Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 3 / Section E / 44

zinc(II) should bind more strongly to 1. The macrocycle presents six amine donors that can chelate the dication in a roughly octahedral environment. Multiple donor contacts, the chelate effect and preorganization favour this binding. lithium is small and strongly prefers an appropriately sized oxygen-rich pocket; it gains less from this large nitrogen-donor cavity. Charge density alone is insufficient to rank the complexes: donor type, geometry, solvation and the strain of wrapping the host around each ion also matter.

The predominant self-sorted distribution is $[\mathrm{Zn}(1){]}^{2+}$, $[\mathrm{Li}(2){]}^{+}$ and free 3, so the reporter remains mainly in its 554 nm state. zinc benefits from the six amine donors of 1 without forcing 2 into its strained zinc-binding conformation. lithium occupies 2 because its lithium affinity exceeds that of 3. Each metal is consumed in the preferred complex, leaving the reporter unoccupied.

This is a dominant-species prediction. A tenfold affinity difference alone would not guarantee quantitative lithium sorting if the absolute affinities were weak or if free metal and all competing complexes had appreciable populations. Concentration and equilibrium constants are not supplied, so an exact species fraction is not justified.

protonation of the basic amine host weakens its zinc binding. zinc transfers to 2, displacing lithium, which can then bind the crown-like site of 3. The predicted switched distribution is protonated 1, $[\mathrm{Zn}(2){]}^{2+}$ and $[\mathrm{Li}(3){]}^{+}$, giving 512 nm emission. The strain penalty for zinc binding 2 is accepted when the better competing host is protonated.

Without fluorescence, compare ${}^1$H NMR spectra of the mixture with independently prepared free and metal-bound hosts, looking for changes near the amine, pyridyl and crown-ether donors. ${}^7$Li NMR can follow lithium environments; chemical-shift changes and exchange-dependent line shapes should be interpreted using titrations rather than treating one peak as definitive proof of one complex. zinc(II) is diamagnetic, so ordinary NMR observation is possible. UV–visible absorption can independently track changes in 2 and 3. Acid-only controls for each component test whether direct protonation shifts the reporter independently of lithium; metal-only and acid titrations test the proposed redistribution. The stipulated one-equivalent response is an idealized acid–base sorting cycle, not a pH measurement in aqueous buffer.

DBU removes the proton from 1, restoring its zinc-binding ability. zinc returns from 2 to 1; the regenerated free 2 captures lithium from 3, restoring the preferred initial sorting. Thus the reporter returns predominantly to 554 nm, while DBU becomes its conjugate acid and trifluoroacetate remains as counterion. This assumes the added base is strong enough under the solvent conditions and does not itself compete effectively for either metal. Reversing a fluorescence shift without checking speciation would not establish all these transfers on its own.

The acid initially protonates 1 and switches the system into the lithium-bound reporter state, so 512 nm intensity rises rapidly. The resulting carboxylate then decarboxylates irreversibly. Its carbanion removes the proton from 1, giving neutral waste 5 and restoring the original zinc/lithium distribution. Thus the 512 nm signal is a transient pulse followed by recovery to its initial low baseline; no repeated oscillations follow from one fuel addition.

For first-order decarboxylation the surviving fuel-derived carboxylate fraction is $e^{-kt}$ with $k=\ln 2/(75\min )$. If proton exchange and metal redistribution are fast, background is subtracted, and the population of the switched state is proportional to remaining protonated 1, the illustrative recovery isHalf the initial excess signal remains after 75 min and one quarter after 150 min in that limiting model. Actual binding equilibria can make the intensity nonlinear in remaining fuel; the supplied half-life fixes the fuel decay, not an exact reporter-intensity law. Monitor ${}^1$H NMR fuel consumption and waste formation alongside the optical trace to distinguish dissipation-driven recovery from photobleaching or simple dilution.