The volume percentage of `N_(2)` in air is 78. The Weight percentage of the same

Options

A. 75
B. 78
C. 80
D. 85

Answer

To find the weight percentage of nitrogen in air given its volume percentage, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Volume Percentage**:
The volume percentage of nitrogen (N₂) in air is given as 78%. This means that in 100 liters of air, there are 78 liters of nitrogen.

2. **Assume a Volume of Air**:
For simplicity, we can assume we have 100 liters of air.

3. **Calculate the Mass of Air**:
The average molecular mass of air is approximately 28.97 g/mol. To find the mass of 100 liters of air, we can use the formula:
\[ \text{Mass of air} = \frac{\text{Molecular mass of air}}{\text{Molar volume}} \times \text{Volume of air} \]
Here, the molar volume at standard temperature and pressure (STP) is 22.4 liters/mol.
\[ \text{Mass of air} = \frac{28.97 \text{ g/mol}}{22.4 \text{ L/mol}} \times 100 \text{ L} \approx 129.33 \text{ g} \]

4. **Calculate the Mass of Nitrogen**:
The molecular mass of nitrogen (N₂) is 28 g/mol. Since we have 78 liters of nitrogen, we can calculate its mass:
\[ \text{Mass of nitrogen} = \frac{\text{Molecular mass of nitrogen}}{\text{Molar volume}} \times \text{Volume of nitrogen} \]
\[ \text{Mass of nitrogen} = \frac{28 \text{ g/mol}}{22.4 \text{ L/mol}} \times 78 \text{ L} \approx 97.5 \text{ g} \]

5. **Calculate the Weight Percentage of Nitrogen**:
The weight percentage of nitrogen in air can be calculated using the formula:
\[ \text{Weight percentage of nitrogen} = \left( \frac{\text{Mass of nitrogen}}{\text{Mass of air}} \right) \times 100 \]
\[ \text{Weight percentage of nitrogen} = \left( \frac{97.5 \text{ g}}{129.33 \text{ g}} \right) \times 100 \approx 75.3\% \]

6. **Conclusion**:
Therefore, the weight percentage of nitrogen in air is approximately 75.3%, which can be rounded to 75%.

### Final Answer:
The weight percentage of nitrogen (N₂) in air is approximately **75%**.