Thermodynamics and Thermochemistry
Thermodynamics and Thermochemistry tests state functions, the first law, enthalpy, Hess's law, entropy, Gibbs energy, and spontaneity. The exam rewards correct sign conventions and careful use of standard conditions.
Core rules
- First law: ΔU = q + w. For work done on the system, w is positive; for expansion work against constant pressure, w = −PΔV.
- Enthalpy: ΔH = ΔU + Δ(PV). For ideal-gas reactions, ΔH = ΔU + Δn_gRT.
- Hess's law: enthalpy change is path-independent; add reactions and their ΔH values accordingly.
- Entropy rises with temperature, phase change to gas, and more particles. ΔS_universe = ΔS_system + ΔS_surroundings.
- Gibbs energy: ΔG = ΔH − TΔS. Negative ΔG means spontaneous at constant T and P; ΔG = 0 at equilibrium.
Worked example
A reaction has ΔH = −92 kJ and ΔS = −198 J/K at 298 K. Find ΔG. Convert ΔS to kJ/K: −0.198 kJ/K. TΔS = 298 × (−0.198) = −59.0 kJ. ΔG = −92 − (−59.0) = −33 kJ. The reaction is spontaneous at 298 K, although the negative entropy term opposes it; at much higher T, the positive TΔS term can make ΔG positive.
Traps
Do not mix J and kJ. Do not treat heat and work as state functions. Do not say a reaction with positive ΔH is always nonspontaneous; entropy can drive it. Standard enthalpy of formation of an element in its standard state is zero, not the enthalpy of formation of any compound.