In Duma's method for estimation of nitrogen 0.4 gm of an organic compound gave 60 ml of nitrogen collected at 300 K and 715 mm pressure. Calculate the percentage composition of nitrogen in the compound : (Aqueous tension at 300 K=20 mm)

Options

A. `16.72%`
B. `15.93%`
C. `15.59%`
D. `9.46%`

Answer

To solve the problem of calculating the percentage composition of nitrogen in the organic compound using Duma's method, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of the organic compound (m) = 0.4 g
- Volume of nitrogen collected (V1) = 60 mL
- Pressure of the gas collected (P1) = 715 mm Hg
- Temperature (T1) = 300 K
- Aqueous tension at 300 K = 20 mm Hg

2. **Calculate the Actual Pressure of Dry Nitrogen:**
\[ P_{\text{dry}} = P_1 - \text{Aqueous Tension} = 715 \, \text{mm Hg} - 20 \, \text{mm Hg} = 695 \, \text{mm Hg} \]

3. **Convert the Volume of Nitrogen Collected to STP Conditions:**
- Standard Pressure (P2) = 760 mm Hg
- Standard Temperature (T2) = 273 K

Using the gas equation \( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \):
\[ V_2 = \frac{P_1 \cdot V_1 \cdot T_2}{P_2 \cdot T_1} \]
Substituting the values:
\[ V_2 = \frac{695 \, \text{mm Hg} \cdot 60 \, \text{mL} \cdot 273 \, \text{K}}{760 \, \text{mm Hg} \cdot 300 \, \text{K}} \]
\[ V_2 = \frac{695 \cdot 60 \cdot 273}{760 \cdot 300} \approx 49.9 \, \text{mL} \]

4. **Calculate the Mass of Nitrogen at STP:**
- Molar mass of nitrogen (N2) = 28 g/mol
- Volume of 1 mole of gas at STP = 22400 mL

The mass of nitrogen in 49.9 mL:
\[ \text{Mass of } N_2 = \frac{28 \, \text{g}}{22400 \, \text{mL}} \cdot 49.9 \, \text{mL} \approx 0.062 \, \text{g} \]

5. **Calculate the Percentage Composition of Nitrogen in the Compound:**
\[ \text{Percentage of } N = \left( \frac{\text{Mass of } N_2}{\text{Mass of compound}} \right) \times 100 \]
\[ \text{Percentage of } N = \left( \frac{0.062 \, \text{g}}{0.4 \, \text{g}} \right) \times 100 \approx 15.5\% \]

### Final Answer:
The percentage composition of nitrogen in the organic compound is approximately **15.5%**.

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