Enthalpy changes — OCR A-Level Chemistry

Enthalpy change, ∆H, is the heat energy transferred at constant pressure, and its sign shows direction: negative for exothermic, positive for endothermic. Four standard definitions must be distinguished. ∆H of reaction is the enthalpy change for the equation as written. ∆H of formation is the change when one mole of a compound forms from its elements in their standard states, with all substances in standard conditions. ∆H of combustion is the change when one mole of a substance burns completely in oxygen, with reactants and products in standard states. ∆H of neutralisation is the change when an acid and alkali react to form one mole of water. Each definition fixes a quantity of one mole of a specified substance, so the balanced equation and state symbols matter.

Enthalpy change (∆H) measures the heat energy exchanged with the surroundings at constant pressure. In an exothermic reaction the system loses enthalpy to the surroundings, so the surroundings warm and ∆H carries a negative sign; combustion of methane is a familiar example. In an endothermic reaction the system gains enthalpy from the surroundings, so the surroundings cool and ∆H carries a positive sign; thermal decomposition of calcium carbonate is a familiar example. The sign is a convention fixed relative to the system, not a statement about magnitude, so a large exothermic change is more negative, not more positive. Learners should classify a described reaction, assign the correct sign and explain the direction of energy transfer in words.

An enthalpy profile diagram plots enthalpy on the vertical axis against reaction progress on the horizontal axis. Reactants sit at one enthalpy level and products at another; the vertical difference between these two levels is ΔH. For an exothermic reaction the products lie lower than the reactants, so ΔH is negative and the arrow points downwards from reactants to products. For an endothermic reaction the products lie higher, so ΔH is positive and the arrow points upwards. Activation energy is shown separately as the height from reactants to the peak. Label both levels, the axes and the direction of ΔH.

Activation energy is the minimum energy that colliding particles must possess for a reaction to occur. On an enthalpy profile diagram the vertical axis shows enthalpy and the horizontal axis shows the reaction pathway from reactants to products. The reactants sit at one enthalpy level and the products at another; the difference between them is the enthalpy change ΔH. Between them lies a peak representing the transition state at the maximum enthalpy along the route. The activation energy is the vertical height from the reactants' enthalpy level up to that peak. A large activation energy means few collisions have enough energy, so the reaction is slow at a given temperature. Catalysts provide an alternative route with a lower peak, so the activation energy falls.

This statement introduces a list of terms whose explanation and use you must master within enthalpy changes. The published statement ends at the colon, so the individual terms are set by the specification's following list rather than by this row alone. Read the specification's own list of terms and learn each one: what it means, the symbol and units where relevant, and how it is used in calculations and explanations. For each term, prepare a short definition, a worked example of its use, and a note of the sign convention. Check units carefully, for example kJ mol⁻¹ for enthalpy change, and keep any negative signs that show energy released. Use the terms precisely when explaining whether a reaction is exothermic or endothermic.

Standard conditions are the agreed reference conditions used so that enthalpy values can be compared between reactions: a pressure of 100 kPa (1.00 × 10⁵ Pa) and a stated temperature, conventionally 298 K (25 °C). A standard state is the physical state of an element or compound under those standard conditions — for example, water is liquid, bromine is liquid, iodine is solid and oxygen is gas at 298 K and 100 kPa. The standard state of a substance is not simply its most common state anywhere; it is the state at the specified reference conditions. When you write a standard enthalpy change, the equation must show each species in its standard state, so state symbols matter. A substance whose standard state differs from the state in a given equation cannot be used directly as a reference without accounting for the change of state.

The enthalpy change of reaction, ∆rH, is the enthalpy change associated with a stated equation, with all species in their standard states and under standard conditions. Because the value depends on the equation as written, the same reaction can have different ∆rH values if the equation is scaled or reversed. For example, forming 2 mol of water from hydrogen and oxygen releases twice the energy of forming 1 mol, and reversing the equation reverses the sign. The symbol ∆rH is quoted per the equation as written, so the stoichiometric coefficients matter. When you compare or calculate ∆rH, always read the equation first: its coefficients and direction fix the magnitude and sign of the value.

