Enthalpy Changes and Definitions

Energetics is one of the most fundamental topics in A-Level Chemistry. It deals with the energy changes that accompany chemical reactions and physical processes. To tackle this topic with confidence, you need to understand what enthalpy is, how we define different types of enthalpy change, and how to interpret energy profile diagrams. This lesson lays the groundwork for every calculation you will meet later in the course.

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Enthalpy and Enthalpy Change

Enthalpy (symbol H) is the total energy content of a system at constant pressure. We cannot measure the absolute enthalpy of a substance directly, but we can measure the enthalpy change (ΔH) when a reaction occurs.

ΔH = H(products) − H(reactants)

The sign of ΔH tells us about the direction of energy transfer:

• Exothermic reactions have a negative ΔH. The system releases energy to the surroundings, so the products have less enthalpy than the reactants. The temperature of the surroundings increases.
• Endothermic reactions have a positive ΔH. The system absorbs energy from the surroundings, so the products have more enthalpy than the reactants. The temperature of the surroundings decreases.

This sign convention is essential — always check whether you are being asked for an exothermic or endothermic process and assign the correct sign.

Common sign error: Students sometimes write a positive value for an exothermic reaction because "the temperature went up." Remember: a temperature rise in the surroundings means the system lost energy, so ΔH is negative.

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Standard Conditions

When we quote enthalpy changes, we do so under standard conditions so that values can be compared fairly. Standard conditions are:

• A pressure of 100 kPa
• A temperature of 298 K (25 °C)
• All substances in their standard states (the most stable physical form of the element or compound at 100 kPa and 298 K)

Standard enthalpy changes are denoted with the symbol ΔH° (the superscript ° indicates standard conditions). For example, the standard state of carbon is graphite (not diamond), the standard state of oxygen is O₂(g), and the standard state of water is H₂O(l).

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Standard Enthalpy of Formation (ΔH°f)

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.

For example, the formation of water:

H₂(g) + ½O₂(g) → H₂O(l) ΔH°f = −286 kJ mol⁻¹

Key points:

• The equation must produce exactly one mole of product.
• Elements in their standard states have a ΔH°f of zero by definition (they are already in their most stable form).
• Fractional coefficients (like ½) are permitted and often necessary.

Reference Table: Standard Enthalpies of Formation

Substance	ΔH°f / kJ mol⁻¹	Notes
H₂O(l)	−286	Liquid water at 298 K
H₂O(g)	−242	Steam — less exothermic because vaporisation is endothermic
CO₂(g)	−394	Very stable product of combustion
CH₄(g)	−75	Methane
C₂H₅OH(l)	−277	Ethanol
NH₃(g)	−46	Ammonia
NaCl(s)	−411	Sodium chloride
MgO(s)	−602	Magnesium oxide
O₂(g)	0	Element in standard state
C(s, graphite)	0	Element in standard state
Fe(s)	0	Element in standard state

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Standard Enthalpy of Combustion (ΔH°c)

The standard enthalpy of combustion is the enthalpy change when one mole of a substance undergoes complete combustion in excess oxygen, under standard conditions, with all reactants and products in their standard states.

For example, the combustion of methane:

CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l) ΔH°c = −890 kJ mol⁻¹

Key points:

• Combustion is always exothermic, so ΔH°c is always negative.
• Water must be written as H₂O(l) (liquid), not H₂O(g), under standard conditions.
• Complete combustion means all carbon is converted to CO₂ and all hydrogen to H₂O.

Reference Table: Standard Enthalpies of Combustion

Substance	Formula	ΔH°c / kJ mol⁻¹
Hydrogen	H₂(g)	−286
Carbon (graphite)	C(s)	−394
Methane	CH₄(g)	−890
Ethane	C₂H₆(g)	−1560
Propane	C₃H₈(g)	−2220
Methanol	CH₃OH(l)	−726
Ethanol	C₂H₅OH(l)	−1367
Propan-1-ol	C₃H₇OH(l)	−2021

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Standard Enthalpy of Neutralisation (ΔH°neut)

The standard enthalpy of neutralisation is the enthalpy change when an acid and a base react to produce one mole of water, under standard conditions.

For a strong acid and strong base:

HCl(aq) + NaOH(aq) → NaCl(aq) + H₂O(l) ΔH°neut ≈ −57.1 kJ mol⁻¹

Key points:

• Neutralisation is always exothermic.
• Strong acid–strong base neutralisations give a value close to −57.1 kJ mol⁻¹ because the net ionic equation is always H⁺(aq) + OH⁻(aq) → H₂O(l).
• Weak acid or weak base neutralisations give a less negative value because some energy is used to dissociate the weak acid or base.

