Dumas Method Nitrogen Percentage Calculation

 

❓ 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 Explanation

This problem is based on:

👉 Dumas method
👉 Ideal gas equation
👉 Percentage composition.

Main idea:

First calculate moles of dry nitrogen gas using:

$$PV=nRT$$

Then find mass of nitrogen and percentage.

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🔷 Step 1 — Correct Pressure of Dry Nitrogen 💯

Observed pressure:

$$715\text{ mm Hg}$$

Aqueous tension:

$$15\text{ mm Hg}$$

Dry nitrogen pressure:

$$P=715-15$$
$$=700\text{ mm Hg}$$

Convert into atm:

$$P=\frac{700}{760}$$
$$=0.921\text{ atm}$$

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🔷 Step 2 — Convert Volume into Litres

$$50\text{ mL}=0.050\text{ L}$$

Temperature:

$$T=300\text{ K}$$

Use:

$$R=0.0821$$

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🔷 Step 3 — Calculate Moles of $N_2$

Using:

$$PV=nRT$$
$$n=\frac{PV}{RT}$$

Substitute:

$$n= \frac{0.921\times0.050}{0.0821\times300}$$
$$\approx1.87\times10^{-3}\text{ mol}$$

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🔷 Step 4 — Calculate Mass of Nitrogen

Molar mass of:

$$N_2=28$$

Thus mass:

$$m=n\times28$$
$$=1.87\times10^{-3}\times28$$
$$\approx0.0524\text{ g}$$
$$=52.4\text{ mg}$$

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🔷 Step 5 — Percentage of Nitrogen

Mass of compound:

$$292\text{ mg}$$

Thus:

$$\%\ N= \frac{52.4}{292}\times100$$
$$\approx17.95\%$$

Nearest integer:

$$\boxed{ 18\% }$$

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🔷 Step 6 — JEE Trap Alert 🚨

❌ Aqueous tension subtract karna bhool jaana

❌ mL to L conversion mistake

❌ $N_2$ molar mass 14 lena

Remember:

Dumas method:

Always use dry gas pressure.

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✅ Final Answer

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

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