= Chemical relaxation time
{title2=$\tau_{\rm chem}$}
The chemical relaxation time estimates how rapidly a perturbed abundance returns toward <chemical equilibrium>. Comparing it with the <eddy mixing time> identifies a <chemical quench level>.
For the A-to-B model in <chemical equilibrium>, deviations decay by <exponential decay> with $\tau_{\rm chem}=1/(k_f+k_r)=2.5\,\mathrm s$. After one such interval, $1/e$ of the initial deviation remains; reaching one percent takes $\ln(100)\tau_{\rm chem}\simeq11.51\,\mathrm s$. Multiplying both <rate constants> by two preserves their ratio and the equilibrium composition, but halves $\tau_{\rm chem}$ to $1.25\,\mathrm s$. The equilibrium exchange rates double to $0.15\,\mathrm{M/s}$. Faster exchange therefore coexists with the same final composition and the same <free energy> minimum.
\Image[/equilibrium-vs-rate.png]
{title=Doubling both rates changes the approach time but preserves equilibrium}
{description=Left: B <concentration> for two pairs of <rate constants> with the same ratio. Right: the shared ideal-mixture <Helmholtz free energy>, shifted to zero at its constrained minimum.}
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