Related Formula
Pdry N₂ = Ptotal - Aqueous Tension$$P_{\text{dry } \text{N}_2} = P_{\text{total}} - \text{Aqueous Tension} $$
PV = nRT n = (PV)/(RT)$$PV = nRT \implies n = \frac{PV}{RT} $$
%N = Mass of NitrogenMass of organic compound × 100$$\%\text{N} = \frac{\text{Mass of Nitrogen}}{\text{Mass of organic compound}} \times 100 $$
Core Logic
First, isolate the pressure contribution of the dry nitrogen gas:
Pdry N2 = 715 - 15 = 700 mm Hg = (700)/(760) atm$$P_{\text{dry } \text{N}2} = 715 - 15 = 700\text{ mm Hg} = \frac{700}{760}\text{ atm} $$
Using the ideal gas parameters:
- V = 50 mL = 0.050 L$V = 50\text{ mL} = 0.050\text{ L}$ [cite: 1073, 1076]
- T = 300 K$T = 300\text{ K}$
- R = 0.0821 L atm mol⁻¹K⁻¹$R = 0.0821\text{ L atm mol}^{-1}\text{K}^{-1}$
Step 1: Compute Moles and Mass
Calculate total moles of N₂$\text{N}_2$ molecules collected:
nN2 = (((700)/(760)) × 0.050)/(0.0821 × 300) ≈ 1.868 × 10⁻³ mol$$n{\text{N}2} = \frac{\left(\frac{700}{760}\right) \times 0.050}{0.0821 \times 300} \approx 1.868 \times 10^{-3}\text{ mol} $$
Compute corresponding mass of atomic Nitrogen elements (2 × 14 = 28 g/mol$2 \times 14 = 28\text{ g/mol}$): [cite: 1016, 1017]
Mass of N = nN2 × 28 = 1.868 × 10⁻³ × 28 ≈ 0.0523 g = 52.3 mg$$\text{Mass of N} = n{\text{N}2} \times 28 = 1.868 \times 10^{-3} \times 28 \approx 0.0523\text{ g} = 52.3\text{ mg}$$
Step 2: Calculate Percentage Composition
Applying the fraction formulation against total sample mass: [cite: 1021, 1022]
%N = 52.3 mg292 mg × 100 ≈ 17.91% ≈ 18%$$\%\text{N} = \frac{52.3\text{ mg}}{292\text{ mg}} \times 100 \approx 17.91\% \approx 18\% $$
Pattern Recognition
Dumas analysis safety check: Always strip away the vapor pressure of water (aqueous tension) from the measured barometric value before computing the chemical molar counts. For standard conditions shortcuts, remember that 1 mole = 22400 mL$1\text{ mole} = 22400\text{ mL}$ at STP can act as an alternate path if values are normalized.
Chapter Mix
Class 11 Chemistry: Organic Chemistry - Some Basic Principles and Techniques