= Equilibrium constant
{title2=$K$}
{wiki}
For a specified <chemical reaction> and <standard state> convention, the dimensionless <equilibrium constant> is the equilibrium value of the <reaction quotient> $Q=\prod_i a_i^{\nu_i}$, where $a_i$ denotes <thermodynamic activity> and $\nu_i$ a signed <stoichiometric vector> entry. <Thermodynamic activities> incorporate the reference state and departures from ideal behavior. See https://goldbook.iupac.org/terms/view/E02177[IUPAC Gold Book, equilibrium constant].
In the ideal concentration model for A converting to B, use $a_{\mathrm A}=[\mathrm A]/c^\circ$ and $a_{\mathrm B}=[\mathrm B]/c^\circ$ with the same reference $c^\circ=1\,\mathrm M$. Their ratio gives $Q=[\mathrm B]/[\mathrm A]$ and $K=0.75/0.25=3$. Equality $K=k_f/k_r$ applies to this elementary first-order pair; it is not a universal ratio of two measured <rate constants> for an arbitrary multistep <chemical reaction>.
At a specified constant <temperature>, with consistent <standard states>, the standard molar reaction <Gibbs free energy> is
$$
\Delta_rG^\circ=\sum_i\nu_i\mu_i^\circ=-RT\ln K,
\qquad \Delta_rG=\Delta_rG^\circ+RT\ln Q=RT\ln(Q/K).
$$
Here $\Delta_rG$ is the local slope per <mole> of <extent of reaction> at fixed <temperature> and <pressure>, rather than the finite total <Gibbs free energy> change between two mixtures. At equilibrium $\Delta_rG=0$, while $\Delta_rG^\circ$ generally remains nonzero. For $K=3$ at $298\,\mathrm K$, it is about $-2.72\,\mathrm{kJ/mol}$. For positive activities, $Q<K$ favors forward conversion and $Q>K$ favors reverse conversion; neither sign supplies a <reaction rate>. See https://ocw.mit.edu/courses/5-111sc-principles-of-chemical-science-fall-2014/ec12f084d867a5e5532b12ee99bdc767_MIT5_111F14_Lec18.pdf[MIT 5.111, Lecture 18, reaction free energy and equilibrium].
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