Step 1: Understanding the Concept:
To determine the number of atoms, we must follow a three-step conversion pathway: Volume \( \rightarrow \) Moles \( \rightarrow \) Molecules \( \rightarrow \) Atoms.
At Standard Temperature and Pressure (STP), which is defined as 273.15 K and 1 atm pressure, one mole of any ideal gas occupies a specific volume known as the molar volume.
Avogadro's hypothesis states that equal volumes of all gases at the same temperature and pressure contain the same number of molecules.
Step 2: Key Formula or Approach:
1. Molar Volume at STP = 22.4 L/mol.
2. Number of moles (\( n \)) = \( \frac{\text{Given Volume}}{\text{Molar Volume}} \).
3. Number of molecules = \( n \times N_A \), where \( N_A = 6.022 \times 10^{23} \).
4. Total Atoms = Number of molecules \( \times \) Atomicity.
Step 3: Detailed Explanation:
First, we calculate the number of moles of Nitrogen (\( N_2 \)) gas:
\[ n = \frac{11.2 \text{ L}}{22.4 \text{ L/mol}} = 0.5 \text{ moles} \]
Next, we find the number of \( N_2 \) molecules:
\[ \text{Molecules} = 0.5 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} \]
\[ \text{Molecules} = 3.011 \times 10^{23} \text{ molecules} \]
Nitrogen gas is diatomic, meaning each molecule of \( N_2 \) consists of 2 nitrogen atoms.
Therefore, the atomicity is 2.
\[ \text{Total Atoms} = 2 \times 3.011 \times 10^{23} \]
\[ \text{Total Atoms} = 6.022 \times 10^{23} \text{ atoms} \]
This value is equivalent to one Avogadro's number of atoms.
Step 4: Final Answer:
The number of atoms in 11.2 L of nitrogen gas at STP is \( 6.02 \times 10^{23} \).