During estimation of nitrogen by Dumas' method of compound X(0.42 g)
_________mL of N₂ gas will be liberated at STP. (nearest integer)
(Given molar mass in g mol⁻¹: C: 12, H: 1, N: 14 )

Solution

Chemistry ma’am · 3 steps

Read the formula off the ring first; each piperazine molecule gives exactly one molecule of N2.

1. Formula of X. X is piperazine, a six-membered ring of four CH₂ groups and two NH groups. That gives C₄H₁₀N₂, with molar mass 48 + 10 + 28 = 86 g mol⁻¹.
2. Moles of N2. Moles of X = 0.42/86 = 4.88 × 10⁻³ mol. Each molecule has two N atoms, and two N atoms make one N₂. So moles of N₂ equal moles of X.

   V_(N₂) = 0.42/86 × 22400 mL = 109.4 mL

3. So. About 109.4 mL of N₂ is liberated at STP, which rounds to 109.

The common slip: 219. Treating the two N atoms as two moles of gas, instead of one mole of N₂, doubles the volume to 219 mL.

The idea to keep. In Dumas' method, all the nitrogen of the compound comes out as N₂. Count N atoms per molecule, halve that for moles of N₂, then use 22400 mL per mole at STP.

Answer from the NTA final answer key. Solution by PrepWiser.