Thermochemistry and thermodynamics
This domain covers Hess's law, enthalpies of formation and bond energies, entropy changes, and the use of Gibbs energy to decide spontaneity and predict the temperature at which a reaction becomes feasible. Sign conventions carry most of the marks.
Enthalpy and Hess's law
ΔH is negative for exothermic reactions. Standard enthalpy of formation ΔH°f is zero for an element in its standard state. ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants). Hess's law lets you combine reactions: reverse a step and flip the sign, multiply a step and scale the value. Kirchhoff's law adjusts ΔH for temperature using ΔCp.
Bond energies
ΔH = Σ(bonds broken) − Σ(bonds formed), using one consistent data set. Bond energy is the energy to break one mole of bonds in the gas phase, so breaking is always endothermic; results are reliable only for gas-phase reactions.
Entropy
ΔS is positive when gaseous moles increase, when a solid melts or a liquid vaporises, or when a solid dissolves into more disordered particles. The third law sets S = 0 for a perfect crystal at 0 K, so S° values are absolute, unlike ΔH°f. ΔS°rxn = ΣS°(products) − ΣS°(reactants), and ΔS_universe = ΔS_system − ΔH_system/T.
Gibbs energy and spontaneity
ΔG = ΔH − TΔS and ΔG° = −RT ln K. ΔG < 0 means spontaneous in the forward direction, ΔG = 0 means equilibrium, ΔG > 0 means non-spontaneous. If ΔH < 0 with ΔS > 0 the process is spontaneous at all temperatures; if ΔH > 0 with ΔS < 0 it never is; otherwise there is a crossover at T = ΔH/ΔS.
Worked example
A reaction has ΔH° = +58 kJ/mol and ΔS° = +176 J·K⁻¹·mol⁻¹. At 298 K, ΔG° = 58 000 − 298(176) = 58 000 − 52 448 = +5.55 kJ/mol, so it is non-spontaneous. The crossover is T = 58 000/176 = 329 K, so the reaction becomes spontaneous above about 330 K. The kJ/J mismatch is the most frequent numerical error here.
Traps
- Mixing kJ and J in a ΔG calculation.
- Treating ΔG° as a prediction for non-standard conditions; use ΔG = ΔG° + RT ln Q instead.
- Assuming ΔH alone decides spontaneity.
- Getting signs wrong when reversing an equation inside a Hess cycle.