Assertion : Both 44 g `CO_2` and 16 g `CH_4` have same number of carbon atoms.
Reason : Both contain 1 g atom of carbon which contains `6.023 xx 10^(23)` carbon atoms.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Analyze the Assertion
The assertion states that both 44 g of CO₂ and 16 g of CH₄ have the same number of carbon atoms.

1. **Calculate the number of moles of CO₂:**
- Molar mass of CO₂ = 12 (C) + 16 (O) × 2 = 12 + 32 = 44 g/mol
- Number of moles of CO₂ = Given mass / Molar mass = 44 g / 44 g/mol = 1 mole

2. **Determine the number of carbon atoms in CO₂:**
- Each molecule of CO₂ contains 1 carbon atom.
- Therefore, in 1 mole of CO₂, the number of carbon atoms = 1 mole × Avogadro's number (6.022 × 10²³) = 6.022 × 10²³ carbon atoms.

3. **Calculate the number of moles of CH₄:**
- Molar mass of CH₄ = 12 (C) + 1 (H) × 4 = 12 + 4 = 16 g/mol
- Number of moles of CH₄ = Given mass / Molar mass = 16 g / 16 g/mol = 1 mole

4. **Determine the number of carbon atoms in CH₄:**
- Each molecule of CH₄ contains 1 carbon atom.
- Therefore, in 1 mole of CH₄, the number of carbon atoms = 1 mole × Avogadro's number (6.022 × 10²³) = 6.022 × 10²³ carbon atoms.

### Conclusion for Assertion
Both 44 g of CO₂ and 16 g of CH₄ contain the same number of carbon atoms, which is 6.022 × 10²³. Thus, the assertion is **correct**.

### Step 2: Analyze the Reason
The reason states that both contain 1 gram atom of carbon, which contains 6.023 × 10²³ carbon atoms.

1. **Understanding the term "gram atom":**
- A gram atom is equivalent to 1 mole of an element, which contains Avogadro's number of atoms (6.022 × 10²³).

2. **Check the number of gram atoms in CO₂ and CH₄:**
- In CO₂, we have 1 mole of carbon (from 1 mole of CO₂).
- In CH₄, we also have 1 mole of carbon (from 1 mole of CH₄).

### Conclusion for Reason
Both CO₂ and CH₄ contain 1 mole (or 1 gram atom) of carbon, which indeed contains 6.022 × 10²³ carbon atoms. Thus, the reason is also **correct** and provides a valid explanation for the assertion.

### Final Conclusion
Both the assertion and the reason are correct, and the reason is the correct explanation of the assertion.

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