Related Formula
pN₂ = ptotal - paq$$p_{\mathrm{N_2}} = p_{\text{total}} - p_{\text{aq}}$$
nN₂ = pN₂ VR T$$n_{\mathrm{N_2}} = \frac{p_{\mathrm{N_2}} V}{R T}$$
% N = Mass of nitrogenMass of organic compound × 100$$\% \mathrm{N} = \frac{\text{Mass of nitrogen}}{\text{Mass of organic compound}} \times 100$$
Core Logic
Dumas' method estimates nitrogen by collecting dry nitrogen gas (N₂$N_2$). We must subtract the aqueous tension (vapor pressure of water) to find the pressure exerted solely by the dry nitrogen gas.
Step 1: Calculate Pressure of Dry Nitrogen
pN₂ = 715~mmHg - 15~mmHg = 700~mmHg$$p_{\mathrm{N_2}} = 715~\mathrm{mmHg} - 15~\mathrm{mmHg} = 700~\mathrm{mmHg}$$
Converting pressure to atmospheres:
pN₂ = (700)/(760)~atm$$p_{\mathrm{N_2}} = \frac{700}{760}~\mathrm{atm}$$
Step 2: Calculate Moles of Nitrogen Gas
Using the ideal gas law with R = 0.0821~ L~atm~mol⁻¹~K⁻¹$R = 0.0821~\mathrm{L~atm~mol^{-1}~K^{-1}}$, T = 300~K$T = 300~\mathrm{K}$, and V = 60~mL = 60 × 10⁻³~L$V = 60~\mathrm{mL} = 60 \times 10^{-3}~\mathrm{L}$:
nN₂ = ((700)/(760)) × 60 × 10⁻³0.0821 × 300$$n_{\mathrm{N_2}} = \frac{\left(\frac{700}{760}\right) \times 60 \times 10^{-3}}{0.0821 \times 300}$$
nN₂ = (0.92105 × 0.060)/(24.63) ≈ 2.244 × 10⁻³~mol$$n_{\mathrm{N_2}} = \frac{0.92105 \times 0.060}{24.63} \approx 2.244 \times 10^{-3}~\mathrm{mol}$$
Step 3: Calculate Mass and Percentage of Nitrogen
The molar mass of N₂$\mathrm{N_2}$ is 28~ g~mol⁻¹$28~\mathrm{g~mol^{-1}}$:
Mass of N₂ = nN₂ × 28 = 2.244 × 10⁻³ × 28 ≈ 0.06283~g$$\text{Mass of } \mathrm{N_2} = n_{\mathrm{N_2}} \times 28 = 2.244 \times 10^{-3} \times 28 \approx 0.06283~\mathrm{g}$$
Now find the percentage in 0.5~g$0.5~\mathrm{g}$ of organic compound:
% N = 0.06283~g0.5~g × 100 = 12.566% ≈ 12.57%$$\% \mathrm{N} = \frac{0.06283~\mathrm{g}}{0.5~\mathrm{g}} \times 100 = 12.566\% \approx 12.57\%$$
Pattern Recognition
Watch out! Always subtract the aqueous tension from the wet gas pressure first to find the dry gas pressure. Forgetting this step is the most common source of error in Dumas calculations.
Chapter Mix
Class 11 Chemistry: Organic Chemistry - Some Basic Principles and Techniques