Which contains more number of molecules?

Options

A. 1 mole of carbon dioxide
B. 4 g of hydrogen
C. 33.6 litres of oxygen at StP
D. 6g of helium

Answer

To determine which option contains more molecules, we will calculate the number of moles for each substance provided in the question. We know that one mole of any substance contains Avogadro's number of molecules (approximately \(6.022 \times 10^{23}\) molecules). Therefore, the number of molecules is directly proportional to the number of moles.

### Step-by-Step Solution:

1. **Calculate the number of moles for each option:**

**Option 1: One mole of carbon dioxide (CO₂)**
- Given: 1 mole
- Number of molecules = 1 mole × \(6.022 \times 10^{23}\) molecules/mole = \(6.022 \times 10^{23}\) molecules

**Option 2: Four grams of hydrogen (H₂)**
- Molar mass of H₂ = 2 g/mol
- Number of moles = Given mass / Molar mass = \(4 \text{ g} / 2 \text{ g/mol} = 2 \text{ moles}\)
- Number of molecules = 2 moles × \(6.022 \times 10^{23}\) molecules/mole = \(1.2044 \times 10^{24}\) molecules

**Option 3: 33.6 liters of oxygen (O₂) at STP**
- At STP, 1 mole of gas occupies 22.4 liters.
- Number of moles = Volume / Molar volume = \(33.6 \text{ L} / 22.4 \text{ L/mol} = 1.5 \text{ moles}\)
- Number of molecules = 1.5 moles × \(6.022 \times 10^{23}\) molecules/mole = \(9.033 \times 10^{23}\) molecules

**Option 4: Six grams of helium (He)**
- Molar mass of He = 4 g/mol
- Number of moles = Given mass / Molar mass = \(6 \text{ g} / 4 \text{ g/mol} = 1.5 \text{ moles}\)
- Number of molecules = 1.5 moles × \(6.022 \times 10^{23}\) molecules/mole = \(9.033 \times 10^{23}\) molecules

2. **Compare the number of molecules from each option:**
- Option 1: \(6.022 \times 10^{23}\) molecules (CO₂)
- Option 2: \(1.2044 \times 10^{24}\) molecules (H₂)
- Option 3: \(9.033 \times 10^{23}\) molecules (O₂)
- Option 4: \(9.033 \times 10^{23}\) molecules (He)

3. **Conclusion:**
- The option with the highest number of molecules is **four grams of hydrogen (H₂)**, which contains \(1.2044 \times 10^{24}\) molecules.

### Final Answer:
**Four grams of hydrogen (H₂) contains the most number of molecules.**