The number of mole of nitrogen in one litre of air containing 10% nitrogen by volume, under standard conditions, is

Options

A. 0.03 mole
B. 2.10 mole
C. 0.186 mole
D. ` 4.46 xx 10^(-3) "mole"`

Answer

To solve the question regarding the number of moles of nitrogen in one liter of air containing 10% nitrogen by volume under standard conditions, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the volume of nitrogen in 1 liter of air:**
- Given that the air contains 10% nitrogen by volume, we can calculate the volume of nitrogen in 1 liter of air.
- Volume of nitrogen = 10% of 1 liter = \( \frac{10}{100} \times 1 \) liter = 0.1 liters.

2. **Use the molar volume of a gas at STP:**
- At standard temperature and pressure (STP), 1 mole of any ideal gas occupies 22.4 liters.
- We will use this information to find the number of moles of nitrogen in the calculated volume.

3. **Calculate the number of moles of nitrogen:**
- The number of moles of nitrogen can be calculated using the formula:
\[ \text{Number of moles} = \frac{\text{Volume of gas (liters)}}{\text{Molar volume at STP (liters/mole)}} \]
- Substituting the values:
\[ \text{Number of moles of } N_2 = \frac{0.1 \text{ liters}}{22.4 \text{ liters/mole}} = \frac{0.1}{22.4} \text{ moles} \]

4. **Perform the calculation:**
- Calculating the above expression:
\[ \text{Number of moles of } N_2 = 0.1 \div 22.4 \approx 0.004464 \text{ moles} \]
- This can be expressed in scientific notation:
\[ \text{Number of moles of } N_2 \approx 4.46 \times 10^{-3} \text{ moles} \]

5. **Conclusion:**
- Therefore, the number of moles of nitrogen in 1 liter of air containing 10% nitrogen by volume under standard conditions is approximately \( 4.46 \times 10^{-3} \) moles.
- The correct answer is option D: \( 4.46 \times 10^{-3} \) moles.