0.44 g of colourless oxide of nitrogen occupies 224 ml at STP. The molecular formula is

Options

A. NO
B. `NO_2`
C. `N_2O`
D. `N_2O_5`

Answer

To solve the problem step by step, we will determine the molecular formula of the nitrogen oxide based on the given data.

### Step 1: Calculate the number of moles of the gas at STP
We know that at standard temperature and pressure (STP), 1 mole of any gas occupies 22,400 mL. Given that the volume of the gas is 224 mL, we can calculate the number of moles.

\[ \text{Number of moles} = \frac{\text{Volume of gas at STP}}{\text{Molar volume at STP}} = \frac{224 \, \text{mL}}{22400 \, \text{mL/mol}} = 0.01 \, \text{mol} \]

### Step 2: Calculate the molar mass of the gas
We have 0.01 moles of the gas weighing 0.44 g. To find the molar mass (molecular weight) of the gas, we use the formula:

\[ \text{Molar mass} = \frac{\text{mass}}{\text{number of moles}} = \frac{0.44 \, \text{g}}{0.01 \, \text{mol}} = 44 \, \text{g/mol} \]

### Step 3: Identify the molecular formula
Now, we need to identify which nitrogen oxide has a molar mass of 44 g/mol. We will calculate the molar masses of the given options:

1. **NO (Nitric oxide)**:
- N: 14 g/mol
- O: 16 g/mol
- Total: 14 + 16 = 30 g/mol

2. **NO2 (Nitrogen dioxide)**:
- N: 14 g/mol
- O: 16 g/mol × 2 = 32 g/mol
- Total: 14 + 32 = 46 g/mol

3. **N2O (Dinitrogen monoxide)**:
- N: 14 g/mol × 2 = 28 g/mol
- O: 16 g/mol
- Total: 28 + 16 = 44 g/mol

4. **N2O5 (Dinitrogen pentoxide)**:
- N: 14 g/mol × 2 = 28 g/mol
- O: 16 g/mol × 5 = 80 g/mol
- Total: 28 + 80 = 108 g/mol

From the calculations, we see that the only nitrogen oxide with a molar mass of 44 g/mol is **N2O**.

### Conclusion
The molecular formula of the colorless oxide of nitrogen is **N2O**.

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