0.11 gm of a colourless oxide of nitrogen occupies 28 ml at `0^(@)C` and 2 atm. Identify the oxide.

Options

A. `CO_(2)`
B. `N_(2)O`
C. 1 and 2 both
D. `CO`

Answer

To identify the colorless oxide of nitrogen based on the given data, we can follow these steps:

### Step 1: Gather the given data
- Mass of the oxide (m) = 0.11 g
- Volume (V) = 28 mL = 28/1000 L = 0.028 L
- Temperature (T) = 0°C = 273 K
- Pressure (P) = 2 atm

### Step 2: Use the Ideal Gas Law
The Ideal Gas Law is given by the equation:
\[ PV = nRT \]
Where:
- \( P \) = pressure in atm
- \( V \) = volume in liters
- \( n \) = number of moles
- \( R \) = ideal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = temperature in Kelvin

### Step 3: Rearrange the equation to find the number of moles (n)
From the Ideal Gas Law, we can rearrange it to find \( n \):
\[ n = \frac{PV}{RT} \]

### Step 4: Substitute the values into the equation
Substituting the known values into the equation:
\[ n = \frac{(2 \, \text{atm}) \times (0.028 \, \text{L})}{(0.0821 \, \text{L·atm/(K·mol)}) \times (273 \, \text{K})} \]

### Step 5: Calculate the number of moles (n)
Calculating the right-hand side:
\[ n = \frac{0.056}{22.414} \approx 0.00249 \, \text{mol} \]

### Step 6: Calculate the molecular weight
The molecular weight (M) can be calculated using the formula:
\[ M = \frac{m}{n} \]
Where:
- \( m \) = mass of the substance
- \( n \) = number of moles

Substituting the values:
\[ M = \frac{0.11 \, \text{g}}{0.00249 \, \text{mol}} \approx 44.2 \, \text{g/mol} \]

### Step 7: Identify the oxide of nitrogen
Now we need to identify the oxide of nitrogen with a molecular weight of approximately 44 g/mol. The possible nitrogen oxides are:
- N2O (dinitrogen monoxide)
- NO (nitric oxide)
- NO2 (nitrogen dioxide)
- N2O4 (dinitrogen tetroxide)

Among these, N2O has a molecular weight of:
\[ 2(14) + 16 = 28 + 16 = 44 \, \text{g/mol} \]

### Conclusion
Thus, the colorless oxide of nitrogen that fits the given conditions is:
**N2O (dinitrogen monoxide)**