While azanonatetraene is comparatively stable at room temperature, \(\mathrm{N}\) -carbethoxyazanonatetraene rapidly isomerizes under the same conditions. Account for this difference.

First, let's draw the structures of both molecules: Azanonatetraene (C9H9N) has a linear structure with alternating single and double bonds, similar to an extended allyl group.\\\[ \ce{H2C=CH-CH=CH-N-CH=CH-CH=CH2} \]\\\ N-carbethoxyazanonatetraene (C11H11NO2) has an additional carbethoxy group (COOC2H5) attached to the nitrogen atom.\\\[ \ce{H2C=CH-CH=CH-N(COOC2H5)-CH=CH-CH=CH2} \]

In azanonatetraene, there are three conjugated double bonds which result in a delocalized π-electron system. This strong delocalization of π-electrons over the entire molecule provides stability similar to allylic systems. Moreover, there are no significant steric hindrances or electronic perturbations present. For N-carbethoxyazanonatetraene, the nitrogen atom carries a positive charge due to the carbethoxy group. The presence of this electron-withdrawing group disrupts the π-electron delocalization to a certain extent and makes the molecule less stable.

As mentioned earlier, azanonatetraene has a stable, extended allyl structure with strong π-electron delocalization. This structure provides good thermodynamic stability at room temperature. However, in N-carbethoxyazanonatetraene, the electron-withdrawing group attached to the nitrogen destabilizes the delocalized π-electron system. This destabilization makes the molecule more prone to isomerization in an attempt to achieve a more stable configuration. Consequently, N-carbethoxyazanonatetraene rapidly isomerizes under the same conditions as azanonatetraene. In conclusion, the difference in stability between azanonatetraene and N-carbethoxyazanonatetraene is due to the effect of the electron-withdrawing carbethoxy group on the delocalized π-electron system. This group destabilizes the molecule, making it more susceptible to isomerization at room temperature.