Solution:

To find the density of the gaseous oxide relative to oxygen, we need to compare the molar mass of the oxide to the molar mass of oxygen.

Given:
- The gaseous oxide contains 30.4% nitrogen.
- One molecule of the oxide contains one nitrogen atom.

Let's assume the molecular formula of the oxide is NxOy, where x is the number of nitrogen atoms and y is the number of oxygen atoms.

Step 1: Calculation of the molar mass of nitrogen:
The molar mass of nitrogen (N) is approximately 14.01 g/mol.

Step 2: Calculation of the molar mass of the oxide:
Since the oxide contains 30.4% nitrogen, it means that the remaining percentage (100% - 30.4% = 69.6%) is oxygen.

Let's assume the molar mass of the oxide is M.

The molar mass of the nitrogen atoms in the oxide is 30.4% of M.

Therefore, the molar mass of the oxygen atoms in the oxide is 69.6% of M.

The total molar mass of the oxide can be calculated as follows:

M = (30.4% of M) + (69.6% of M)

Simplifying the equation, we get:

M = 0.304M + 0.696M

M = 1M

So, the molar mass of the oxide (M) is equal to 1 times the molar mass of oxygen.

Step 3: Calculation of the density of the oxide relative to oxygen:
The density of a gas can be calculated using the ideal gas law equation:

Density = (molar mass) / (molar volume)

Since we are comparing the density of the oxide to oxygen, we can write:

Density of the oxide relative to oxygen = (molar mass of the oxide) / (molar mass of oxygen)

Using the values we obtained earlier:

Density of the oxide relative to oxygen = M / (molar mass of oxygen)

Substituting the value of M (molar mass of the oxide) from Step 2:

Density of the oxide relative to oxygen = 1 / (molar mass of oxygen)

The molar mass of oxygen is approximately 16.00 g/mol.

Therefore:

Density of the oxide relative to oxygen = 1 / 16.00

Density of the oxide relative to oxygen = 0.0625 g/mL

Since the density is expressed in grams per milliliter (g/mL), we need to convert it to grams per liter (g/L):

Density of the oxide relative to oxygen = 0.0625 g/mL x 1000 mL/L

Density of the oxide relative to oxygen = 62.5 g/L

The density of the oxide relative to oxygen is 62.5 g/L.

Comparing the options given, the correct answer is option 'B' - 1.44