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Step-by-Step Solution
Step 1: Recognize the Significance of Duma's Method
Duma's method is used for the estimation of nitrogen in an organic compound. When the organic compound is heated with cupric oxide (CuO), carbon and hydrogen are oxidized to carbon dioxide ($CO_2$) and water ($H_2O$), while nitrogen is released as nitrogen gas ($N_2$). By measuring the amounts of these products, we can determine the relative number of each element (C, H, and N) present in the compound.
Step 2: Interpret the Moles of Reaction Products
According to the problem, on complete combustion (and nitrogen release), the following products were obtained:
$6$ moles of $CO_2$
$4$ moles of $H_2O$
$1$ mole of $N_2$
Step 3: Convert Products to Elemental Moles
• Each mole of $CO_2$ corresponds to 1 mole of carbon atoms. So, $6$ moles of $CO_2$ indicates $6$ moles of carbon (C) in the compound.
• Each mole of $H_2O$ contains 2 moles of hydrogen atoms. So, $4$ moles of $H_2O$ corresponds to $4 \times 2 = 8$ moles of hydrogen (H).
• Each mole of $N_2$ has 2 moles of nitrogen atoms. So, $1$ mole of $N_2$ corresponds to $2$ moles of nitrogen (N).
Step 4: Determine the Elemental Ratio
The elemental ratio is therefore:
C : H : N = 6 : 8 : 2.
To simplify, divide by the smallest number in the ratio (which is 2):
6 ÷ 2 : 8 ÷ 2 : 2 ÷ 2 = 3 : 4 : 1.
Step 5: Obtain the Molecular Formula
The simplest whole number ratio (empirical formula) is $C_3H_4N$. However, the question specifies the molecular formula as $C_6H_8N_2$, which is simply a multiple of the empirical formula by 2:
$C_3H_4N \times 2 = C_6H_8N_2$.
Step 6: State the Correct Formula
Therefore, based on the Duma's method estimation, the correct molecular formula for the compound is
$C_6H_8N_2$.
