Question

A compound with molar mass ${\text{180}}$ is acylated with ${\text{C}}{{\text{H}}_{\text{3}}}{\text{COCl}}$ to get a compound with molar mass $390$. The number of amine groups present per molecules of the former compound is:

Answer 1

Hint: We will write the balanced equation for the acylation of amine. Then we will determine the relation between mass gained and the number of the amine group. Then by comparing the number of the amine with mass gained per amine we can determine the number of amine groups present per molecule.

Complete answer:
The primary amines are acrylate with acyl chloride to form amides.
The equation of acylation of a primary amine with acyl chloride is shown as follows:
${\text{RN}}{{\text{H}}_2}\, + \,{\text{C}}{{\text{H}}_{\text{3}}}{\text{COCl}}\, \to \,{\text{RNHCOC}}{{\text{H}}_{\text{3}}}\,{\text{ + }}\,{\text{HCl}}$
Molecular mass of the former compound that is ${\text{RN}}{{\text{H}}_2}$ is $180$ and the molecular mass of the product that is ${\text{RNHCOC}}{{\text{H}}_{\text{3}}}$ is $390$. The gain in mass is,
$ = 390 - 180$
$ = 210$
So, the total mass gain is $210$.
In the equation note that the one hydrogen of amine is replaced with ${\text{ - COC}}{{\text{H}}_{\text{3}}}$ group. So, all the mass increase is due to ${\text{ - COC}}{{\text{H}}_{\text{3}}}$ group. Mass of one proton is $1$ and the mass of one ${\text{ - COC}}{{\text{H}}_{\text{3}}}$ group is $43$.
It is also noted that one amine group releases one proton. During the reaction $1$ mass (of H) is replacing with $43$ mass (of ${\text{ - COC}}{{\text{H}}_{\text{3}}}$).
So, mass increases by $42$ by the replacement of one hydrogen \[\left( {43 - 1} \right)\] or we can say mass is increasing by $42$ per amine group because one amine loses one hydrogen.
Now we will compare the mass gain per amine group with total mass gain to determine the number of amine groups as follows:
Mass gain $42$ = one amine group
Mass gain $120$ = five amine group
So, the number of amine groups present per molecule of the former compound is five.

Therefore the answer is $5$.

Note:
For the stoichiometric calculation a balanced chemical equation is required. During acylation, the acyl group gets attacked by replacing one hydrogen of amine. The nitrogen of primary amine has the second hydrogen also which can also be replaced with acyl group but only one hydrogen gets replaced. ${\text{RC(O)N}}{{\text{H}}_{\text{2}}}$ is known as an amide. One hydrogen is getting replaced with ${\text{COC}}{{\text{H}}_{\text{3}}}$ group, so the increase in the mass is $42$ not $43$. The mass increases will be $43$ if the ${\text{COC}}{{\text{H}}_{\text{3}}}$ group get attached only and no hydrogen is replaced.