Which has maximum molecules?

Options

A. ` 7 g N_(2)O`
B. `20 g H_(2)`
C. `16 g NO_(2)`
D. `16 g SO_(2)`

Answer

To determine which substance has the maximum number of molecules among the given options, we need to calculate the number of moles for each substance and then convert that to the number of molecules using Avogadro's number (approximately \(6.022 \times 10^{23}\) molecules per mole).

### Step-by-Step Solution:

1. **Identify the Given Data:**
- 7 g of N₂O
- 20 g of H₂
- 16 g of N₂
- 16 g of SO₂

2. **Calculate the Molar Mass of Each Compound:**
- **N₂O:**
- Molar mass = (2 × 14) + 16 = 28 + 16 = 44 g/mol
- **H₂:**
- Molar mass = 2 × 1 = 2 g/mol
- **N₂:**
- Molar mass = 2 × 14 = 28 g/mol
- **SO₂:**
- Molar mass = 32 + (2 × 16) = 32 + 32 = 64 g/mol

3. **Calculate the Number of Moles for Each Substance:**
- **N₂O:**
\[ \text{Moles of N₂O} = \frac{7 \text{ g}}{44 \text{ g/mol}} = 0.159 \text{ moles} \]
- **H₂:**
\[ \text{Moles of H₂} = \frac{20 \text{ g}}{2 \text{ g/mol}} = 10 \text{ moles} \]
- **N₂:**
\[ \text{Moles of N₂} = \frac{16 \text{ g}}{28 \text{ g/mol}} = 0.571 \text{ moles} \]
- **SO₂:**
\[ \text{Moles of SO₂} = \frac{16 \text{ g}}{64 \text{ g/mol}} = 0.25 \text{ moles} \]

4. **Convert Moles to Number of Molecules:**
- **N₂O:**
\[ \text{Molecules of N₂O} = 0.159 \text{ moles} \times 6.022 \times 10^{23} = 9.57 \times 10^{22} \text{ molecules} \]
- **H₂:**
\[ \text{Molecules of H₂} = 10 \text{ moles} \times 6.022 \times 10^{23} = 6.022 \times 10^{24} \text{ molecules} \]
- **N₂:**
\[ \text{Molecules of N₂} = 0.571 \text{ moles} \times 6.022 \times 10^{23} = 3.44 \times 10^{23} \text{ molecules} \]
- **SO₂:**
\[ \text{Molecules of SO₂} = 0.25 \text{ moles} \times 6.022 \times 10^{23} = 1.51 \times 10^{23} \text{ molecules} \]

5. **Compare the Number of Molecules:**
- N₂O: \(9.57 \times 10^{22}\) molecules
- H₂: \(6.022 \times 10^{24}\) molecules
- N₂: \(3.44 \times 10^{23}\) molecules
- SO₂: \(1.51 \times 10^{23}\) molecules

6. **Conclusion:**
- The substance with the maximum number of molecules is **H₂** with \(6.022 \times 10^{24}\) molecules.

### Final Answer:
**H₂ has the maximum number of molecules.**