Which among the following has highest number of atoms?

Options

A. `5 g of CO_2`
B. `4 g of CO`
C. `1 g of H_2`
D. `6 g of O_3`

Answer

To determine which among the given options has the highest number of atoms, we will calculate the number of atoms for each option using the formula:

\[ \text{Number of atoms} = \text{Number of moles} \times N_A \]

where \( N_A \) (Avogadro's number) is approximately \( 6.022 \times 10^{23} \) mol\(^{-1}\).

### Step 1: Calculate the number of moles for each substance

1. **Option A: 5 g of CO2**
- Molar mass of CO2 = 12 (C) + 2 × 16 (O) = 44 g/mol
- Number of moles = \(\frac{5 \text{ g}}{44 \text{ g/mol}} = 0.1136 \text{ mol}\)

2. **Option B: 4 g of C2H4**
- Molar mass of C2H4 = 2 × 12 (C) + 4 × 1 (H) = 28 g/mol
- Number of moles = \(\frac{4 \text{ g}}{28 \text{ g/mol}} = 0.1429 \text{ mol}\)

3. **Option C: 1 g of H2**
- Molar mass of H2 = 2 × 1 (H) = 2 g/mol
- Number of moles = \(\frac{1 \text{ g}}{2 \text{ g/mol}} = 0.5 \text{ mol}\)

4. **Option D: 6 g of O3**
- Molar mass of O3 = 3 × 16 (O) = 48 g/mol
- Number of moles = \(\frac{6 \text{ g}}{48 \text{ g/mol}} = 0.125 \text{ mol}\)

### Step 2: Calculate the number of atoms for each option

1. **Option A: CO2**
- Number of atoms = \(0.1136 \text{ mol} \times 6.022 \times 10^{23} \text{ mol}^{-1} \approx 0.684 \times 10^{23} \text{ atoms}\)

2. **Option B: C2H4**
- Number of atoms = \(0.1429 \text{ mol} \times 6.022 \times 10^{23} \text{ mol}^{-1} \approx 0.858 \times 10^{23} \text{ atoms}\)

3. **Option C: H2**
- Number of atoms = \(0.5 \text{ mol} \times 6.022 \times 10^{23} \text{ mol}^{-1} \approx 3.011 \times 10^{23} \text{ atoms}\)

4. **Option D: O3**
- Number of atoms = \(0.125 \text{ mol} \times 6.022 \times 10^{23} \text{ mol}^{-1} \approx 0.75275 \times 10^{23} \text{ atoms}\)

### Step 3: Compare the number of atoms

- Option A: \(0.684 \times 10^{23}\) atoms
- Option B: \(0.858 \times 10^{23}\) atoms
- Option C: \(3.011 \times 10^{23}\) atoms
- Option D: \(0.75275 \times 10^{23}\) atoms

### Conclusion

The option with the highest number of atoms is **Option C: 1 g of H2**, which has approximately \(3.011 \times 10^{23}\) atoms.

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