= Solution
The <exponential function> makes modest <Gibbs free energy> differences correspond to extreme equilibrium ratios. At 298 K, $RT\simeq2.48\,\mathrm{kJ\,mol^{-1}}$; for example,
$$
\Delta_rG^\circ=+100\,\mathrm{kJ\,mol^{-1}}\Rightarrow K\simeq3.0\times10^{-18},\qquad
\Delta_rG^\circ=-100\,\mathrm{kJ\,mol^{-1}}\Rightarrow K\simeq3.4\times10^{17}.
$$
The minor equilibrium component may therefore lie below detection, or a species' required <thermodynamic activity> may be experimentally inaccessible. Apparently complete conversion supplies a bound on $K$, rather than an accurate finite value. Additionally, some reactions do not reach <chemical equilibrium> within a practicable observation <time> because of kinetic barriers. The thermodynamic identity still holds even when direct room-temperature determination of both sides of the equilibrium ratio fails.
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