Animated Solution for Chemistry - Organic Chemistry: A compound with molecular mass $180\mu$ is acylated with ${\text{CH}}_3\text{COCl}$, to get a compound with molecular mass $390\mu$. The number of amino groups present per molecule of the former compound is

Welcome, future chemists and problem-solvers! Today, we are diving into a fascinating puzzle that blends the elegance of organic chemistry with the precision of mathematical accounting. Imagine you are a molecular architect, and your job is to modify a complex organic structure. You are given a starting material, a specific reagent, and the final mass of your product. Your mission? To deduce exactly how many functional groups were modified during the reaction. This is not just a textbook problem; it is a real-world scenario that synthetic chemists face every day in the laboratory. Let's embark on this thrilling journey of molecular deduction!

In chemistry, mass is never created or destroyed; it is simply rearranged. When an organic molecule undergoes a chemical reaction, its molecular mass changes in a highly predictable manner based on the atoms that are added or removed.

In our specific problem, we are dealing with the acetylation of an amine. We start with an unknown organic compound containing an unknown number of amino groups ($-{\text{NH}}_2$). The initial molecular mass is given as $180\mu$. After reacting it completely with acetyl chloride (${\text{CH}}_3\text{COCl}$), the final molecular mass balloons up to $390\mu$. Our goal is to find out how many amino groups were present initially.

To solve this, we first need to understand what happens at the microscopic level during acetylation. When a primary amine reacts with acetyl chloride, a nucleophilic acyl substitution takes place.

The reaction can be represented as:

Look closely at the transformation of the functional group. The original $-{\text{NH}}_2$ group loses one hydrogen atom and gains an acetyl group ($-{\text{COCH}}_3$). The chlorine from the acetyl chloride and the lost hydrogen atom pair up to form a molecule of hydrogen chloride ($\text{HCl}$), which leaves as a byproduct.

Now, let's do some chemical accounting for a single amino group.

What is the mass of the incoming acetyl group? Carbon has an atomic mass of $12\mu$, Oxygen is $16\mu$, and Hydrogen is $1\mu$. So, the mass of the ${\text{CH}}_3\text{CO}$ group is $12+(3\times 1)+12+16=43\mu$.

What is the mass of the outgoing atom? We are losing one hydrogen atom, which has a mass of $1\mu$.

Therefore, the net increase in mass for every single amino group that gets acetylated is:

This is our magic number! Every time an amino group is acetylated, the molecule gets heavier by exactly $42\mu$.

Now let's zoom out and look at the entire molecule. We know the initial mass and the final mass, so we can easily calculate the total mass gained by the molecule during the reaction.

The entire molecule gained $210\mu$ in mass.

We have all the pieces of the puzzle. We know that the total mass increased by $210\mu$, and we know that each individual amino group contributes exactly $42\mu$ to that increase.

To find the total number of amino groups ($n$), we simply divide the total mass increase by the mass increase per group:

And there we have it! The original organic compound contained exactly 5 amino groups.

This problem beautifully illustrates how macroscopic measurements (like total molecular mass) can give us precise microscopic structural information.

As a thought experiment, consider what would happen if the starting material contained secondary amines ($-\text{NHR}$) instead of primary amines. Secondary amines also have one replaceable hydrogen atom, so they would undergo acetylation with the exact same mass increase of $42\mu$ per group! However, tertiary amines ($-{\text{NR}}_2$) lack a replaceable hydrogen atom and would not undergo this reaction at all.

Keep this analytical mindset sharp, as it is the key to unlocking the structural secrets of complex organic molecules!