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

### Step 1: Determine the mass of nitrogen and oxygen in the nitrogen oxide.
Given that the nitrogen oxide contains 30.4% nitrogen, we can assume the total mass of the nitrogen oxide is 100 grams for simplicity.

- Mass of nitrogen = 30.4% of 100 g = 30.4 g
- Mass of oxygen = Total mass - Mass of nitrogen = 100 g - 30.4 g = 69.6 g

### Step 2: Calculate the number of moles of nitrogen and oxygen.
To find the number of moles, we will use the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]

- Molar mass of nitrogen (N) = 14 g/mol
- Molar mass of oxygen (O) = 16 g/mol

Calculating moles:
- Moles of nitrogen = \( \frac{30.4 \text{ g}}{14 \text{ g/mol}} = 2.17 \text{ moles} \)
- Moles of oxygen = \( \frac{69.6 \text{ g}}{16 \text{ g/mol}} = 4.35 \text{ moles} \)

### Step 3: Determine the mole ratio of nitrogen to oxygen.
To find the simplest ratio of moles of nitrogen to moles of oxygen:
- Ratio = \( \frac{2.17}{4.35} \approx \frac{1}{2} \)

This indicates that the formula of the nitrogen oxide is \( NO_2 \) (1 nitrogen atom and 2 oxygen atoms).

### Step 4: Calculate the molar mass of \( NO_2 \).
The molar mass of \( NO_2 \) can be calculated as follows:
- Molar mass of \( NO_2 = \text{Molar mass of N} + 2 \times \text{Molar mass of O} \)
- Molar mass of \( NO_2 = 14 \text{ g/mol} + 2 \times 16 \text{ g/mol} = 14 + 32 = 46 \text{ g/mol} \)

### Step 5: Calculate the density of \( NO_2 \) relative to oxygen.
The density of a gas relative to another gas is given by the ratio of their molar masses:
\[ \text{Relative density} = \frac{\text{Molar mass of } NO_2}{\text{Molar mass of } O_2} \]

- Molar mass of \( O_2 = 2 \times 16 \text{ g/mol} = 32 \text{ g/mol} \)

Calculating the relative density:
\[ \text{Relative density} = \frac{46 \text{ g/mol}}{32 \text{ g/mol}} = 1.4375 \]

### Step 6: Round the result.
Rounding 1.4375 gives approximately 1.44.

### Final Answer:
The density of the nitrogen oxide relative to oxygen gas is approximately **1.44**.

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