Question

During estimation of Nitrogen by Dumas' method of compound X (0.42 g) :
 
mL of $ N_2 $ gas will be liberated at STP. (nearest integer) $\text{(Given molar mass in g mol}^{-1}\text{ : C : 12, H : 1, N : 14})$

Hint:

In Dumas' method, all the nitrogen in the organic compound is converted to \( N_2 \) gas. Use the molar ratio of nitrogen in the compound to the moles of \( N_2 \) produced and then calculate the volume at STP.

Answer 1

Correct Answer: 109

To determine the volume of \(N_2\) gas produced by the Dumas method at STP, we first identify the compound. The provided structure is piperazine, with the molecular formula \(C_4H_{10}N_2\).

Molecular Weight Calculation:
Piperazine's molecular weight is calculated as: $4 \times 12\ (\text{C}) + 10 \times 1\ (\text{H}) + 2 \times 14\ (\text{N}) = 48 + 10 + 28 = 86\ \text{g/mol}$.

Calculating Moles of Compound:
Given the compound's mass is $0.42\ \text{g}$.
The moles of the compound are $\frac{0.42}{86}\ \text{mol} \approx 0.0048845\ \text{mol}$.

Moles and Volume of \(N_2\) Gas:
One molecule of piperazine yields one molecule of \(N_2\).
Therefore, the moles of \(N_2\) are $0.0048845\ \text{mol}$.
The volume of \(N_2\) at STP is $0.0048845\ \text{mol} \times 22.4\ \text{L/mol} = 0.109\ \text{L}$, which is equivalent to $109\ \text{mL}$.

Conclusion:
The liberated \(N_2\) gas has a volume of 109 mL, consistent with the provided range of 109,109.