In Duma's method for estimation of nitrogen. `0.25 g `of an organic compound gave `40mL` of nitrogen collected at `300K` temperature of `725 mm` pressure. If the aqueous tension at `300K` is `25 mm`, the percentage of nitrogen in the compound is

Options

A. `16.76`
B. `15.76`
C. `17.36`
D. `18.20`

Explanation

To solve the problem of estimating the percentage of nitrogen in the organic compound using Duma's 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.

\[ P_{\text{N}_2} = P_{\text{total}} - P_{\text{aqueous}} \]

Given:
- Total pressure, \( P_{\text{total}} = 725 \, \text{mm Hg} \)
- Aqueous tension, \( P_{\text{aqueous}} = 25 \, \text{mm Hg} \)

\[ P_{\text{N}_2} = 725 \, \text{mm Hg} - 25 \, \text{mm Hg} = 700 \, \text{mm Hg} \]

### Step 2: Convert the Volume of Nitrogen to Liters
The volume of nitrogen collected is given in milliliters, so we need to convert it to liters.

\[ V = 40 \, \text{mL} = \frac{40}{1000} \, \text{L} = 0.040 \, \text{L} \]

### Step 3: Use the Ideal Gas Equation
We can use the Ideal Gas Law, \( PV = nRT \), to find the number of moles of nitrogen.

Where:
- \( P = 700 \, \text{mm Hg} \) (convert to atm for calculations)
- \( R = 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1} \)
- \( T = 300 \, \text{K} \)

First, convert pressure from mm Hg to atm:

\[ P = \frac{700 \, \text{mm Hg}}{760 \, \text{mm Hg/atm}} \approx 0.9211 \, \text{atm} \]

Now, substituting into the Ideal Gas Law:

\[ n = \frac{PV}{RT} = \frac{(0.9211 \, \text{atm})(0.040 \, \text{L})}{(0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1})(300 \, \text{K})} \]

Calculating \( n \):

\[ n \approx \frac{0.03684}{24.63} \approx 0.001496 \, \text{mol} \]

### Step 4: Calculate the Mass of Nitrogen
Now, we can calculate the mass of nitrogen using its molar mass (28 g/mol).

\[ \text{Mass of } N_2 = n \times M = 0.001496 \, \text{mol} \times 28 \, \text{g/mol} \approx 0.0419 \, \text{g} \]

### Step 5: Calculate the Percentage of Nitrogen in the Compound
Finally, we can find the percentage of nitrogen in the organic compound.

\[ \text{Percentage of } N = \left( \frac{\text{Mass of } N_2}{\text{Mass of compound}} \right) \times 100 \]

Given:
- Mass of the compound = 0.25 g

\[ \text{Percentage of } N = \left( \frac{0.0419 \, \text{g}}{0.25 \, \text{g}} \right) \times 100 \approx 16.76\% \]

### Final Answer
The percentage of nitrogen in the compound is approximately **16.76%**.

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