Which of the following $\mathrm{\beta }$-keto carboxylic acid does not undergo decarboxylation on heating ?

$\mathrm{\beta }$-Keto acids undergo decarborylation through the keto form via a cyclic T. S. which results in the formation of the enol form of the ketone product. The enol then changes to the more stable keto form. If decarborylation of the given $\mathrm{\beta }$-keto acid could follow this route, then :

If we draw the acid as shown in (I), it can be seen that the methylene group forms a bridge, which is perpendicular to the cyclohexane ring.

The enol produced would have a double bond in the 1, 2-position. Thus, C - 1 is sp²- hybridised and therefore the bond leading to the methylene bridge (1, 3) would have to be coplanar with the groups joined to C - 2 in the enol, i.e., the bridge would have to flatten. This would require the normal valency angles $~$ 109.5^o) to change to $~$ 120^o. Even if a compromise situation occurred, i.e., all bond angles involved ($\angle$ s 1,3, and 4) underwent change, the resulting strain would be very large, too large to be expected for it to occur. Hence, it is reasonable to argue that since decarboxylation does occur, it does so through a route requiring a much higher activation energy than that required for the 'usual' route. Hence the difficulty of decarboxylation. (Bredt's rule)