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I learned that the $\ce{N-H}$ bonds in a primary amine lead to two signals the infrared spectra at $\sim \pu{3400 cm^-1}$, one for symmetrical stretching and another for asymmetrical stretching. For example, here is the IR spectrum of butylamine, taken from Pavia & Lampman's Introduction to Spectroscopy (5th ed.):

Butylamine

The same is seen in, for example, carbon dioxide, where the asymmetric stretch ($\Sigma_\mathrm u^+$) occurs at $\pu{2348 cm-1}$ and the symmetric stretch ($\Sigma_\mathrm g^+$) at $\pu{1373 cm-1}$ (from ChemTube 3D; the NIST Webbook gives similar values).

Why is this so?

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