The number of moles of oxygen in 1 L of air containing `21%` oxygen by volume , under standard conditions , is

Options

A. (a) 0.0093 mole
B. (b) 2.10 moles
C. (c) 0.186 mole
D. (d) 0.21 mole

Explanation

To find the number of moles of oxygen in 1 L of air containing 21% oxygen by volume under standard conditions, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Volume of Oxygen in 1 L of Air:**
Since the air contains 21% oxygen by volume, we can calculate the volume of oxygen in 1 L of air.
\[ \text{Volume of oxygen} = 21\% \text{ of } 1 \text{ L} = \frac{21}{100} \times 1 \text{ L} = 0.21 \text{ L} \]

2. **Use the Molar Volume of a Gas at STP:**
At standard temperature and pressure (STP), the volume of one mole of any gas is 22.4 L. This means:
\[ 1 \text{ mole of gas} = 22.4 \text{ L} \]

3. **Calculate the Number of Moles of Oxygen:**
To find the number of moles of oxygen in 0.21 L, we can use the relationship between volume and moles:
\[ \text{Number of moles of oxygen} = \frac{\text{Volume of oxygen}}{\text{Molar volume at STP}} = \frac{0.21 \text{ L}}{22.4 \text{ L/mole}} \]
Performing the calculation:
\[ \text{Number of moles of oxygen} = \frac{0.21}{22.4} \approx 0.0093 \text{ moles} \]

4. **Conclusion:**
Therefore, the number of moles of oxygen in 1 L of air containing 21% oxygen by volume under standard conditions is approximately 0.0093 moles.

### Final Answer:
The number of moles of oxygen is **0.0093 moles**.