Which one of the following has maximum number of atoms?

Options

A. 1g of Ag(s) [Atomic mass of Ag =108]
B. 1g of Mg(s) [Atomic mass of Mg =24]
C. 1g of `O_2`(s) [Atomic mass of O =16]
D. 1g of Li(s) [Atomic mass of Li =7]

Answer

To determine which substance has the maximum number of atoms among the given options, we will calculate the number of atoms present in 1 gram of each substance.

### Step-by-Step Solution:

1. **Identify the Molar Masses**:
- Silver (Ag): 108 g/mol
- Magnesium (Mg): 24 g/mol
- Oxygen (O2): 32 g/mol (16 g/mol for O)
- Lithium (Li): 7 g/mol

2. **Calculate the Number of Atoms in 1 gram of Each Substance**:
- **For Silver (Ag)**:
\[ \text{Number of moles in 1 g of Ag} = \frac{1 \text{ g}}{108 \text{ g/mol}} = 0.00926 \text{ moles} \]
\[ \text{Number of atoms} = 0.00926 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole} = 5.57 \times 10^{21} \text{ atoms} \]

- **For Magnesium (Mg)**:
\[ \text{Number of moles in 1 g of Mg} = \frac{1 \text{ g}}{24 \text{ g/mol}} = 0.04167 \text{ moles} \]
\[ \text{Number of atoms} = 0.04167 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole} = 2.51 \times 10^{22} \text{ atoms} \]

- **For Oxygen (O2)**:
\[ \text{Number of moles in 1 g of O2} = \frac{1 \text{ g}}{32 \text{ g/mol}} = 0.03125 \text{ moles} \]
\[ \text{Number of molecules} = 0.03125 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole} = 1.88 \times 10^{22} \text{ molecules} \]
Since each O2 molecule contains 2 oxygen atoms:
\[ \text{Number of atoms} = 1.88 \times 10^{22} \text{ molecules} \times 2 = 3.76 \times 10^{22} \text{ atoms} \]

- **For Lithium (Li)**:
\[ \text{Number of moles in 1 g of Li} = \frac{1 \text{ g}}{7 \text{ g/mol}} = 0.14286 \text{ moles} \]
\[ \text{Number of atoms} = 0.14286 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole} = 8.58 \times 10^{22} \text{ atoms} \]

3. **Compare the Number of Atoms**:
- Silver (Ag): \(5.57 \times 10^{21}\) atoms
- Magnesium (Mg): \(2.51 \times 10^{22}\) atoms
- Oxygen (O2): \(3.76 \times 10^{22}\) atoms
- Lithium (Li): \(8.58 \times 10^{22}\) atoms

### Conclusion:
Among the substances, **Lithium (Li)** has the maximum number of atoms in 1 gram.

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