The standard enthalpy change of formation, ∆fH, is the enthalpy change when one mole of a compound forms from its elements in their standard states under standard conditions. Two features define it: the product is exactly 1 mol of the compound, and the reactants are the elements themselves, not other compounds. For water, ∆fH refers to forming 1 mol of H₂O from H₂ and O₂ in their standard states, not to burning hydrogen in a way that yields 2 mol. Elements in their standard states have ∆fH = 0 by definition, so a formation equation always starts from elements. Values are usually negative for stable compounds because bond formation releases energy. In an MCQ, check that the equation shows 1 mol of product and only elements as reactants, and that the sign matches whether energy is released or absorbed.

The standard enthalpy change of combustion, ∆cH, is the enthalpy change when one mole of a substance burns completely in excess oxygen under standard conditions. Two features define it: exactly 1 mol of the substance is combusted, and combustion is complete, so carbon forms CO₂ and hydrogen forms H₂O. For ethanol, ∆cH refers to burning 1 mol of C₂H₅OH completely, not to a partial or incomplete burn producing CO. Combustion of fuels releases energy, so ∆cH values are usually negative. In an MCQ, check that the equation shows 1 mol of the substance reacting with oxygen and that the products are the complete combustion products. Compare the coefficient of the fuel and the products to confirm complete combustion.

The enthalpy change of neutralisation, ∆neutH, is the enthalpy change when an acid and a base react in aqueous solution to form one mole of water. Because the definition fixes the amount of water at 1 mol, values are quoted per mole of water and are usually close to −57 kJ mol⁻¹ for strong acid–strong base reactions, since the reaction is essentially H⁺(aq) + OH⁻(aq) → H₂O(l). A weak acid gives a smaller magnitude because some energy is used in ionising it. Learners should write the equation, identify how many moles of water form, and scale the measured energy to one mole, keeping the sign negative for an exothermic neutralisation.

Enthalpy changes can be found experimentally by measuring a temperature change and using q = mc∆T, where q is the heat energy transferred in joules, m is the mass of the substance heated or cooled in grams, c is the specific heat capacity in J g⁻¹ K⁻¹ and ∆T is the temperature change in kelvin or degrees Celsius. For a solution, m is taken as the mass of the solution, often approximated as its volume in cm³ because the density is close to 1 g cm⁻³. The energy q is then divided by the number of moles reacting to give the enthalpy change per mole, with a sign that reflects whether the reaction is exothermic or endothermic.

Bond enthalpy is the enthalpy change when one mole of a specified covalent bond is broken in gaseous molecules, so it is always endothermic and positive. Because the strength of a bond varies between compounds, the specification distinguishes the mean bond enthalpy, averaged over many gaseous compounds, from the bond enthalpy in one particular molecule. Mean bond enthalpies let you estimate the enthalpy change of a gas-phase reaction: add the mean bond enthalpies of the bonds broken and subtract the mean bond enthalpies of the bonds formed. The estimate is approximate because the actual bonds in the reacting molecules differ from the averaged values, and because the calculation assumes all species are gaseous.

The average bond enthalpy is the enthalpy change when one mole of a specified covalent bond is broken in gaseous molecules, averaged over a range of gaseous compounds containing that bond. The same bond, such as an O–H bond, has slightly different strengths in different molecules, so a single averaged value is used for calculations. Breaking bonds absorbs energy, so the average bond enthalpy is positive and the process is endothermic. The gaseous condition matters: the value applies to gaseous molecules, not to liquids or solids. Average bond enthalpies allow an approximate enthalpy change of reaction to be estimated by comparing bonds broken with bonds formed.

Bond breaking and bond making carry opposite enthalpy changes. Breaking a covalent bond requires energy from the surroundings, so it is endothermic and has a positive enthalpy change. Making a bond releases energy to the surroundings, so it is exothermic and has a negative enthalpy change. For a reaction, compare total energy absorbed in breaking bonds in the reactants with total energy released in making bonds in the products. If breaking absorbs more than making releases, the overall reaction is endothermic (ΔH positive). If making releases more than breaking absorbs, the overall reaction is exothermic (ΔH negative). For example, in the combustion of methane, breaking bonds in CH₄ and O₂ absorbs energy, but forming CO₂ and H₂O releases more, so the reaction is exothermic.

