A gaseous nitrogen oxide contains `30.4%` of nitrogen, one molecule of which contains one nitrogen atom. The density of the oxide relative to oxygen gas is :

Options

A. 0.94
B. 1.44
C. 1.5
D. 2.75

Answer

To determine the density of the nitrogen oxide relative to oxygen gas, we can follow these steps:

### Step 1: Determine the percentage composition of the nitrogen oxide
Given that the nitrogen oxide contains `30.4%` nitrogen, we can find the percentage of oxygen:
\[ \text{Percentage of oxygen} = 100\% - 30.4\% = 69.6\% \]

### Step 2: Calculate the number of moles of nitrogen and oxygen
Using the percentage composition, we can calculate the number of moles of nitrogen and oxygen based on their molar masses.

- **Moles of Nitrogen (N)**:
\[ \text{Moles of N} = \frac{\text{Mass of N}}{\text{Molar mass of N}} = \frac{30.4}{14} \approx 2.17 \text{ moles} \]

- **Moles of Oxygen (O)**:
\[ \text{Moles of O} = \frac{\text{Mass of O}}{\text{Molar mass of O}} = \frac{69.6}{16} \approx 4.35 \text{ moles} \]

### Step 3: Find the mole ratio of nitrogen to oxygen
Now, we can find the ratio of moles of nitrogen to moles of oxygen:
\[ \text{Ratio of N to O} = \frac{2.17}{4.35} \approx \frac{1}{2} \]

### Step 4: Write the empirical formula of the nitrogen oxide
From the mole ratio, we can deduce that the empirical formula of the nitrogen oxide is:
\[ \text{NO}_2 \]

### Step 5: Calculate the molar mass of the nitrogen oxide (NO₂)
Now, we calculate the molar mass of NO₂:
\[ \text{Molar mass of NO}_2 = \text{Molar mass of N} + 2 \times \text{Molar mass of O} = 14 + 2 \times 16 = 46 \text{ g/mol} \]

### Step 6: Calculate the relative density of the nitrogen oxide to oxygen
The relative density (or density ratio) of the nitrogen oxide to oxygen gas is given by the ratio of their molar masses:
\[ \text{Relative density} = \frac{\text{Molar mass of NO}_2}{\text{Molar mass of O}_2} = \frac{46}{32} \approx 1.43 \]

### Final Answer
The density of the nitrogen oxide relative to oxygen gas is approximately **1.43**.

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