In Dumas method 0.5 g of an organic compound containing nitrogen gave 112 ml of nitrogen at S.T.P The percentage of nitrogen in the given compound is

Options

A. 28
B. 38
C. 18
D. 48

Answer

To find the percentage of nitrogen in the given organic compound using the Dumas method, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Data:**
- Mass of the organic compound = 0.5 g
- Volume of nitrogen gas (N₂) at STP = 112 ml

2. **Convert Volume of Nitrogen to Liters:**
- Since 1 liter = 1000 ml, we convert 112 ml to liters:
\[ 112 \, \text{ml} = \frac{112}{1000} = 0.112 \, \text{L} \]

3. **Use Ideal Gas Law to Find Moles of Nitrogen:**
- At STP (Standard Temperature and Pressure), 1 mole of gas occupies 22.4 L. Therefore, we can find the number of moles of nitrogen gas:
\[ \text{Moles of } N_2 = \frac{\text{Volume of } N_2}{\text{Molar Volume at STP}} = \frac{0.112 \, \text{L}}{22.4 \, \text{L/mol}} = 0.005 \, \text{mol} \]

4. **Calculate Mass of Nitrogen:**
- The molar mass of nitrogen (N₂) is approximately 28 g/mol. Therefore, the mass of nitrogen in the compound can be calculated as:
\[ \text{Mass of } N_2 = \text{Moles of } N_2 \times \text{Molar Mass of } N_2 = 0.005 \, \text{mol} \times 28 \, \text{g/mol} = 0.14 \, \text{g} \]

5. **Calculate Percentage of Nitrogen in the Organic Compound:**
- The percentage of nitrogen in the organic compound is given by the formula:
\[ \text{Percentage of } N = \left( \frac{\text{Mass of } N_2}{\text{Mass of organic compound}} \right) \times 100 \]
- Substituting the values:
\[ \text{Percentage of } N = \left( \frac{0.14 \, \text{g}}{0.5 \, \text{g}} \right) \times 100 = 28\% \]

### Final Answer:
The percentage of nitrogen in the given organic compound is **28%**.

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