Animated Solution for Chemistry - Organic Chemistry: The monomer (X) involved in the synthesis of Nylon 6,6 gives positive carbylamine test. If 10 moles of X are analyzed using Dumas method, the amount (in grams) of nitrogen gas evolved is _______. Use: Atomic mass of N (in amu) = 14

The journey to solving this problem is a beautiful blend of organic polymer chemistry and quantitative analysis. It tests your ability to identify a compound from its chemical properties and then apply stoichiometric principles to a classic analytical method. Let's break it down step by step.

The problem begins by introducing a monomer, labeled X, which is used in the synthesis of Nylon 6,6.

Nylon 6,6 is a well-known condensation polymer. It is synthesized from two specific monomers: 1. Hexamethylenediamine: $H_{2}N-(C{H}_2{)}_6-N{H}_2$ 2. Adipic acid: $HOOC-(C{H}_2{)}_4-COOH$

We are given a crucial piece of evidence: monomer X gives a positive carbylamine test. The carbylamine test (also known as the isocyanide test) is a definitive chemical test used exclusively to detect the presence of primary amines ($1^{\circ }$ amines).

Looking at our two candidates, adipic acid is a dicarboxylic acid and will not respond to this test. Hexamethylenediamine, on the other hand, possesses two primary amine groups. Therefore, we can confidently conclude that monomer X is hexamethylenediamine.

To proceed with any quantitative analysis, we need the exact molecular formula of hexamethylenediamine.

Let's count the atoms in $H_{2}N-(C{H}_2{)}_6-N{H}_2$: - Carbon (C): There are 6 carbon atoms in the central chain. - Hydrogen (H): There are $6\times 2=12$ hydrogens in the chain, plus 2 on each nitrogen, giving a total of $12+2+2=16$ hydrogen atoms. - Nitrogen (N): There is one nitrogen atom at each end, totaling 2 nitrogen atoms.

This gives us the molecular formula: $C_6{H}_{16}{N}_2$.

The problem then states that 10 moles of this monomer are analyzed using the Dumas method.

The Dumas method is a classic quantitative technique used to determine the nitrogen content in an organic compound. In this method, a known mass of the organic compound is strongly heated with copper(II) oxide ($CuO$) in an atmosphere of carbon dioxide.

During this vigorous oxidation, the carbon and hydrogen in the compound are converted into carbon dioxide and water, respectively. The most important part for us is that all the nitrogen present in the compound is liberated as free nitrogen gas ($N_2$).

The general chemical equation for this process is:

Let's apply this to our monomer, $C_6{H}_{16}{N}_2$. Here, the number of nitrogen atoms per molecule, $z$, is 2.

According to the stoichiometry of the Dumas method, 1 mole of the compound will produce $\frac{z}{2}$ moles of $N_2$ gas.

This means there is a simple 1:1 molar ratio between hexamethylenediamine and the nitrogen gas evolved.

The problem asks us to analyze 10 moles of monomer X. Since 1 mole of X yields 1 mole of $N_2$, it naturally follows that 10 moles of X will yield exactly 10 moles of $N_2$ gas.

Finally, we need to find the mass of this evolved gas in grams. We know the atomic mass of nitrogen is $14\text{ amu}$, so the molar mass of $N_2$ gas is $2\times 14=28\text{ g/mol}$.

The total amount of nitrogen gas evolved is 280 grams.