In the following reaction sequence, major products X and Y are acyclic monomers.
CH3I - (1. KCN, 2.

Q: Why does caprolactam ring open with acid?

Caprolactam is a cyclic amide. Aqueous acid hydrolyzes the amide bond, breaking the ring to form an amino group at one end and a carboxylic acid at the other.

Q: What is the role of Red P and Br2?

This is the Hell-Volhard-Zelinsky (HVZ) reaction. It selectively brominates the alpha-carbon of a carboxylic acid.

Q: Why do we subtract 999 water molecules instead of 1000?

To form a single continuous acyclic chain from 1000 monomer units, exactly 999 linkages must be formed. Each linkage releases one water molecule.

Q: Can I just multiply the repeating unit mass by 500?

Almost! The repeating unit mass accounts for the internal chain, but the two ends of the acyclic polymer still have an unreacted -H and -OH group. You must add their mass (18 g/mol) to get the exact total mass.

Q: What is the structure of the repeating unit?

The repeating unit is formed by one molecule of X and one molecule of Y joining together, with the loss of two water molecules to connect to the rest of the chain. Its mass is Mass(X) + Mass(Y) - 2*Mass(H2O).

Question

In the following reaction sequence, major products X and Y are acyclic monomers.

500 mol of X completely reacts with 500 mol of Y to give 1 mol of a single biodegradable acyclic copolymer Z as the only product. The amount of Z formed in grams is _____.
Given:
Atomic mass (in amu): H : 1, C : 12, N : 14, O : 16, Br : 80

Sigma Percentile · Accepted Answer

The beauty of this problem lies in its seamless integration of classic organic synthesis with the quantitative rigor of polymer chemistry. It tests not only your recall of standard reactions but also your ability to meticulously account for every single atom in a macromolecule. Let's embark on this molecular journey!

### Decoding Monomer X: A Four-Step Synthesis

We begin with methyl iodide ($CH_3I$) and subject it to a sequence of four distinct reagents.

**Step 1: Nucleophilic Substitution**
Reacting $CH_3I$ with $KCN$ triggers a classic $S_N2$ reaction. The cyanide ion acts as a nucleophile, displacing the iodide to form acetonitrile ($CH_3CN$). This step is crucial because it adds a carbon atom to our chain, stepping up the carbon count.

**Step 2: Acidic Hydrolysis**
Next, we treat acetonitrile with aqueous acid and heat ($H_3O^+, \Delta$). The cyano group undergoes complete hydrolysis, converting the triple-bonded nitrogen into a carboxylic acid. Our molecule is now acetic acid ($CH_3COOH$).

**Step 3: The Hell-Volhard-Zelinsky (HVZ) Reaction**
This is where the magic happens. By reacting acetic acid with red phosphorus and bromine ($Red P, Br_2$), we selectively brominate the $\alpha$-carbon (the carbon adjacent to the carboxyl group). This yields $\alpha$-bromoacetic acid ($Br-CH_2-COOH$).

**Step 4: Amination**
Finally, treating the $\alpha$-bromoacetic acid with excess ammonia ($NH_3$) replaces the bromine atom with an amino group via nucleophilic substitution. The result? $NH_2-CH_2-COOH$, which is **Glycine**, the simplest amino acid. This is our monomer **X**.

### Decoding Monomer Y: Ring Opening

The second sequence is much shorter but equally elegant. We start with **Caprolactam**, a seven-membered cyclic amide. When heated with aqueous acid ($H_3O^+, \Delta$), the amide bond undergoes hydrolysis. The ring springs open, leaving an amino group at one terminus and a carboxylic acid at the other.

This gives us 6-aminohexanoic acid: $NH_2-(CH_2)_5-COOH$. This is our monomer **Y**.

### The Copolymerization: Building the Chain

The problem states that 500 moles of X and 500 moles of Y react to form a single acyclic copolymer **Z**. Because both monomers possess an amino group and a carboxylic acid group, they will undergo **condensation polymerization**.

For every amide bond formed between the monomers, one molecule of water ($H_2O$) is eliminated. The repeating unit of this alternating copolymer will consist of one X and one Y residue linked together.

Let's calculate the mass of this repeating unit:
- Molar mass of X (Glycine) = $75 	ext{ g/mol}$
- Molar mass of Y (6-aminohexanoic acid) = $131 	ext{ g/mol}$

When they join to form the internal repeating unit $-[NH-CH_2-CO-NH-(CH_2)_5-CO]-$, two water molecules are lost (one for the bond between X and Y, and one for the bonds connecting this unit to the rest of the chain).
$$	ext{Mass of repeating unit} = 75 + 131 - 2(18) = 170 	ext{ g/mol}$$

### The Final Calculation: Beware the End Groups!

We have 500 such repeating units in our polymer chain. 
$$	ext{Mass of internal chain} = 500 	imes 170 = 85000 	ext{ g}$$

**Here is the trap!** The problem specifies that the copolymer is *acyclic* (a straight chain). This means the very ends of the polymer chain have not reacted to form a loop. One end of the chain will have an unreacted hydrogen atom ($-H$) on the amino group, and the other end will have an unreacted hydroxyl group ($-OH$) on the carboxyl group.

We must add the mass of these end groups to our total:
$$	ext{Mass of end groups} = 1 (	ext{for H}) + 17 (	ext{for OH}) = 18 	ext{ g}$$

Adding this to the mass of the internal chain gives us the exact total mass:
$$	ext{Total Mass of Z} = 85000 + 18 = \mathbf{85018 	ext{ g}}$$

**Alternative Perspective:**
Imagine 1000 individual monomer units (500 X and 500 Y) lining up. To connect 1000 units into a single continuous chain, you need to form exactly 999 links. Therefore, exactly 999 water molecules are eliminated.
$$	ext{Total Mass} = 500(75) + 500(131) - 999(18)$$
$$	ext{Total Mass} = 37500 + 65500 - 17982 = \mathbf{85018 	ext{ g}}$$

Both logical paths lead to the same beautiful, precise integer. Always cross-verify your reasoning!

Enter Numerical Value:

Visualized Solution

$S_{N} 2$ Substitution

Hydrolysis of Nitrile

Hell-Volhard-Zelinsky Reaction

Amination

Hydrolysis of Caprolactam

Copolymerization

Mass of Repeating Unit

Total Mass of Polymer Z

Alternative Method

The Sigma Insight: Polymers

Decoding Monomer X

Decoding Monomer Y

The Copolymerization

The Final Calculation

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