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Energetics

14 min read

Enthalpy changes

The enthalpy change ΔH of a reaction is the heat taken in or given out at constant pressure. In an exothermic reaction ΔH is negative; in an endothermic reaction ΔH is positive. Standard enthalpy changes are measured at 298 K and 100 kPa.

Breaking bonds takes in energy; making stronger bonds in CO₂ and H₂O gives out more, so burning is exothermic.
Energy profilesTwo energy diagrams. In an exothermic reaction the products are lower in energy than the reactants, so energy is given out. In an endothermic reaction the products are higher in energy, so energy is taken in. Both need an activation energy to start.progress of reactionenergyreactantsproductsprogress of reactionenergyreactantsproductsactivationΔH negativeactivationΔH positiveExothermic: heat given outEndothermic: heat taken in
Standard enthalpy changeDefinitionExample
Formation, ΔH_f°One mole of a compound formed from its elements in their standard statesC(s) + O₂(g) → CO₂(g); ΔH = −394 kJ/mol
Combustion, ΔH_c°One mole of a substance completely burned in oxygenCH₄ + 2O₂ → CO₂ + 2H₂O; ΔH = −890 kJ/mol
NeutralisationOne mole of water formed from an acid and an alkaliAbout −57 kJ/mol for strong acid and alkali
AtomisationOne mole of gaseous atoms formed from the elementNa(s) → Na(g)
Bond enthalpyEnergy to break one mole of a bond in the gas phaseC–H: +413 kJ/mol

Hess's law

Hess's law
The total enthalpy change of a reaction is the same whatever route is taken, provided the starting and finishing conditions are the same.
A Hess’s law cycleA triangle of reactions. The enthalpy change of formation of a compound from its elements, delta H1, equals the sum of the enthalpy changes of two steps by a different route: delta H2 to burn the elements to products and delta H3 for the reverse of the compound’s combustion. The energy change does not depend on the route.elementscompoundcombustion productsΔH₁ (direct)ΔH₂ΔH₃ΔH₁ = ΔH₂ − ΔH₃same total by either route
Worked exampleEnthalpy of formation from combustion data

Find ΔH_f of ethane gas from these values: C(s) burns to CO₂ with ΔH = −394 kJ/mol, H₂(g) burns to H₂O(l) with ΔH = −286 kJ/mol, and ethane C₂H₆ burns with ΔH = −1560 kJ/mol. (Equation: 2C + 3H₂ → C₂H₆)

  1. Add the combustion of the elements (2 C and 3 H₂) and subtract the combustion of ethane.

Answer: ΔH_f of ethane is −86 kJ/mol.

Bond enthalpies and calorimetry

Breaking bonds takes in energy (+); making bonds gives it out (−). In a calorimeter q = m c ΔT, with c = 4.18 J g⁻¹ K⁻¹ for water. Then ΔH = −q ÷ moles.
Try itCalorimetry

A reaction in 100 g of water heats it by ΔT. The reaction used the stated moles. Find ΔH per mole. (c = 4.18 J g⁻¹ K⁻¹)

Entropy and spontaneity

Entropy (S) measures the disorder of a system: gases have more entropy than liquids, and liquids more than solids. A reaction tends to happen spontaneously if the Gibbs free energy change is negative: ΔG = ΔH − TΔS. A reaction can be spontaneous when ΔH is negative (energy released), when ΔS is positive (disorder increases), or both. An endothermic reaction can still occur at high temperature if ΔS is positive.

Check yourself Which has the highest entropy?
Check yourself Energy is given out when…
Check yourself Heat of 8.36 kJ is released when 0.15 mol reacts. What is ΔH?

Key terms

Enthalpy change
The heat energy change of a reaction at constant pressure.
Standard enthalpy of formation
The enthalpy change when one mole of a compound is formed from its elements in their standard states.
Entropy
A measure of disorder.
Gibbs free energy
ΔG = ΔH − TΔS; negative for a spontaneous change.

Summary

  • Exothermic ΔH < 0; endothermic ΔH > 0. Define formation, combustion and neutralisation enthalpies.
  • Hess's law: the enthalpy change is independent of the route.
  • ΔH = bonds broken − bonds made; q = m c ΔT in calorimetry.
  • A change is spontaneous if ΔG = ΔH − TΔS is negative.
Two Component Systems Periodic Classification