You are provided with 64 g of solid sulphur in container A and 64 g of oxygen in container B. Which will have more number of molecules? (Atomic mass of S = 32, O = 16)

Options

A. 64 g of `S_(8)`
B. 64 g of `O_(2)`
C. Both have equal number of molecules.
D. Cannot be calculated with the given information.

Explanation

To determine which container has more molecules, we need to calculate the number of molecules in each container based on the given mass of sulfur and oxygen.

### Step-by-Step Solution:

**Step 1: Calculate the number of molecules of sulfur (S8) in container A.**

1. **Identify the mass of sulfur**:
- Mass of sulfur = 64 g

2. **Determine the molar mass of S8**:
- Atomic mass of sulfur (S) = 32 g/mol
- Molar mass of S8 = 8 × 32 g/mol = 256 g/mol

3. **Calculate the number of moles of S8 in 64 g**:
\[ \text{Number of moles of S8} = \frac{\text{mass}}{\text{molar mass}} = \frac{64 \text{ g}}{256 \text{ g/mol}} = \frac{1}{4} \text{ moles} \]

4. **Calculate the number of molecules of S8**:
- Using Avogadro's number (Na = \(6.022 \times 10^{23}\) molecules/mol):
\[ \text{Number of molecules of S8} = \frac{1}{4} \times Na = \frac{1}{4} \times 6.022 \times 10^{23} \approx 1.5055 \times 10^{23} \text{ molecules} \]

**Step 2: Calculate the number of molecules of oxygen (O2) in container B.**

1. **Identify the mass of oxygen**:
- Mass of oxygen = 64 g

2. **Determine the molar mass of O2**:
- Atomic mass of oxygen (O) = 16 g/mol
- Molar mass of O2 = 2 × 16 g/mol = 32 g/mol

3. **Calculate the number of moles of O2 in 64 g**:
\[ \text{Number of moles of O2} = \frac{64 \text{ g}}{32 \text{ g/mol}} = 2 \text{ moles} \]

4. **Calculate the number of molecules of O2**:
\[ \text{Number of molecules of O2} = 2 \times Na = 2 \times 6.022 \times 10^{23} \approx 1.2044 \times 10^{24} \text{ molecules} \]

**Step 3: Compare the number of molecules in both containers.**

- Number of molecules of S8 in container A: \( \approx 1.5055 \times 10^{23} \)
- Number of molecules of O2 in container B: \( \approx 1.2044 \times 10^{24} \)

### Conclusion:
Container B (with oxygen) has more molecules than container A (with sulfur).

### Final Answer:
Container B has more number of molecules.

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