The ratio between the number of molecules in equal masses of nitrogen and oxygen is

Options

A. `7:8`
B. `1:9`
C. `9:1`
D. `8:7`

Answer

To find the ratio between the number of molecules in equal masses of nitrogen (N₂) and oxygen (O₂), we can follow these steps:

### Step-by-Step Solution:

1. **Assume Equal Masses**:
Let's assume we have W grams of nitrogen and W grams of oxygen.

2. **Calculate Molar Masses**:
- The molar mass of nitrogen (N₂) is calculated as:
\[ \text{Molar mass of N₂} = 2 \times 14 \, \text{g/mol} = 28 \, \text{g/mol} \]
- The molar mass of oxygen (O₂) is calculated as:
\[ \text{Molar mass of O₂} = 2 \times 16 \, \text{g/mol} = 32 \, \text{g/mol} \]

3. **Calculate Number of Moles**:
- The number of moles of nitrogen (N₂) is given by:
\[ \text{Number of moles of N₂} = \frac{W}{28} \]
- The number of moles of oxygen (O₂) is given by:
\[ \text{Number of moles of O₂} = \frac{W}{32} \]

4. **Calculate Number of Molecules**:
- The number of molecules in nitrogen (N₂) can be calculated using Avogadro's number (Nₐ):
\[ \text{Number of molecules of N₂} = \left(\frac{W}{28}\right) \times Nₐ \]
- The number of molecules in oxygen (O₂) can be calculated similarly:
\[ \text{Number of molecules of O₂} = \left(\frac{W}{32}\right) \times Nₐ \]

5. **Find the Ratio of Molecules**:
- The ratio of the number of molecules of nitrogen to the number of molecules of oxygen is:
\[ \text{Ratio} = \frac{\left(\frac{W}{28} \times Nₐ\right)}{\left(\frac{W}{32} \times Nₐ\right)} \]
- Simplifying this gives:
\[ \text{Ratio} = \frac{W}{28} \div \frac{W}{32} = \frac{32}{28} = \frac{8}{7} \]

6. **Final Answer**:
- Therefore, the ratio between the number of molecules in equal masses of nitrogen and oxygen is:
\[ \text{Ratio} = 8 : 7 \]