A compound $$x$$ with molar mass 108 g mol$$^{-1}$$ undergoes acetylation to give product with molar mass 192 g mol$$^{-1}$$. The number of amino groups in the compound $$x$$ is

We need to find the number of amino groups in compound $$X$$ (molar mass 108), which upon acetylation gives a product of molar mass 192.

In acetylation, each amino group ($$-\text{NH}_2$$) reacts with acetyl chloride or acetic anhydride to form an amide, as shown by the equation: $$-\text{NH}_2 + \text{CH}_3\text{COCl} \rightarrow -\text{NHCOCH}_3 + \text{HCl}$$. In this reaction, an H atom (mass 1) on the $$-\text{NH}_2$$ group is replaced by an acetyl group $$-\text{COCH}_3$$ (mass 43). The net increase in molar mass per amino group is $$43 - 1 = 42$$ g/mol.

Since the product’s molar mass increases from 108 to 192, the total increase in molar mass is $$\Delta M = 192 - 108 = 84 \, \text{g/mol}$$.

Substituting into the relation for the number of amino groups gives $$n = \frac{\Delta M}{42} = \frac{84}{42} = 2$$.

Therefore, the compound $$X$$ has 2 amino groups, corresponding to Option 2.