Which of the following has maximum number of atoms?

Options

A. 18g of `H_(2)O`
B. 18 g of `O_(2)`
C. 18 g of `CO_(2)`
D. 18 g of `CH_(4)`

Explanation

To determine which substance has the maximum number of atoms among the given options, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula**:
The number of atoms in a substance can be calculated using the formula:
\[ \text{Number of atoms} = \left( \frac{\text{Given weight}}{\text{Molar mass}} \right) \times N_A \times n \]
where \( N_A \) (Avogadro's number) is \( 6.022 \times 10^{23} \) and \( n \) is the number of atoms in one molecule of the substance.

2. **Calculate for Each Substance**:
We will calculate the number of atoms for each substance given a weight of 18 grams.

- **For Water (H2O)**:
- Molar mass = 18 g/mol
- Number of atoms (n) = 3 (2 H + 1 O)
\[ \text{Number of atoms} = \left( \frac{18}{18} \right) \times 6.022 \times 10^{23} \times 3 = 1.806 \times 10^{24} \text{ atoms} \]

- **For Oxygen (O2)**:
- Molar mass = 32 g/mol
- Number of atoms (n) = 2 (2 O)
\[ \text{Number of atoms} = \left( \frac{18}{32} \right) \times 6.022 \times 10^{23} \times 2 = 6.774 \times 10^{23} \text{ atoms} \]

- **For Carbon Dioxide (CO2)**:
- Molar mass = 44 g/mol
- Number of atoms (n) = 3 (1 C + 2 O)
\[ \text{Number of atoms} = \left( \frac{18}{44} \right) \times 6.022 \times 10^{23} \times 3 = 7.39 \times 10^{23} \text{ atoms} \]

- **For Methane (CH4)**:
- Molar mass = 16 g/mol
- Number of atoms (n) = 5 (1 C + 4 H)
\[ \text{Number of atoms} = \left( \frac{18}{16} \right) \times 6.022 \times 10^{23} \times 5 = 3.38 \times 10^{24} \text{ atoms} \]

3. **Compare the Results**:
- H2O: \( 1.806 \times 10^{24} \) atoms
- O2: \( 6.774 \times 10^{23} \) atoms
- CO2: \( 7.39 \times 10^{23} \) atoms
- CH4: \( 3.38 \times 10^{24} \) atoms

4. **Conclusion**:
The substance with the maximum number of atoms is Methane (CH4) with \( 3.38 \times 10^{24} \) atoms.

### Final Answer:
**Methane (CH4) has the maximum number of atoms.**

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