The ratio of masses of oxygen and nitrogen of a particular gaseous mixture is 1:4. The ratio of number of molecules is

Options

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

Answer

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

### Step 1: Define the Masses
Let the mass of oxygen (O) be 1 g and the mass of nitrogen (N) be 4 g, according to the given ratio.

### Step 2: Calculate Moles of Each Gas
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]

- Molar mass of oxygen (O) = 32 g/mol
- Molar mass of nitrogen (N) = 28 g/mol

Now, calculate the moles:
- Moles of oxygen:
\[ n_O = \frac{1 \text{ g}}{32 \text{ g/mol}} = \frac{1}{32} \text{ mol} \]

- Moles of nitrogen:
\[ n_N = \frac{4 \text{ g}}{28 \text{ g/mol}} = \frac{4}{28} \text{ mol} = \frac{1}{7} \text{ mol} \]

### Step 3: Find the Ratio of Moles
Now, we find the ratio of the number of moles of oxygen to nitrogen:
\[ \text{Ratio of moles} = \frac{n_O}{n_N} = \frac{\frac{1}{32}}{\frac{1}{7}} = \frac{1}{32} \times \frac{7}{1} = \frac{7}{32} \]

### Step 4: Convert to Ratio of Molecules
Since the number of molecules is directly proportional to the number of moles, the ratio of the number of molecules of oxygen to nitrogen will be the same as the ratio of their moles:
\[ \text{Ratio of molecules} = \frac{n_O}{n_N} = \frac{7}{32} \]

### Final Answer
Thus, the ratio of the number of molecules of oxygen to nitrogen is:
\[ \text{Ratio of molecules} = 7:32 \]

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