Dumas Method Quick Trick — Find %N in Organic Compound (50 mL N₂) 🔬

 

❓ Question

In Dumas' method, 292 mg of an organic compound released 50.0 mL of nitrogen gas (N₂) at 300 K and 715 mm Hg total pressure. Aqueous tension at 300 K = 15 mm Hg.
Find the percentage composition of nitrogen (N) in the organic compound. (Nearest integer)

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🖼️ Question Image

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✍️ Short Solution

Step 1 — Correct the gas pressure for water vapor

Total pressure above the collected gas includes water vapor. The partial pressure of dry N₂ is:

$$P_{N_2}=P_{\text{total}}-P_{{\text{H}}_2\text{O}}=715-15=700\text{ mm Hg}\mathrm{.}$$

Step 2 — Use ideal gas law to find moles of N₂

Use $PV=nR\mathrm{T.\; Convert\; volume\; to\; litres: }$$V = 50.0\ \text{mL} = 0.0500\ \text{L}$. Use gas constant in mmHg·L units:

$$R=62.3637{\text{L}\text{<span style="color: black;"></span>}\text{mmHg}\text{<span style="color: black;"></span>}\text{mol}}^{-1}{\text{<span style="color: black;"></span>}\text{K}}^{-1}\mathrm{.}$$

So

$$n_{N_2}=\frac{P_{N_2}V}{RT}=\frac{700\times 0.0500}{62.3637\times 300}\mathrm{.}$$

Calculate numerator: $700\times0.0500 = 35.0$.

Denominator: $62.3637\times300 = 18709.11$.

Thus

$$n_{N_2}=\frac{35.0}{18709.11}\approx 1.871\times {10}^{-3}\text{ mol}\mathrm{.}$$

Step 3 — Convert moles of N₂ to mass of elemental N

Each mole of N₂ contains 2 mol of N atoms, so

$$n_N=2\times n_{N_2}=2\times 1.871\times {10}^{-3}=3.742\times {10}^{-3}\text{ mol}\mathrm{.}$$

Mass of N atoms $= n_N \times M_N$ where $M_N \approx 14.01\ \text{g·mol}^{-1}$:

$$m_N=3.742\times {10}^{-3}\times 14.01\approx 0.05240\text{ g}=52.40\text{ mg}\mathrm{.}$$

Step 4 — Percentage of N in the sample

Sample mass = 292 mg. So

$$\mathrm{\%}N=\frac{52.40\text{ mg}}{292\text{ mg}}\times 100\mathrm{\%}\approx 17.95\mathrm{\%}\mathrm{.}$$

Rounded to the nearest integer:

$$\boxed{{\displaystyle 18\mathrm{\%}}}$$

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🧮 Image Solution

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✅ Conclusion & Quick Notes

• Correct for water vapor (aqueous tension) before applying the ideal gas law.

• Use consistent units: pressure in mmHg, volume in L, $R=62.3637$ L·mmHg·mol⁻¹·K⁻¹.

• Final answer (nearest integer): $\boxed{18\%}$ nitrogen in the organic compound.