Editing Reaction quotient (section)

== Relationship to ''K'' (the equilibrium constant) ==
As the reaction proceeds with the passage of time, the species' activities, and hence the reaction quotient, change in a way that reduces the free energy of the chemical system.  The direction of the change is governed by the [[Gibbs free energy]] of reaction by the relation
:<math>\Delta_{\mathrm{r}}G=RT\ln(Q_{\mathrm{r}}/K)</math>,
where ''K'' is a constant independent of initial composition, known as the [[equilibrium constant]].  The reaction proceeds in the forward direction (towards larger values of ''Q''<sub>r</sub>) when Δ<sub>r</sub>''G'' < 0 or in the reverse direction (towards smaller values of ''Q''<sub>r</sub>) when Δ<sub>r</sub>''G'' > 0.  Eventually, as the reaction mixture reaches chemical equilibrium, the activities of the components (and thus the reaction quotient) approach constant values.  The equilibrium constant is defined to be the asymptotic value approached by the reaction quotient: 
:<math>Q_{\mathrm{r}}\to K</math> and <math>\Delta_{\mathrm{r}}G\to 0\quad (t\to\infty)</math>.

The timescale of this process depends on the rate constants of the forward and reverse reactions.  In principle, equilibrium is approached asymptotically at ''t'' → ∞; in practice, equilibrium is considered to be reached, in a practical sense, when concentrations of the equilibrating species no longer change perceptibly with respect to the analytical instruments and methods used.

If a reaction mixture is initialized with all components having an activity of unity, that is, in their [[Standard state|standard states]], then
:<math>Q_{\mathrm{r}}=1</math> and <math>\Delta_{\mathrm{r}}G= \Delta_{\mathrm{r}}G^\circ=-RT\ln K\quad (t=0)</math>.

This quantity, Δ<sub>r</sub>''G°'', is called the ''standard Gibbs free energy of reaction''.<ref>The standard free energy of reaction can be determined using the difference between the sum of the [[Standard Gibbs free energy of formation|standard free energies of formation]] of products and the sum of the standard free energies of formation of reactants, accounting for stoichiometries: <math display="inline">\Delta_{\mathrm{r}} G^\circ=\sum_{\mathrm{prod.}}^i \nu_i\Delta_{\mathrm{f}}G^\circ
-\sum_{\mathrm{react.}}^j\nu_j\Delta_{\mathrm{f}}G^\circ</math>.</ref>

All reactions, regardless of how favorable, are equilibrium processes, though practically speaking, if no starting material is detected after a certain point by a particular analytical technique in question, the reaction is said to go to completion.