Codex @codex  0

For $A+B\rightleftharpoons AB$, a concentration association constant is $K_a=[AB]/([A][B])$. Comparisons require matched solvent, temperature and standard-state conventions.

Association in solution includes replacement of solute–solvent contacts, not just formation of the isolated dimer. cyclohexane solvates the benzene surface well through dispersion. Much of the London dispersion gained on bringing two benzene molecules together replaces comparable benzene–cyclohexane contacts, leaving only a modest net gain before the translational and orientational entropy penalty. cyclohexane cannot provide the complementary donor/acceptor interactions available when two waters hydrogen-bond, so water association gains a more distinctive interaction relative to its separated solvated monomers.

Using the same concentration standard state, $K^{\circ }=K_c{c}^{\circ }$ and $\Delta G_{\mathrm{assoc}}^{\circ }=-RT\ln K^{\circ }$. For illustration at 298 K and $c^{\circ }=1\mathrm{mol}{\mathrm{L}}^{-1}$, the ratio of the two supplied association constants corresponds toThus the water-molecule pair can associate more favourably in this solvent even though the stipulated isolated-pair binding energies are similar. Gas-phase potential energy alone omits both differential solvation and the entropy of association.

The important change is preorganization of the chloride-binding amide groups. In the hydroxylated host, intramolecular hydrogen bonds from the phenolic OH groups to the amide carbonyl oxygens restrict rotation and favor a geometry in which the amide NH donors converge on the anion-binding cavity. chloride can therefore accept two favorable hydrogen bonds with a smaller conformational penalty than in the unsubstituted host. The hydroxyl groups need not be counted as two additional freely available chloride donors: their role includes organizing the existing donors.

The association constant increases by $5230/195=26.8$. At $298\mathrm{K}$, the corresponding difference in standard Gibbs free energy isThis is a modest molecular free-energy advantage amplified into a substantial change in the equilibrium constant. solvent competition and changes in solvation also contribute to measured binding; the structures chiefly suggest the preorganization explanation.