Which of the following contains Avagadro number of atoms?

Options

A. one mole of Helium gas
B. 22.4 lits of `CO_(2)` at STP
C. 11.2 lits of Hydrogen gas at STP
D. 3.2 gms of methane

Answer

To determine which of the given options contains Avogadro's number of atoms, we need to analyze each option based on the concept that one mole of any substance contains Avogadro's number of entities (atoms, molecules, etc.), which is approximately \(6.022 \times 10^{23}\).

### Step-by-Step Solution:

1. **Understanding Avogadro's Number**:
- Avogadro's number (\(N_A\)) is \(6.022 \times 10^{23}\). One mole of any substance contains \(N_A\) entities (atoms, molecules, etc.).

2. **Option 1: One mole of Helium gas**:
- Helium is a monoatomic gas.
- Therefore, one mole of helium contains \(N_A\) atoms.
- **Conclusion**: This option contains Avogadro's number of atoms.

3. **Option 2: 22.4 liters of Carbon Dioxide at STP**:
- At STP (Standard Temperature and Pressure), one mole of any gas occupies 22.4 liters.
- Therefore, 22.4 liters of carbon dioxide corresponds to 1 mole of CO₂.
- Each molecule of CO₂ contains 3 atoms (1 carbon + 2 oxygen).
- Thus, the total number of atoms in 1 mole of CO₂ is:
\[ 1 \text{ mole CO₂} \times 3 \text{ atoms/molecule} = 3N_A \text{ atoms} \]
- **Conclusion**: This option contains \(3N_A\) atoms, which is also Avogadro's number of atoms.

4. **Option 3: 11.2 liters of Hydrogen gas at STP**:
- At STP, 11.2 liters of hydrogen corresponds to:
\[ \frac{11.2 \text{ liters}}{22.4 \text{ liters/mole}} = 0.5 \text{ moles} \]
- Hydrogen (H₂) is a diatomic molecule, meaning each molecule contains 2 atoms.
- Therefore, the total number of atoms in 0.5 moles of H₂ is:
\[ 0.5 \text{ moles} \times 2 \text{ atoms/molecule} = N_A \text{ atoms} \]
- **Conclusion**: This option contains Avogadro's number of atoms.

5. **Option 4: 3.2 grams of Methane (CH₄)**:
- The molar mass of methane (CH₄) is:
\[ 12 \text{ (C)} + 4 \times 1 \text{ (H)} = 16 \text{ g/mol} \]
- The number of moles of methane in 3.2 grams is:
\[ \frac{3.2 \text{ grams}}{16 \text{ g/mol}} = 0.2 \text{ moles} \]
- Each molecule of methane contains 5 atoms (1 carbon + 4 hydrogen).
- Therefore, the total number of atoms in 0.2 moles of CH₄ is:
\[ 0.2 \text{ moles} \times 5 \text{ atoms/molecule} = N_A \text{ atoms} \]
- **Conclusion**: This option also contains Avogadro's number of atoms.

### Final Answer:
All options contain Avogadro's number of atoms:
- One mole of helium gas
- 22.4 liters of carbon dioxide at STP
- 11.2 liters of hydrogen gas at STP
- 3.2 grams of methane