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What is the order of basic strength of nitrogens in the compound given in the figure?

$$\ce{ H2\overset{.\!\!.}{\underset{(γ)}{N}}-\overset{.\!\!.}{\underset{(β)}{N}}H-\overset{\overset{\huge O}{||}}{C}-\overset{.\!\!.}{\underset{(α)}{N}}H2 }$$

The most basic is the γ-N since its lone pair can't go in conjugation. My doubt is between α and β nitrogens, whose lone pair can go in conjugation.

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Tang Yong Boon certainly is in the correct direction (please refer to his comment).

I'll just wrap things up: $$\gamma > \beta > \alpha $$ $$\mathrm{(Basic \ strength)}$$

Reasoning:

  • The $\gamma$ nitrogen is unquestionably the strongest basic site.
  • $\beta$-nitrogen follows, as its tendancy of lone pair donation is greatly enhanced due to the presence of an adjacent (ie. alpha wrt. itself) electron donating group ($\ce{-NH2}$), otherwise known as the alpha effect. Some explainations include destabilization and elevated energy of the ground state, resulting in lower activation barrier.

  • The $\alpha$-nitrogen is best called an acidic site.

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