what is the difference between disymmetric and asymmetic molecule of organic compoud?

Whether the stretch of a bond in a molecule is asymmetric or symmetric depends on the relative movement of the atoms connected by the bond.Letstake aCH2CHX2group as an example. If the two hydrogen atoms connected to the carbon move in the same direction during stretching, it s a symmetric stretch, if they are going in opposite directions, the stretch is asymmetric (see alsohere):



Left: symmetric stretch, right: asymmetric stretch

A bond vibration like stretching will only be IR-active (i.e. give a band in the IR spectrum) if it is accompanied by a change of dipole moment. In the case of theC−HC−Hbond, carbon is slightly negatively and hydrogen slightly positively polarized. A symmetric stretch increases and decreases the distance between these partial charges periodically, and therefore also changes the dipole moment, because the latter is dependentfromthe distance between charges (source). During an asymmetric stretch, the elongation of oneC−HC−Hbond is compensated by the shortening of the other, so the overall change of dipole moment should be weaker.

In the case of 2-(4-tert-butylphenyl)ethanol (the correct name for yourcompond), the band at 3006cm−1cm−1can either be assigned to theCH2CHX2groups of the substituted ethanol or toC−HC−Hbonds in the benzene ring. In the first case, you can distinguish between symmetrical and asymmetrical stretch (symmetrical seems more likely to me), while in the latter case, a single hydrogen is attached to a carbon, and a distinction of the stretching, like in the case of two substituents at the same carbon, cannot be made.