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This lesson covers enthalpy changes, calorimetry, Hess's law, Born-Haber cycles, enthalpy of solution and hydration, entropy, and Gibbs free energy. Energetics is a fundamental topic that links thermodynamics to chemical reactions and helps predict whether reactions are feasible. The content here covers both AS and A2 material for AQA and OCR A specifications.
Key Definition: The enthalpy change (ΔH) of a reaction is the heat energy transferred between a system and its surroundings at constant pressure, measured in kJ mol⁻¹.
An energy level diagram (enthalpy profile diagram) has enthalpy on the vertical axis and progress of reaction on the horizontal axis. For an exothermic reaction, the products are drawn at a lower energy level than the reactants, and the downward arrow between them represents ΔH (negative). The hump above the reactant level represents the activation energy (Ea) — the minimum energy that colliding particles must have for a reaction to occur.
For an endothermic reaction, the products are drawn at a higher energy level than the reactants, and the upward arrow represents ΔH (positive). The activation energy is measured from the reactant level to the top of the energy hump.
Standard conditions are 100 kPa and a stated temperature (usually 298 K). All substances must be in their standard states. Important standard enthalpy changes include:
| Symbol | Name | Definition |
|---|---|---|
| ΔfH⦵ | Standard enthalpy of formation | Enthalpy change when one mole of a compound is formed from its elements in their standard states |
| ΔcH⦵ | Standard enthalpy of combustion | Enthalpy change when one mole of a substance is completely burned in excess oxygen under standard conditions |
| ΔrH⦵ | Standard enthalpy of reaction | Enthalpy change for the molar quantities shown in the balanced equation |
| ΔneutH⦵ | Standard enthalpy of neutralisation | Enthalpy change when one mole of water is formed from the neutralisation of an acid by a base |
| ΔatH⦵ | Standard enthalpy of atomisation | Enthalpy change when one mole of gaseous atoms is formed from an element in its standard state |
| ΔLE | Lattice enthalpy (formation) | Enthalpy change when one mole of an ionic solid is formed from its gaseous ions under standard conditions |
| ΔhydH⦵ | Enthalpy of hydration | Enthalpy change when one mole of gaseous ions is dissolved in sufficient water to form an infinitely dilute solution |
| ΔsolH⦵ | Enthalpy of solution | Enthalpy change when one mole of a solute dissolves in sufficient water to form an infinitely dilute solution |
Key Definition: The standard enthalpy of formation is the enthalpy change when one mole of a compound is formed from its elements in their standard states under standard conditions. By definition, ΔfH⦵ of any element in its standard state is zero.
Calorimetry is the experimental measurement of enthalpy changes. The key equation is:
q = mcΔT
where:
In a Required Practical experiment, 50.0 cm³ of 1.00 mol dm⁻³ HCl is mixed with 50.0 cm³ of 1.00 mol dm⁻³ NaOH in a polystyrene cup. The temperature rises by 6.8 °C. Calculate the enthalpy of neutralisation. Assume the density of the solution is 1.00 g cm⁻³ and the specific heat capacity is 4.18 J g⁻¹ K⁻¹.
Solution:
Step 1: Calculate q.
Total volume of solution = 50.0 + 50.0 = 100.0 cm³
Mass of solution = 100.0 g (assuming density = 1.00 g cm⁻³)
q = mcΔT = 100.0 × 4.18 × 6.8 = 2842.4 J = 2.842 kJ
Step 2: Calculate moles of water formed.
Moles of HCl = 0.0500 × 1.00 = 0.0500 mol
Moles of NaOH = 0.0500 × 1.00 = 0.0500 mol
Moles of water formed = 0.0500 mol
Step 3: Calculate ΔneutH.
ΔneutH = −q / n = −2.842 / 0.0500 = −56.8 kJ mol⁻¹
(Negative because the reaction is exothermic — the temperature increased.)
Exam Tip: In calorimetry, always use the mass of the solution (not the solute) and remember to include the negative sign for exothermic reactions. Common sources of error include heat loss to the surroundings, the assumption that the specific heat capacity equals that of water, and incomplete reactions.
Key Definition: Hess's law states that the total enthalpy change for a reaction is independent of the route taken, provided the initial and final conditions are the same. This is a consequence of the law of conservation of energy.
Hess's law allows us to calculate enthalpy changes that cannot be measured directly. Two common calculation routes:
A Hess's law cycle is drawn as a triangle or rectangle. The direct route (horizontal arrow from reactants to products) represents the unknown ΔrH. The indirect route goes via an intermediate — either the elements (when using formation data) or the combustion products (when using combustion data). Arrows pointing downward from compounds to elements/combustion products are labelled with the relevant ΔcH or −ΔfH values.
graph LR
A["Reactants"] -->|"ΔrH (direct route)"| B["Products"]
A -->|"−Σ ΔfH (reactants)"| C["Elements in<br/>standard states"]
C -->|"Σ ΔfH (products)"| B
Calculate the standard enthalpy of reaction for:
CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l)
Given: ΔfH⦵[CH₄(g)] = −74.8 kJ mol⁻¹, ΔfH⦵[CO₂(g)] = −393.5 kJ mol⁻¹, ΔfH⦵[H₂O(l)] = −285.8 kJ mol⁻¹, ΔfH⦵[O₂(g)] = 0 (element in standard state).
Solution:
ΔrH⦵ = Σ ΔfH⦵(products) − Σ ΔfH⦵(reactants)
ΔrH⦵ = [ΔfH⦵(CO₂) + 2 × ΔfH⦵(H₂O)] − [ΔfH⦵(CH₄) + 2 × ΔfH⦵(O₂)]
ΔrH⦵ = [(−393.5) + 2(−285.8)] − [(−74.8) + 2(0)]
ΔrH⦵ = [−393.5 − 571.6] − [−74.8]
ΔrH⦵ = −965.1 + 74.8
ΔrH⦵ = −890.3 kJ mol⁻¹
The mean bond enthalpy is the average energy required to break one mole of a particular type of bond in the gaseous state, averaged over many different compounds. Bond enthalpies can be used to estimate enthalpy changes:
ΔrH ≈ Σ (bond enthalpies of bonds broken) − Σ (bond enthalpies of bonds formed)
This method gives only an approximate value because mean bond enthalpies are averages and do not account for the specific chemical environment in a given molecule.
Key Definition: A Born-Haber cycle is an application of Hess's law used to calculate the lattice enthalpy of an ionic compound — the enthalpy change when one mole of an ionic compound is formed from its gaseous ions.
The Born-Haber cycle for NaCl is drawn as a series of steps, typically arranged vertically as an enthalpy level diagram:
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