1 mole of methane (`CH_4`) contains

Options

A. `6.02 xx 10^23` atoms of H
B. 4 gram atoms of hydrogen
C. `1.81 xx 10^23` molecules of methane
D. 3.0 g of carbon.

Answer

To solve the question "1 mole of methane (CH₄) contains," we will analyze the composition of methane and use Avogadro's number to find the correct answer.

### Step-by-Step Solution:

1. **Understanding Moles and Avogadro's Number**:
- One mole of any substance contains Avogadro's number of molecules, which is approximately \(6.02 \times 10^{23}\).

2. **Identifying the Composition of Methane**:
- The molecular formula for methane is CH₄. This indicates that each molecule of methane contains:
- 1 Carbon atom
- 4 Hydrogen atoms

3. **Calculating the Number of Molecules in 1 Mole of Methane**:
- Since 1 mole of methane contains \(6.02 \times 10^{23}\) molecules, we can denote this as:
\[ \text{Number of CH₄ molecules} = 6.02 \times 10^{23} \text{ molecules} \]

4. **Calculating the Number of Hydrogen Atoms**:
- Each molecule of methane (CH₄) contains 4 Hydrogen atoms. Therefore, the total number of Hydrogen atoms in 1 mole of methane is:
\[ \text{Total Hydrogen atoms} = 4 \times (6.02 \times 10^{23}) = 2.408 \times 10^{24} \text{ Hydrogen atoms} \]

5. **Calculating the Number of Carbon Atoms**:
- Each molecule of methane contains 1 Carbon atom. Therefore, the total number of Carbon atoms in 1 mole of methane is:
\[ \text{Total Carbon atoms} = 1 \times (6.02 \times 10^{23}) = 6.02 \times 10^{23} \text{ Carbon atoms} \]

6. **Calculating the Mass of Carbon and Hydrogen**:
- The molar mass of Carbon (C) is approximately 12 g/mol. Therefore, the mass of Carbon in 1 mole of methane is:
\[ \text{Mass of Carbon} = 1 \text{ mol} \times 12 \text{ g/mol} = 12 \text{ g} \]
- The molar mass of Hydrogen (H) is approximately 1 g/mol. Therefore, the mass of Hydrogen in 1 mole of methane is:
\[ \text{Mass of Hydrogen} = 4 \text{ mol} \times 1 \text{ g/mol} = 4 \text{ g} \]

7. **Final Comparison with Options**:
- Now, we can compare our findings with the given options:
- \(6.02 \times 10^{23}\) atoms of Hydrogen: **True**
- 4 gram atom of Hydrogen: **True**
- \(1.8 \times 10^{23}\) molecules of methane: **False**
- 3 grams of Carbon: **False**

### Conclusion:
The correct answers based on our calculations are:
- 6.02 × 10²³ atoms of Hydrogen
- 4 gram atoms of Hydrogen