Which of the following contains the maximum number of atoms?

Options

A. 32 g of solid sulphur
B. 32 g of oxygen gas
C. 32 g of sulphur vapours
D. 32 mol of oxygen gas

Answer

To determine which of the given substances contains the maximum number of atoms, we will calculate the number of atoms in each case based on the provided information.

### Step-by-Step Solution:

1. **Calculate the number of atoms in 32 grams of solid sulfur (S):**
- Molar mass of sulfur (S) = 32 g/mol.
- Number of moles of sulfur = mass / molar mass = 32 g / 32 g/mol = 1 mole.
- Atomicity of sulfur = 8 (since it is S8).
- Number of atoms = number of moles × Avogadro's number × atomicity = 1 mole × 6.022 × 10²³ atoms/mole × 8 = 48.176 × 10²³ atoms.

2. **Calculate the number of atoms in 32 grams of oxygen gas (O2):**
- Molar mass of O2 = 32 g/mol.
- Number of moles of O2 = mass / molar mass = 32 g / 32 g/mol = 1 mole.
- Each molecule of O2 contains 2 atoms.
- Number of atoms = number of moles × Avogadro's number × atomicity = 1 mole × 6.022 × 10²³ atoms/mole × 2 = 12.044 × 10²³ atoms.

3. **Calculate the number of atoms in 32 grams of sulfur vapors (S):**
- The molar mass of sulfur vapor (S) is the same as solid sulfur, which is 32 g/mol.
- Number of moles of sulfur vapor = mass / molar mass = 32 g / 32 g/mol = 1 mole.
- Atomicity of sulfur vapor = 8 (as it is still S8).
- Number of atoms = number of moles × Avogadro's number × atomicity = 1 mole × 6.022 × 10²³ atoms/mole × 8 = 48.176 × 10²³ atoms.

4. **Calculate the number of atoms in 32 grams of sulfur dioxide (SO2):**
- Molar mass of SO2 = 64 g/mol.
- Number of moles of SO2 = mass / molar mass = 32 g / 64 g/mol = 0.5 moles.
- Each molecule of SO2 contains 3 atoms (1 sulfur + 2 oxygen).
- Number of atoms = number of moles × Avogadro's number × atomicity = 0.5 moles × 6.022 × 10²³ atoms/mole × 3 = 9.033 × 10²³ atoms.

### Summary of Results:
- **Solid Sulfur (S8):** 48.176 × 10²³ atoms.
- **Oxygen Gas (O2):** 12.044 × 10²³ atoms.
- **Sulfur Vapors (S8):** 48.176 × 10²³ atoms.
- **Sulfur Dioxide (SO2):** 9.033 × 10²³ atoms.

### Conclusion:
The substances with the maximum number of atoms are solid sulfur and sulfur vapors, both containing **48.176 × 10²³ atoms**.