Topic 4: Reactivity 1: What drives chemical reactions

Every chemical change involves an exchange of energy with its surroundings, usually as heat. This theme explains how we measure that energy as an enthalpy change, how to predict it from data, and (for HL) how entropy and Gibbs free energy decide whether a reaction happens at all.

Exothermic vs endothermic and enthalpy changes

Chemical reactions break bonds (which costs energy) and make new bonds (which releases energy). The net difference is the enthalpy change, deltaH, measured at constant pressure. In an exothermic reaction the products store less chemical energy than the reactants, so energy is released to the surroundings and the temperature rises; deltaH is negative. In an endothermic reaction the products store more energy, so heat is absorbed from the surroundings and the temperature falls; deltaH is positive. On an energy profile diagram, exothermic reactions show products lower than reactants, and endothermic reactions show products higher. The activation energy (Ea) is the energy hump that must be climbed before the reaction can proceed, regardless of whether the overall change is exo or endothermic.

Measuring enthalpy by calorimetry

Calorimetry measures the heat transferred to or from a known mass of water (or solution) using the equation q = m c deltaT, where q is heat in joules, m is the mass of liquid in grams, c is the specific heat capacity (4.18 J/g/K for water), and deltaT is the temperature change. The reaction enthalpy per mole is then deltaH = -q / n, where n is the moles of the limiting reactant; the negative sign converts a temperature rise (exothermic) into a negative deltaH. Worked example: 50.0 g of water absorbs heat from a reaction and rises by 8.0 K. Then q = 50.0 x 4.18 x 8.0 = 1672 J = 1.672 kJ. If 0.010 mol of reactant was used, deltaH = -1.672 / 0.010 = -167 kJ/mol. Heat lost to the surroundings, evaporation, and incomplete reaction all make experimental values less exothermic than data-book values.

Standard enthalpy changes

To compare values fairly, chemists define standard conditions: a pressure of 100 kPa and a stated temperature, usually 298 K, with all substances in their standard states and solutions at 1 mol/dm3. A standard enthalpy change carries the symbol deltaH with a standard-state superscript. Key examples include the standard enthalpy of formation (deltaHf, forming one mole of a compound from its elements in their standard states, which is zero for an element), the standard enthalpy of combustion (deltaHc, burning one mole of a substance completely in oxygen), and the standard enthalpy of neutralisation. Using consistent standard conditions lets values from different experiments be combined reliably.

Hess's law and energy cycles (HL)

Hess's law states that the total enthalpy change for a reaction is independent of the route taken, because enthalpy is a state function that depends only on the initial and final states. This lets us calculate enthalpy changes that are hard to measure directly by adding the steps of an alternative route. A common formula uses formation enthalpies: deltaH(reaction) = sum of deltaHf(products) - sum of deltaHf(reactants). When manipulating equations, reversing an equation flips the sign of deltaH, and multiplying an equation by a factor multiplies its deltaH by the same factor. Energy cycles drawn as triangles or boxes give a visual way to track these routes and signs.

Born-Haber cycles and lattice enthalpy (HL)

Lattice enthalpy is the energy change when one mole of an ionic compound forms from its gaseous ions; it reflects the strength of the ionic lattice and cannot be measured directly. A Born-Haber cycle is a specialised Hess's law cycle that builds an ionic solid step by step: atomisation of the metal and non-metal, ionisation energies of the metal, electron affinities of the non-metal, and finally lattice formation, all linked back to the enthalpy of formation. Setting the direct route (formation) equal to the indirect route (sum of all steps) lets the unknown lattice enthalpy be found. Lattice enthalpy increases with greater ionic charge and smaller ionic radius, because higher charge density gives stronger electrostatic attraction between the ions.

Bond enthalpy calculations

Bond enthalpy is the average energy needed to break one mole of a particular covalent bond in the gas phase. Because breaking bonds absorbs energy and forming bonds releases it, the enthalpy of a reaction can be estimated as deltaH = (sum of bonds broken) - (sum of bonds made). A positive total means more energy was needed to break bonds than was released, giving an endothermic reaction. These values are averages taken across many molecules, so bond-enthalpy estimates are only approximate and apply strictly to gaseous species; they will differ from precise calorimetric or formation-based values, especially where liquids or solids are involved.

Energy from fuels and combustion

Fuels release energy through exothermic combustion, with hydrocarbons such as methane and octane burning in oxygen to form carbon dioxide and water. The more negative the enthalpy of combustion, the more energy a fuel delivers per mole, though energy per gram and per litre also matter in practice. Incomplete combustion, caused by limited oxygen, produces carbon monoxide, soot, and less energy, and is both wasteful and hazardous. Biofuels and hydrogen offer lower net carbon emissions, but each has trade-offs in storage, production, and energy density that the IB syllabus links to wider environmental and social questions.

Entropy, Gibbs free energy and spontaneity (HL)

Entropy (S) measures the dispersal of energy and matter; greater disorder, such as gases forming or more particles being produced, means higher entropy. The entropy change of a reaction is deltaS = sum of S(products) - sum of S(reactants). Whether a reaction is spontaneous depends not only on enthalpy but on the Gibbs free energy change, deltaG = deltaH - T deltaS, where T is the absolute temperature in kelvin. A reaction is spontaneous when deltaG is negative. Exothermic reactions with increasing entropy are always spontaneous, while endothermic reactions with decreasing entropy never are; the remaining cases depend on temperature, so heating or cooling can switch spontaneity on or off.