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Past exam of the chemistry B course of the University of Cambridge / 2021 / Paper 1 / B5 / b / iii / Solution 2026-10-20

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The strongest donor belongs to the acid,

α_{1} = 3.5

, and the strongest acceptor to the aminopyridine,

β_{2} = 8.5

. The cocrystal pairs the strongest donor with the strongest acceptor, while the reciprocal amino-NH···carbonyl contact closes a complementary two-contact motif.

Using the simple favorable-contact score

α β

, one heterodimer gives

S_{hetero} = α_{1} β_{2} + α_{2} β_{1} = (3.5) (8.5) + (3.0) (5.5) = 46.25.

(1)

The self-associated comparison, normalized to the same two molecules and two hydrogen bonds, is half an acid dimer plus half an aminopyridine dimer:

S_{self} = α_{1} β_{1} + α_{2} β_{2} = (3.5) (5.5) + (3.0) (8.5) = 44.75.

(2)

Thus

Δ S = 1.50 = (α_{1} - α_{2}) (β_{2} - β_{1}) > 0 .

(3)

In a model where bond free energy contains

- α β

, this is a favorable energy change. No bonds have been artificially added to one side of the comparison: both alternatives contain two contacts per acid/aminopyridine pair.

The calculation rationalizes the hydrogen-bond preference. It is not a complete crystal free energy: packing, additional contacts, entropy and possible solvent effects also matter. Without a specified calibration, the numerical score should not be promoted to a measured cocrystallization free energy.

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