thermodynamic equilibrium constant
/ K-naught /
The everyday equilibrium constants Kc and Kp work well, but they carry units and can give different numbers for the same reaction, which is a little unsatisfying. The thermodynamic equilibrium constant is the cleaned-up, rigorous version: a single pure number, with no units, that thermodynamics regards as the 'real' equilibrium constant. It is the quantity that connects equilibrium directly to energy.
It is built from activities rather than raw concentrations or pressures. An activity is an effective amount measured relative to a chosen standard state (for a gas, its pressure divided by the standard pressure; for a solute, its concentration divided by the standard concentration, each adjusted by an activity coefficient). Because every term is a ratio, the units cancel, and the result, written K° or simply K, is dimensionless. This is the constant that appears in the bridge equation ΔG° = −RT ln K, tying the standard Gibbs free-energy change of a reaction to its equilibrium constant.
Why bother: only the dimensionless K can legitimately sit inside a logarithm and link to free energy, so it is the version thermodynamics demands. The honest reconciliation is that in dilute, near-ideal conditions the activity coefficients are close to 1, so the rigorous K and the practical Kc or Kp nearly coincide — which is why the simpler constants work so well in introductory chemistry.
For a gas reaction, each pressure is divided by the standard pressure (1 bar) before going into the constant, so p/p° is a pure ratio. The resulting K is unitless and slots straight into ΔG° = −RT ln K, turning a measured equilibrium into a free-energy value.
Activities make K dimensionless, so it can link to free energy.
Strictly, only the activity-based K is dimensionless and tied to ΔG°. The familiar Kc and Kp, with their lingering units, are approximations that coincide with K when activity coefficients are near 1.