Animated Solution for Chemistry - Organic Chemistry: An organic compound is estimated through Dumas method and was found to evolved 6 moles of $C{O}_2$, 4 moles of $H_{2}O$ and 1 mole of nitrogen gas. The formula of the compound is

The Dumas method is a classic and highly reliable technique used in organic chemistry to estimate the amount of nitrogen present in an unknown compound. Unlike the Kjeldahl method, which can sometimes fail depending on the chemical structure (like if nitrogen is in a ring or an azo group), the Dumas method is universally applicable.

In this problem, we are given the exact moles of the combustion products, and our mission is to work backward to find the molecular formula of the original organic compound. Let's dive into the stoichiometry and unravel this molecular mystery!

Imagine you are handed a vial containing an unknown organic compound. You know it contains carbon, hydrogen, and nitrogen, but you have no idea about the exact number of atoms.

To start our mathematical journey, we assume a general molecular formula for this compound: $C_x{H}_y{N}_z$. Our goal is simply to find the values of $x$, $y$, and $z$.

In the Dumas method, we take a known amount of this compound—let's say exactly $1\text{ mole}$ to keep our calculations elegant—and heat it strongly with cupric oxide ($CuO$). The cupric oxide acts as a powerful oxidizing agent.

When the compound is heated, a complete combustion reaction occurs. Every single carbon atom is oxidized to form carbon dioxide ($C{O}_2$), every hydrogen atom is oxidized to form water ($H_{2}O$), and the nitrogen atoms are liberated as free nitrogen gas ($N_2$).

We can write the balanced chemical equation for $1\text{ mole}$ of our compound as follows:

This equation is our master key. It tells us that $1\text{ mole}$ of $C_x{H}_y{N}_z$ will theoretically produce: - $x\text{ moles}$ of $C{O}_2$ - $\frac{y}{2}\text{ moles}$ of $H_{2}O$ - $\frac{z}{2}\text{ moles}$ of $N_2$

Now, let's look at the experimental data provided in the question. We are told that the reaction evolved exactly $6\text{ moles}$ of $C{O}_2$ gas.

According to our master equation, the number of moles of $C{O}_2$ produced should be $x$. By simply equating our theoretical yield to the experimental yield, we get:

Just like that, we have found the number of carbon atoms! The compound has $6$ carbon atoms.

Next, we turn our attention to the water molecules. The problem states that $4\text{ moles}$ of $H_{2}O$ were formed during the combustion.

Looking back at our balanced equation, the theoretical yield of water is $\frac{y}{2}\text{ moles}$. Why divided by two? Because each water molecule ($H_{2}O$) contains two hydrogen atoms. Equating the theoretical and experimental values gives us:

Solving for $y$, we multiply both sides by $2$:

Excellent! We now know that there are $8$ hydrogen atoms in the molecule.

Finally, let's determine the nitrogen content. The question mentions that $1\text{ mole}$ of nitrogen gas ($N_2$) was evolved.

From our master equation, the theoretical yield of nitrogen gas is $\frac{z}{2}\text{ moles}$. Again, we divide by two because nitrogen gas is diatomic. Equating this to the given value:

Solving for $z$, we get:

This is a crucial step where many students make a silly mistake by assuming $z=1$. Always remember that the gas evolved is $N_2$, not atomic nitrogen!

We have successfully found all the missing pieces of our puzzle: $x=6$, $y=8$, and $z=2$.

By substituting these values back into our assumed general formula $C_x{H}_y{N}_z$, we arrive at the final molecular formula of the unknown organic compound:

This perfectly matches option (d). The beauty of this problem lies in how a complex chemical process can be decoded using simple, logical stoichiometry. Keep practicing these fundamental concepts, and you'll master organic quantitative analysis in no time!