Related Formula
Moles of Compound X = Moles of N₂$$\text{Moles of Compound X} = \text{Moles of } \mathrm{N_2}$$
VN₂ (at STP) = nN₂ × 22400~mL$$V_{\mathrm{N_2}} (\text{at STP}) = n_{\mathrm{N_2}} \times 22400\mathrm{~mL}$$
Core Logic
From the molecular structure of compound X, its molecular formula is C₅H₁₀N₂$\mathrm{C_5H_{10}N_2}$.
Molar Mass of X = (5 × 12) + (10 × 1) + (2 × 14) = 60 + 10 + 28 = 86 ~g~mol⁻¹$= (5 \times 12) + (10 \times 1) + (2 \times 14) = 60 + 10 + 28 = 86\mathrm{~g~mol^{-1}}$.
Step 1: Calculation
Moles of compound X in 0.42~g$0.42\mathrm{~g}$:
nX = (0.42)/(86)~mol$$n_{\text{X}} = \frac{0.42}{86}\mathrm{~mol}$$
By Conservation of Atomic Mass (POAC) on Nitrogen atoms:
2 × nX = 2 × nN₂ nN₂ = nX = (0.42)/(86)~mol$$2 \times n_{\text{X}} = 2 \times n_{\mathrm{N_2}} \implies n_{\mathrm{N_2}} = n_{\text{X}} = \frac{0.42}{86}\mathrm{~mol}$$
Volume of N₂$\mathrm{N_2}$ liberated at STP:
VN₂ = (0.42)/(86) × 22400~mL ≈ 109.395~mL$$V_{\mathrm{N_2}} = \frac{0.42}{86} \times 22400\mathrm{~mL} \approx 109.395\mathrm{~mL}$$
Using 22.7~L$22.7\mathrm{~L}$ standard STP molar volume: (0.42)/(86) × 22700 ≈ 110.88~mL ≈ 111~mL$\frac{0.42}{86} \times 22700 \approx 110.88\mathrm{~mL} \approx 111\mathrm{~mL}$.
Pattern Recognition
Dumas method volume calculation:
V = mMcompound × 22.4 L/mol × 1000 mL = 111 mL$V = \frac{m}{M_{\text{compound}}} \times 22.4\text{ L/mol} \times 1000\text{ mL} = 111\text{ mL}$.
Chapter Mix
Class 11 Chemistry: Organic Chemistry - Some Basic Principles and Techniques