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 solve the problem step by step, we will follow the Dumas method to determine the percentage of nitrogen in the organic compound.

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

### Step 2: Convert Volume of Nitrogen to Liters
Since standard temperature and pressure (STP) is usually expressed in liters, we need to convert the volume from milliliters to liters:
\[ 112 \text{ ml} = \frac{112}{1000} \text{ L} = 0.112 \text{ L} \]

### Step 3: Calculate Moles of Nitrogen Gas
Using the molar volume of a gas at STP (22.4 L/mol), we can calculate the number of moles of nitrogen gas produced:
\[ \text{Moles of } N_2 = \frac{\text{Volume of } N_2}{\text{Molar Volume at STP}} = \frac{0.112 \text{ L}}{22.4 \text{ L/mol}} = 0.005 \text{ moles} \]

### Step 4: Calculate Mass of Nitrogen Gas
Next, we calculate the mass of nitrogen gas produced using its molar mass (molar mass of N₂ = 28 g/mol):
\[ \text{Mass of } N_2 = \text{Moles of } N_2 \times \text{Molar Mass of } N_2 = 0.005 \text{ moles} \times 28 \text{ g/mol} = 0.14 \text{ g} \]

### Step 5: Calculate Percentage of Nitrogen in the Organic Compound
Now, we can calculate the percentage of nitrogen in the organic compound using the formula:
\[ \text{Percentage of Nitrogen} = \left( \frac{\text{Mass of } N_2}{\text{Mass of organic compound}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage of Nitrogen} = \left( \frac{0.14 \text{ g}}{0.5 \text{ g}} \right) \times 100 = 28\% \]

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

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