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Standard Enthalpy of Atomisation (ΔH°at)

The standard enthalpy of atomisation is the enthalpy change when one mole of gaseous atoms is formed from the element in its standard state, under standard conditions.

For example:

½Cl₂(g) → Cl(g) ΔH°at = +121 kJ mol⁻¹

Na(s) → Na(g) ΔH°at = +107 kJ mol⁻¹

Key points:

• Atomisation is always endothermic (bonds must be broken), so ΔH°at is always positive.
• The equation must produce exactly one mole of gaseous atoms.

Worked Example: Linking Atomisation to Bond Energy

The standard enthalpy of atomisation of chlorine is +121 kJ mol⁻¹. This means:

½Cl₂(g) → Cl(g) ΔH = +121 kJ mol⁻¹

To break one mole of Cl–Cl bonds (producing 2 moles of Cl atoms):

Cl₂(g) → 2Cl(g) ΔH = 2 × 121 = +242 kJ mol⁻¹

So the Cl–Cl bond energy is +242 kJ mol⁻¹. Always check whether the question asks for the atomisation enthalpy (one mole of atoms) or the bond energy (one mole of bonds broken).

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Energy Profile Diagrams

Energy profile diagrams (also called reaction profiles or enthalpy level diagrams) show how the enthalpy of the system changes as a reaction proceeds.

For an exothermic reaction, the products sit lower than the reactants on the diagram. The difference in height represents ΔH (which is negative). There is a peak between reactants and products called the transition state, and the height from reactants to this peak is the activation energy (Ea).

For an endothermic reaction, the products sit higher than the reactants. ΔH is positive. There is still an activation energy peak — the height from reactants to the transition state.

Activation energy (Ea) is the minimum energy that colliding particles must possess for a reaction to occur. Even exothermic reactions need an initial input of activation energy to get started. A catalyst lowers the activation energy by providing an alternative reaction pathway, but it does not change ΔH.

Worked Example: Activation Energy for the Reverse Reaction

An endothermic reaction has ΔH = +178 kJ mol⁻¹ and Ea(forward) = +253 kJ mol⁻¹.

The products sit 178 kJ mol⁻¹ above the reactants. The transition state sits 253 kJ mol⁻¹ above the reactants. For the reverse (exothermic) reaction, the activation energy is measured from the products down to the transition state:

Ea(reverse) = 253 − 178 = 75 kJ mol⁻¹

This makes sense: the reverse reaction is exothermic, so it needs less activation energy.

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Real-World Applications

Understanding enthalpy changes has direct practical importance:

• Hand warmers use an exothermic reaction (e.g. the crystallisation of a supersaturated sodium ethanoate solution or the oxidation of iron powder) to release heat. The ΔH is negative and the energy is transferred to your hands.
• Cold packs used in sports medicine contain ammonium nitrate, which dissolves endothermically in water (ΔH°sol = +25.7 kJ mol⁻¹). The pack feels cold because the reaction absorbs heat from the surroundings.
• Fuel selection in industry depends on enthalpy of combustion data — a fuel with a more negative ΔH°c per gram releases more energy and is more economically efficient.

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Common Mistakes and How to Avoid Them

Mistake	Correction
Forgetting the sign on ΔH	Exothermic = negative; endothermic = positive. Always state the sign.
Using H₂O(g) instead of H₂O(l)	Under standard conditions (298 K), water is a liquid.
Writing 2 moles of product for ΔH°f	Formation must produce exactly 1 mole of product.
Saying ΔH°f of O₂ is zero "because it is a gas"	It is zero because O₂(g) is the standard state of oxygen, not because of its physical state.
Confusing atomisation enthalpy with bond energy	Atomisation produces 1 mol of gaseous atoms; bond energy breaks 1 mol of bonds (which may produce 2 mol of atoms).

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Bringing It Together

Understanding these definitions precisely is crucial. Exam questions frequently test whether you can write correct equations for standard enthalpy changes (correct coefficients, correct state symbols, exactly one mole where required) and whether you understand the sign conventions. Pay close attention to:

• The difference between one mole of compound formed (formation) and one mole of substance burned (combustion).
• The requirement for standard states in the equation.
• The sign of ΔH: negative for exothermic, positive for endothermic — never the other way around.
• The relationship between atomisation enthalpies and bond energies — they are related but not the same quantity.