In Dumas' method of estimation of nitrogen `0.35 g` of an organic compound gave `55mL` of nitrogen collected at `300K` temperature and `715 mm` pressure. The percentage composition of nitrogen in the compound would be `: (` Aqueous tension at `300K =15 mm)`

Options

A. `14.45`
B. `15.45`
C. `16.45`
D. `17.45`

Explanation

To solve the problem of estimating the percentage composition of nitrogen in the organic compound using Dumas' method, we can follow these steps:

### Step 1: Calculate the Effective Pressure of Nitrogen
The effective pressure of nitrogen can be calculated by subtracting the aqueous tension from the total pressure.

Given:
- Total pressure (P_total) = 715 mm
- Aqueous tension (P_aqueous) = 15 mm

**Calculation:**
\[ P_{N_2} = P_{total} - P_{aqueous} = 715 \, \text{mm} - 15 \, \text{mm} = 700 \, \text{mm} \]

### Step 2: Convert Pressure to Atmospheres
To use the ideal gas law, we need to convert the pressure from mm to atm.

**Conversion:**
\[ P_{N_2} = \frac{700 \, \text{mm}}{760 \, \text{mm}} = 0.9211 \, \text{atm} \]

### Step 3: Convert Volume to Liters
The volume of nitrogen collected needs to be converted from mL to L.

**Conversion:**
\[ V = \frac{55 \, \text{mL}}{1000} = 0.055 \, \text{L} \]

### Step 4: Use the Ideal Gas Law to Find Moles of Nitrogen
Using the ideal gas equation \( PV = nRT \), we can solve for the number of moles (n) of nitrogen.

**Given:**
- R (ideal gas constant) = 0.0821 L·atm/(K·mol)
- T (temperature) = 300 K

**Calculation:**
\[ n = \frac{PV}{RT} \]
\[ n = \frac{(0.9211 \, \text{atm}) \times (0.055 \, \text{L})}{(0.0821 \, \text{L·atm/(K·mol)}) \times (300 \, \text{K})} \]
\[ n = \frac{0.05066}{24.63} \approx 0.00206 \, \text{mol} \]

### Step 5: Calculate Mass of Nitrogen
Now, we can find the mass of nitrogen using the number of moles and the molar mass of nitrogen (N₂ = 28 g/mol).

**Calculation:**
\[ \text{Mass of } N_2 = n \times \text{Molar mass} \]
\[ \text{Mass of } N_2 = 0.00206 \, \text{mol} \times 28 \, \text{g/mol} \approx 0.05768 \, \text{g} \]

### Step 6: Calculate the Percentage Composition of Nitrogen
Finally, we can calculate the percentage of nitrogen in the organic compound.

**Given:**
- Mass of organic compound = 0.35 g

**Calculation:**
\[ \text{Percentage of } N = \left( \frac{\text{Mass of } N_2}{\text{Mass of organic compound}} \right) \times 100 \]
\[ \text{Percentage of } N = \left( \frac{0.05768 \, \text{g}}{0.35 \, \text{g}} \right) \times 100 \approx 16.49\% \]

### Final Answer
The percentage composition of nitrogen in the compound is approximately **16.49%**.

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