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

Options

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

Answer

To find the ratio of the number of molecules of oxygen (O2) and nitrogen (N2) in a gaseous mixture where the mass ratio of oxygen to nitrogen is 1:4, we can follow these steps:

### Step 1: Define the Masses
Let the mass of oxygen (O2) be \( W \) and the mass of nitrogen (N2) be \( 4W \) based on the given ratio of 1:4.

### Step 2: Calculate the Number of Moles
The number of moles of a substance can be calculated using the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]

- For oxygen (O2):
- Molar mass of O2 = 32 g/mol
- Number of moles of O2 = \( \frac{W}{32} \)

- For nitrogen (N2):
- Molar mass of N2 = 28 g/mol
- Number of moles of N2 = \( \frac{4W}{28} \)

### Step 3: Calculate the Number of Molecules
The number of molecules can be calculated using Avogadro's number (NA), which is approximately \( 6.022 \times 10^{23} \) molecules/mol. However, since we are looking for the ratio, we can ignore NA for now.

- Number of molecules of O2 = \( \frac{W}{32} \times NA \)
- Number of molecules of N2 = \( \frac{4W}{28} \times NA \)

### Step 4: Set Up the Ratio of Molecules
Now, we can set up the ratio of the number of molecules of O2 to the number of molecules of N2:
\[ \text{Ratio} = \frac{\text{Number of molecules of O2}}{\text{Number of molecules of N2}} = \frac{\frac{W}{32}}{\frac{4W}{28}} \]

### Step 5: Simplify the Ratio
Now, simplify the ratio:
\[ \text{Ratio} = \frac{W}{32} \times \frac{28}{4W} \]
The \( W \) cancels out:
\[ = \frac{28}{128} = \frac{7}{32} \]

### Conclusion
The ratio of the number of molecules of oxygen to nitrogen in the mixture is \( 7:32 \).