lnKc

lnKc is the natural logarithm of the equilibrium constant Kc for a reaction defined in terms of concentrations. For a reaction aA + bB ⇌ cC + dD in solution, Kc = [C]^c [D]^d / [A]^a [B]^b, where brackets denote concentrations. In thermodynamics, Kc is most rigorously defined with activities; when using concentrations, Kc is treated as dimensionless by adopting a standard concentration (often 1 M) for activity references, and lnKc refers to the natural log of that dimensionless constant.

The value of Kc reflects the position of equilibrium: Kc > 1 (lnKc > 0) favors products, while Kc < 1 (lnKc < 0) favors reactants. lnKc is related to the standard Gibbs free energy change by ΔG° = -RT ln K, with the understanding that ln K uses activities; for solutions this becomes ΔG° ≈ -RT ln Kc. Thus lnKc provides a compact link between equilibrium composition and thermodynamic spontaneity.

Temperature dependence: The van't Hoff equation describes how Kc varies with temperature: d(ln Kc)/dT = ΔH°/(R T^2). This allows estimation of Kc at different temperatures if the reaction enthalpy change ΔH° is known. For gas-phase reactions, Kp and Kc are related by Kp = Kc (RT)^{Δn}, where Δn is the change in moles of gas.

Practical use: lnKc is widely employed to predict reaction direction, assess the influence of temperature, and relate equilibrium to thermodynamic quantities such as ΔG°.