Remember: ΔS must be in kJ!
The enthalpy of formation equals the sum of all steps in the cycle
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Enthalpy (H) is the total energy content of a chemical system at constant pressure. In chemistry, we measure the enthalpy change (ΔH) — the difference in enthalpy between the products and reactants of a reaction.
If ΔH is negative, the reaction is exothermic — it releases energy to the surroundings. The products have less energy than the reactants, and the temperature of the surroundings increases.
If ΔH is positive, the reaction is endothermic — it absorbs energy from the surroundings. The products have more energy than the reactants, and the temperature of the surroundings decreases.
Standard enthalpy changes are measured under standard conditions: 100 kPa pressure, 298 K (25°C), and 1 mol dm⁻³ concentration for solutions. The symbol for standard enthalpy change is ΔH°.
Calorimetry is the experimental technique used to measure enthalpy changes by monitoring temperature changes in a known mass of water. The formula is:
q = mcΔT
q = energy (J) | m = mass (kg) | c = specific heat capacity (J kg⁻¹ K⁻¹) | ΔT = temperature change (K)
The specific heat capacity tells you how much energy is needed to raise the temperature of 1 kg of a substance by 1 K. Water has a high specific heat capacity of 4186 J kg⁻¹ K⁻¹ (or 4.186 J g⁻¹ K⁻¹), which is why it is commonly used as the surrounding in calorimetry experiments.
| Substance | c (J kg⁻¹ K⁻¹) |
|---|---|
| Water | 4186 |
| Ice | 2090 |
| Steam | 2010 |
| Aluminium | 897 |
| Iron | 449 |
| Copper | 385 |
| Lead | 128 |
| Ethanol | 2440 |
The bond enthalpy (or bond energy) is the energy required to break one mole of a specific covalent bond in the gas phase. Bond enthalpies are always positive because breaking bonds requires energy (endothermic).
We use mean (average) bond enthalpies because the exact energy depends on the molecular environment. The C-H bond in CH₄ has slightly different energy than in C₂H₆, so we use an average across many compounds.
ΔH = Σ(bonds broken) − Σ(bonds formed)
Bonds broken = energy input (endothermic) | Bonds formed = energy output (exothermic)
Hess's Law states that the total enthalpy change for a reaction is the same regardless of the route taken, provided the initial and final conditions are identical. This is a consequence of enthalpy being a state function.
In practice, this means we can calculate ΔH for reactions that are difficult to measure directly by using data from other reactions. There are two main routes:
ΔH°rxn = Σ ΔHf°(products) − Σ ΔHf°(reactants)
ΔH°rxn = Σ ΔHc°(reactants) − Σ ΔHc°(products)
A Born-Haber cycle is an energy cycle used to calculate the lattice enthalpy of an ionic compound. Lattice enthalpy cannot be measured directly, so we use Hess's Law to calculate it from other measurable enthalpy changes.
The cycle combines several enthalpy changes in a specific order:
Gibbs free energy (ΔG) determines whether a reaction is thermodynamically spontaneous (feasible). It combines enthalpy, entropy, and temperature:
ΔG = ΔH − TΔS
ΔG in kJ mol⁻¹ | ΔH in kJ mol⁻¹ | T in K | ΔS in J mol⁻¹ K⁻¹ (convert to kJ!)
⚠ Most common mistake: ΔS is usually given in J mol⁻¹ K⁻¹ but ΔH is in kJ mol⁻¹. You must divide ΔS by 1000 before substituting into the equation!
Spontaneous at all temperatures
Never spontaneous
Spontaneous at low temperatures
Spontaneous at high temperatures
Exothermic reactions release energy (ΔH negative) — e.g., combustion, neutralisation
Endothermic reactions absorb energy (ΔH positive) — e.g., thermal decomposition, citric acid + sodium hydrogencarbonate
Energy is needed to break bonds (endothermic) and released when bonds form (exothermic)
In exothermic reactions, more energy is released making bonds than is needed to break bonds
Temperature change in calorimetry: q = mcΔT (m in kg, c for water = 4186 J kg⁻¹ K⁻¹)
Energy profile diagrams show reactants, products, activation energy, and overall ΔH
A catalyst lowers the activation energy but does not change ΔH
Reaction profiles: exothermic goes down, endothermic goes up (products vs reactants)
Standard conditions: 100 kPa, 298 K, 1 mol dm⁻³. Standard enthalpy changes are measured under these conditions
Hess's Law: ΔH is independent of route. Use formation route (ΔHf°) or combustion route (ΔHc°)
Bond enthalpies are mean values — they give approximate ΔH only, less accurate than Hess's Law
Born-Haber cycles use Hess's Law to find lattice enthalpies of ionic compounds
Lattice enthalpy depends on ionic charge and ionic radius — smaller ions and higher charges give more negative lattice enthalpies
Gibbs free energy: ΔG = ΔH − TΔS. Convert ΔS from J to kJ before substituting!
Crossover temperature: when ΔH and ΔS have the same sign, T = ΔH/ΔS gives the temperature where ΔG = 0
Entropy (ΔS) increases when: gases are produced, number of particles increases, solid → liquid → gas
Enthalpy (H) is the total energy of a system at constant pressure. The enthalpy change (ΔH) tells us how much heat energy is transferred during a reaction.
Exothermic reactions release heat (ΔH < 0, temperature rises). Endothermic reactions absorb heat (ΔH > 0, temperature drops).
ΔH = Σ(bonds broken) − Σ(bonds formed). Add up the energy to break all bonds in reactants, subtract the energy released forming all bonds in products.
Hess's Law states that the enthalpy change for a reaction is independent of the route taken. This lets you calculate ΔH using formation or combustion data.
The exact energy of a bond depends on the molecule it's in. Mean bond enthalpies are averages across many compounds, so they give approximate ΔH values.
A Born-Haber cycle applies Hess's Law to ionic compounds, combining atomisation, ionisation, electron affinity, and lattice enthalpy to find unknown values.
ΔG = ΔH − TΔS determines if a reaction is spontaneous (feasible). If ΔG < 0, the reaction is thermodynamically spontaneous at that temperature.
ΔH is in kJ mol⁻¹ but ΔS is in J mol⁻¹ K⁻¹. You must divide ΔS by 1000 before substituting into ΔG = ΔH − TΔS to get consistent units.
Lattice enthalpy is the energy released when gaseous ions form an ionic lattice. It's always exothermic and depends on ion charge and size.
Yes — when ΔG = 0, the system is at equilibrium. The temperature at which this occurs is the crossover temperature: T = ΔH/ΔS.
Formation route: ΔH = ΣΔHf°(products) − ΣΔHf°(reactants). Combustion route: ΔH = ΣΔHc°(reactants) − ΣΔHc°(products). Note the subtraction is reversed.
When ΔH and ΔS have the same sign, spontaneity depends on temperature. The crossover temperature T = ΔH/ΔS determines the switch point.
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