# An organic compound is estimated through Dumas method and was found to evolve 6 moles of ${\text{C}}{{\text{O}}_{\text{2}}}$, 4 moles of ${{\text{H}}_{\text{2}}}{\text{O}}$ and 1 mole of nitrogen gas. The formula of the compound is:(A)${{\text{C}}_{{\text{12}}}}{{\text{H}}_{\text{8}}}{\text{N}}$ (B)${{\text{C}}_{{\text{12}}}}{{\text{H}}_{\text{8}}}{{\text{N}}_{\text{2}}}$(C)${{\text{C}}_{\text{6}}}{{\text{H}}_{\text{8}}}{\text{N}}$(D)${{\text{C}}_{\text{6}}}{{\text{H}}_{\text{8}}}{{\text{N}}_{\text{2}}}$

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Hint: Dumas method is one of the estimation methods for the amount of total nitrogen present in the organic compound. The gases carbon dioxide, nitrogen and oxygen released by the combustion of the compound are tested and estimated.

Complete Step-by-step solution:
Nitrogen present in the given compound can be estimated by two methods Dumas method and kjeldahl’s process.
Dumas method – the nitrogen compound is heated in the presence of a reducing agent copper oxide releases carbon dioxide $\left( {{\text{C}}{{\text{O}}_{\text{2}}}} \right)$, free nitrogen gas $\left( {{{\text{N}}_{\text{2}}}} \right)$ and oxygen gas $\left( {{{\text{O}}_{\text{2}}}} \right)$. The general formula of the reaction is ${{\text{C}}_{\text{x}}}{{\text{H}}_{\text{y}}}{{\text{N}}_{\text{z}}}{\text{ + }}\left( {{\text{2x + y/2}}} \right){\text{CuO}} \to {\text{xC}}{{\text{O}}_2}{\text{ + y/2HO + z/2N + }}\left( {{\text{2x + y/2}}} \right){\text{Cu}}$.
From the general stoichiometric equation of the method, the number of atoms of carbon, nitrogen and oxygen of the nitrogenous compound are in proportion with the number of moles of gases in products.
Given that 6 moles of carbon dioxide are produced -${\text{6C}}{{\text{O}}_{\text{2}}}$, 4moles of ${{\text{H}}_{\text{2}}}{\text{O}}$ are produced,1mole of nitrogen is produced. Upon substituting the number of moles of carbon dioxide, water and nitrogen in the above equation, we get $\begin{gathered} x = 6 \frac{y }{2} = 4 \Rightarrow y = 8 \frac{z}{2} = 1 \Rightarrow z = 2 \end{gathered}$
Now let us substitute the values of x, y, z in the general formula we obtain, ${{\text{C}}_{\text{6}}}{{\text{H}}_{\text{8}}}{{\text{N}}_{\text{2}}}$.

The answer for the above question is option (D).

NOTE: While calculating the nitrogen produced during the reaction generally, mass can be used to determine the number of moles of each of the products in the reaction. But in the above question already the number of moles of each of the products is given.