Which one of the following will have largest number of atoms ?
(a) 1g Au (s) (b) 1g Na (s) (c) 1g Li (s) (d) 1g of `Cl_(2)`(g)

Answer

To determine which of the given substances has the largest number of atoms in 1 gram, we will calculate the number of moles for each substance and then convert that to the number of atoms using Avogadro's number (6.022 x 10^23 atoms/mole).

### Step-by-Step Solution:

1. **Calculate the number of moles of Gold (Au)**:
- Given mass = 1 g
- Atomic mass of Gold (Au) = 197 g/mol
- Number of moles = Given mass / Atomic mass
\[ \text{Moles of Au} = \frac{1 \text{ g}}{197 \text{ g/mol}} \approx 0.00508 \text{ moles} \]

2. **Calculate the number of moles of Sodium (Na)**:
- Given mass = 1 g
- Atomic mass of Sodium (Na) = 23 g/mol
- Number of moles = Given mass / Atomic mass
\[ \text{Moles of Na} = \frac{1 \text{ g}}{23 \text{ g/mol}} \approx 0.0435 \text{ moles} \]

3. **Calculate the number of moles of Lithium (Li)**:
- Given mass = 1 g
- Atomic mass of Lithium (Li) = 7 g/mol
- Number of moles = Given mass / Atomic mass
\[ \text{Moles of Li} = \frac{1 \text{ g}}{7 \text{ g/mol}} \approx 0.1429 \text{ moles} \]

4. **Calculate the number of moles of Chlorine (Cl₂)**:
- Given mass = 1 g
- Atomic mass of Chlorine (Cl₂) = 35.5 g/mol (since Cl₂ consists of two Cl atoms, we use the atomic mass of Cl which is 35.5 g/mol)
- Number of moles = Given mass / Atomic mass
\[ \text{Moles of Cl₂} = \frac{1 \text{ g}}{35.5 \text{ g/mol}} \approx 0.0282 \text{ moles} \]

5. **Convert moles to number of atoms**:
- For Gold:
\[ \text{Number of atoms} = 0.00508 \text{ moles} \times 6.022 \times 10^{23} \approx 3.06 \times 10^{21} \text{ atoms} \]
- For Sodium:
\[ \text{Number of atoms} = 0.0435 \text{ moles} \times 6.022 \times 10^{23} \approx 2.62 \times 10^{22} \text{ atoms} \]
- For Lithium:
\[ \text{Number of atoms} = 0.1429 \text{ moles} \times 6.022 \times 10^{23} \approx 8.59 \times 10^{22} \text{ atoms} \]
- For Chlorine:
\[ \text{Number of atoms} = 0.0282 \text{ moles} \times 6.022 \times 10^{23} \times 2 \approx 3.39 \times 10^{22} \text{ atoms} \]
(Note: We multiply by 2 because Cl₂ has 2 atoms of Cl).

6. **Comparison of the number of atoms**:
- Gold: \(3.06 \times 10^{21}\) atoms
- Sodium: \(2.62 \times 10^{22}\) atoms
- Lithium: \(8.59 \times 10^{22}\) atoms
- Chlorine: \(3.39 \times 10^{22}\) atoms

### Conclusion:
The substance with the largest number of atoms in 1 gram is **Lithium (Li)**.

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