How many molecules of `CO_2` are present in one litre of air containing 0.03% by volume of `CO_2` at STP ?

Explanation

To solve the problem of how many molecules of \( CO_2 \) are present in one liter of air containing 0.03% by volume of \( CO_2 \) at STP, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Volume Percentage**:
- The problem states that the air contains 0.03% by volume of \( CO_2 \). This means that in 100 liters of air, there are 0.03 liters of \( CO_2 \).

2. **Calculate the Volume of \( CO_2 \) in 1 Liter of Air**:
- To find out how much \( CO_2 \) is present in 1 liter of air, we set up a proportion:
\[ \text{Volume of } CO_2 = \frac{0.03 \text{ liters}}{100 \text{ liters}} \times 1 \text{ liter} = 0.0003 \text{ liters} \]

3. **Use the Molar Volume at STP**:
- At Standard Temperature and Pressure (STP), 1 mole of any gas occupies 22.4 liters. We know that 1 mole contains \( 6.022 \times 10^{23} \) molecules.

4. **Calculate the Number of Moles of \( CO_2 \)**:
- To find the number of moles of \( CO_2 \) in 0.0003 liters, we use the formula:
\[ \text{Number of moles} = \frac{\text{Volume of } CO_2}{\text{Molar volume at STP}} = \frac{0.0003 \text{ liters}}{22.4 \text{ liters/mole}} \approx 1.34 \times 10^{-5} \text{ moles} \]

5. **Calculate the Number of Molecules of \( CO_2 \)**:
- Now, we can find the number of molecules using Avogadro's number:
\[ \text{Number of molecules} = \text{Number of moles} \times 6.022 \times 10^{23} \text{ molecules/mole} \]
\[ \text{Number of molecules} \approx 1.34 \times 10^{-5} \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole} \approx 8.07 \times 10^{18} \text{ molecules} \]

### Final Answer:
Thus, the number of molecules of \( CO_2 \) present in 1 liter of air containing 0.03% by volume of \( CO_2 \) at STP is approximately \( 8.07 \times 10^{18} \) molecules.