A gases mixture contains oxygen and nitrogen in the ratio `1 : 4` by weight. Therefore, the ratio of the number of molecules is:

Options

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

Explanation

To find the ratio of the number of molecules of oxygen (O₂) and nitrogen (N₂) in a gas mixture where they are present in a weight ratio of 1:4, we can follow these steps:

### Step 1: Define the weights
Let the weight of oxygen be \( W_1 \) and the weight of nitrogen be \( W_2 \). According to the problem, we have:
\[ \frac{W_1}{W_2} = \frac{1}{4} \]
This means if we assume \( W_1 = 1 \) g, then \( W_2 = 4 \) g.

### Step 2: Calculate the number of moles
The number of moles (\( n \)) of a substance is given by the formula:
\[ n = \frac{\text{weight}}{\text{molar mass}} \]
For oxygen (O₂), the molar mass is 32 g/mol, and for nitrogen (N₂), the molar mass is 28 g/mol.

Calculating the number of moles for each gas:
- For oxygen:
\[ n_1 = \frac{W_1}{\text{Molar mass of O}_2} = \frac{1}{32} \text{ moles} \]
- For nitrogen:
\[ n_2 = \frac{W_2}{\text{Molar mass of N}_2} = \frac{4}{28} \text{ moles} \]

### Step 3: Calculate the ratio of the number of moles
Now, we need to find the ratio of the number of moles:
\[ \frac{n_1}{n_2} = \frac{\frac{1}{32}}{\frac{4}{28}} = \frac{1 \times 28}{4 \times 32} = \frac{28}{128} = \frac{7}{32} \]

### Step 4: Conclusion
Thus, the ratio of the number of molecules of oxygen to nitrogen is:
\[ \frac{n_1}{n_2} = \frac{7}{32} \]

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

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