Question

In Dumas' method for estimation of nitrogen 1 g of an organic compound gave 150 mL of nitrogen collected at 300 K temperature and 900 mm Hg pressure. The percentage composition of nitrogen in the compound is _______ % (nearest integer). (Aqueous tension at $300 \mathrm{~K}=15 \mathrm{~mm} \mathrm{Hg}$ )

Hint:

Use the ideal gas law to calculate the moles of nitrogen and then determine the percentage composition.

Answer 1

Correct Answer: 20

To determine the percentage composition of nitrogen in a compound via Dumas' method, execute the subsequent steps:

Step 1: Quantify the moles of nitrogen gas.

Employ the ideal gas law: \(PV = nRT\).

Pressure (\(P\)) = 900 mm Hg - 15 mm Hg (aqueous tension) = 885 mm Hg.

Convert pressure to atmospheres: \(P = 885 \text{ mm Hg} \times (1 \text{ atm} / 760 \text{ mm Hg}) \approx 1.164 \text{ atm}\).

Volume (\(V\)) = 150 mL = 0.150 L.

Gas constant (\(R\)) = 0.0821 L·atm/(mol·K).

Temperature (\(T\)) = 300 K.

Substitute these values into the ideal gas equation: \(n = (1.164 \text{ atm} \times 0.150 \text{ L}) / (0.0821 \text{ L·atm/(mol·K)} \times 300 \text{ K})\).

Calculate \(n\), the molar quantity of nitrogen: \(n \approx 0.0071 \text{ mol}\).

Step 2: Compute the mass of nitrogen.

Molar mass of nitrogen (N₂) = 28.02 g/mol.

Mass of nitrogen = 0.0071 mol × 28.02 g/mol ≈ 0.198762 g.

Step 3: Calculate the nitrogen's percentage composition.

Percentage of nitrogen = (mass of nitrogen / mass of compound) × 100%.

Percentage of nitrogen = (0.198762 g / 1 g) × 100% ≈ 19.8762%.

Consequently, the nitrogen's percentage composition is approximately 20%.

Conclusion: The derived percentage composition of nitrogen is consistent with the anticipated range of 20%.