Average bond enthalpies are mean values for a particular bond type across a range of compounds, usually quoted in kJ mol⁻¹ for gaseous species. To calculate the enthalpy change of a reaction, sum the average bond enthalpies of all bonds broken in the reactants and subtract the sum of the average bond enthalpies of all bonds made in the products: ΔH = Σ(bonds broken) − Σ(bonds made). A positive result indicates an endothermic reaction; a negative result indicates an exothermic reaction. Because the values are averages, the calculated ΔH is an estimate and may differ from a measured value. Related quantities can be found by rearranging the same relationship, for example to find the total energy of bonds broken or made.

Hess’ law states that the enthalpy change of a reaction is independent of the route taken, provided the initial and final states are the same. This lets you find an enthalpy change that is hard to measure directly by building an enthalpy cycle from changes you can measure, such as standard enthalpies of formation or combustion. For example, to find the enthalpy of formation of a compound that cannot be made directly, combine the standard enthalpies of combustion of the elements and the compound, reversing arrows where the route runs the other way. Add the values around the cycle so the total equals the direct change, then solve for the unknown. Always keep the same states and the same direction of arrows, and check signs carefully.

This statement requires you to use Hess’ law both to construct enthalpy cycles and to carry out calculations that determine an enthalpy change indirectly. Construction means drawing a cycle in which the direct route from reactants to products is set equal to an alternative route through intermediate substances, with arrows showing each step. The calculation then sums the known enthalpy changes along the alternative route, reversing signs where an arrow is reversed, to obtain the unknown value. Typical cases use standard enthalpies of formation from elements or standard enthalpies of combustion to the same oxides. Keep states consistent, label each arrow, and solve the arithmetic to give the indirect enthalpy change with its correct sign and units.

A Hess cycle using enthalpy changes of combustion starts from the reactants and products of the reaction and routes both down to the same combustion products, such as CO₂(g) and H₂O(l). Because combustion is exothermic, each combustion enthalpy is negative. The enthalpy change of reaction equals the sum of the combustion enthalpies of the reactants minus the sum of the combustion enthalpies of the products: ΔrH = ΣΔcH(reactants) − ΣΔcH(products). Multiply each value by its stoichiometric coefficient. Fully oxidised species such as CO₂ and H₂O have a standard enthalpy of combustion of zero, so they are omitted. Check the sign and direction of the cycle before calculating.

This skill uses Hess's law with standard enthalpy changes of formation, ΔH_f. Formation means forming one mole of a compound from its elements in their standard states, so elements have ΔH_f = 0. The route is: reactants → elements → products, giving ΔH_reaction = Σ ΔH_f(products) − Σ ΔH_f(reactants), each multiplied by its coefficient. Worked example: for CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l), using ΔH_f(CH₄) = −75 kJ mol⁻¹, ΔH_f(CO₂) = −394 kJ mol⁻¹ and ΔH_f(H₂O) = −286 kJ mol⁻¹, the answer is [(−394) + 2 × (−286)] − [(−75) + 0] = (−966) − (−75) = −891 kJ mol⁻¹. Note the order is products minus reactants, the reverse of the combustion route. Check coefficients, signs and zero values before choosing an option.

Unfamiliar enthalpy cycles test whether you can apply Hess's law to a route you have not memorised. Draw the cycle so that each known enthalpy change sits on a labelled arrow, then close the loop with the unknown. Apply Hess's law: the total enthalpy change is independent of route, so the sum of the steps one way equals the sum of the steps the other way. For example, if formation enthalpies are given for the reactants and products of an unfamiliar reaction, the reaction enthalpy equals the sum of the products' formation enthalpies minus the sum of the reactants'. Watch signs: reversing an arrow reverses the sign, and multiplying a step multiplies its value. Then solve for the unknown and check units are kJ mol⁻¹.

Direct determination measures heat evolved or absorbed in a calorimeter: a known mass of water is heated or cooled by a reaction, and q = mcΔT gives the heat, with c the specific heat capacity of water (4.18 J g⁻¹ K⁻¹). Divide q by the moles reacting to get ΔH in kJ mol⁻¹, converting joules to kilojoules. Indirect determination uses Hess's law when a reaction cannot be measured directly, for example combining enthalpy of combustion or formation data, or measuring a related reaction and reversing or scaling steps. Account for heat loss, incomplete combustion and non-standard conditions as sources of error. Always record temperature change, mass and moles precisely.