Alkali metals form strong complexes with cryptate ligands. The structure of one such crypt given below is of :
2.2.2 crypt
The stem carries a drawn cryptand structure; the four options are text and are reproduced in full above.
Cryptands are bicyclic ligands built from two bridgehead nitrogen atoms joined by three polyether chains. The naming convention is simple and is what the question tests: the three numbers give the count of oxygen atoms in each of the three bridging strands.
So [2.2.2]cryptand has three strands carrying two oxygens each, six oxygens in all, plus the two bridgehead nitrogens — eight donor atoms wrapping the metal ion in a three-dimensional cage.
That cage size matters. The [2.2.2] cavity radius is close to the ionic radius of K+, so it binds potassium with enormous selectivity and stability, far exceeding the corresponding crown ether 18-crown-6. This size matching is the whole basis of cryptand chemistry: [2.1.1] with a smaller cavity prefers Li+, [2.2.1] prefers Na+, and [2.2.2] prefers K+.
Because the ligand encapsulates the cation completely, it produces the very large binding constants referred to as the cryptate effect, and it is this that allows otherwise impossible species such as alkalide and electride salts to be isolated.
The remaining options describe strands with four, six or eight oxygens, giving cavities far larger than the structure drawn.
Per the official final answer key the answer is 2.2.2 crypt.
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