Enthalpy change, ΔH

Enthalpy change ($\Delta H$) is the heat energy transferred at constant pressure: $\Delta H = H_{\text{products}} - H_{\text{reactants}}$

• Exothermic — releases heat to the surroundings; products are lower in energy → ΔH is negative (e.g. combustion).
• Endothermic — absorbs heat from the surroundings; products are higher in energy → ΔH is positive (e.g. thermal decomposition).

Reaction pathway (energy profile) diagrams plot enthalpy against reaction progress. They show the enthalpy change (ΔH) between reactants and products, and the activation energy ($E_a$) — the energy barrier that must be overcome.

Standard conditions (symbol $^{\ominus}$): a temperature of 298 K and a pressure of 101 kPa, with substances in their standard states.

The standard enthalpy definitions — each is per mole:

Term	Definition
$\Delta H_r^{\ominus}$ (reaction)	Enthalpy change when the molar quantities in the equation react under standard conditions.
$\Delta H_f^{\ominus}$ (formation)	Enthalpy change when one mole of a compound is formed from its elements in their standard states.
$\Delta H_c^{\ominus}$ (combustion)	Enthalpy change when one mole of a substance is completely burned in oxygen.
$\Delta H_{neut}^{\ominus}$ (neutralisation)	Enthalpy change when an acid and base react to form one mole of water.

Note. $\Delta H_f^{\ominus}$ of an element in its standard state is zero. Combustion is always exothermic; formation can be either.

Energy changes in reactions come from breaking and making bonds:

• Breaking bonds is endothermic (requires energy, +).
• Making bonds is exothermic (releases energy, −).

$\Delta H = \sum(\text{bond energies of bonds broken}) - \sum(\text{bond energies of bonds made})$

If more energy is released making bonds than is used breaking them, the reaction is exothermic (ΔH negative).

Worked. For $\text{H}_2 + \text{Cl}_2 \rightarrow 2\text{HCl}$ (bond energies: H–H 436, Cl–Cl 242, H–Cl 431 kJ mol⁻¹):

• Broken: $436 + 242 = 678$.
• Made: $2 \times 431 = 862$.
• $\Delta H = 678 - 862 = -184\,\text{kJ mol}^{-1}$ (exothermic).

Exact vs average bond energies. Some bond energies are exact (a specific bond in a specific molecule, e.g. H–H in H₂). Most quoted values are averages taken over many different molecules, so bond-energy calculations give an approximate ΔH.

In a calorimetry experiment, the heat released/absorbed is found from the temperature change of the water (or solution): $q = mc\Delta T$ where $m$ = mass of water (g), $c$ = specific heat capacity ($4.18\,\text{J g}^{-1}\text{K}^{-1}$ for water), $\Delta T$ = temperature change (K or °C).

Then convert to a molar enthalpy change: $\Delta H = -\frac{q}{n} \quad(\text{per mole of the substance})$

The sign: a temperature rise means heat was released → exothermic → ΔH negative (hence the minus sign).

Worked. Burning $0.0100\,\text{mol}$ of a fuel raises $100\,\text{g}$ of water by $20.0\,°\text{C}$:

• $q = 100 \times 4.18 \times 20.0 = 8360\,\text{J} = 8.36\,\text{kJ}$.
• $\Delta H = -\dfrac{8.36}{0.0100} = -836\,\text{kJ mol}^{-1}$.