Electronic partition function 2026-10-20
The electronic partition function includes electronic excitation energies and degeneracies . If only an exactly degenerate ground manifold of size is populated, and its molar entropy is . Resolved splittings require a state sum rather than replacing all components by one degeneracy.
Past exam of the chemistry A course of the University of Cambridge 2024 Paper 2 A8 a Solution 2026-10-20
Set the ground electronic energy to zero and write the excitation energy as , or the characteristic temperature K. Counting each doubly degenerate manifold once gives the single-molecule electronic partition functionFor independent molecules the electronic factor is . Hence the electronic internal energy isThe equal degeneracies cancel from the excited-state probability. At low temperature the ground manifold dominates and ; at high temperature both manifolds have equal populations, giving . These are electronic contributions only, excluding translation, rotation and vibration.
Past exam of the chemistry A course of the University of Cambridge 2025 Paper 2 A8 c ii 1 Solution 2026-10-20
If the relevant ground manifolds have electronic degeneracies , and , and their components are treated as energetically degenerate, multiply the result byOnly reactive transition-state electronic channels should be counted. Resolved electronic splittings require electronic partition functions rather than simple integer degeneracies.