The ratio of masses of oxygen and nitrogen in a particular gaseous mixture `1:4`. The ratio of number of their molecule is :

Options

A. `1:8`
B. `3:16`
C. `1:4`
D. `7:32`

Explanation

To find the ratio of the number of molecules of oxygen and nitrogen in a gaseous mixture where the mass ratio of oxygen to nitrogen is given as 1:4, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Mass Ratio**:
The mass ratio of oxygen (O) to nitrogen (N) is given as:
\[ \frac{m_O}{m_N} = \frac{1}{4} \]
This means if the mass of oxygen is \( m_O = 1 \) unit, then the mass of nitrogen is \( m_N = 4 \) units.

2. **Use Molar Masses**:
The molar mass (atomic mass) of oxygen (O) is 16 g/mol and that of nitrogen (N) is 14 g/mol.

3. **Calculate the Number of Moles**:
The number of moles (\( n \)) can be calculated using the formula:
\[ n = \frac{\text{mass}}{\text{molar mass}} \]
- For oxygen:
\[ n_O = \frac{m_O}{\text{Molar mass of O}} = \frac{1}{16} \]
- For nitrogen:
\[ n_N = \frac{m_N}{\text{Molar mass of N}} = \frac{4}{14} \]

4. **Calculate the Ratio of Moles**:
Now, we can find the ratio of the number of moles of oxygen to nitrogen:
\[ \frac{n_O}{n_N} = \frac{\frac{1}{16}}{\frac{4}{14}} = \frac{1}{16} \times \frac{14}{4} = \frac{14}{64} = \frac{7}{32} \]

5. **Relate Moles to Molecules**:
The number of molecules is directly proportional to the number of moles. Therefore, the ratio of the number of molecules of oxygen to nitrogen is the same as the ratio of their moles:
\[ \frac{\text{Number of molecules of O}}{\text{Number of molecules of N}} = \frac{n_O}{n_N} = \frac{7}{32} \]

### Final Answer:
The ratio of the number of molecules of oxygen to nitrogen in the mixture is:
\[ \frac{7}{32} \]