To determine how methane gas cannot be prepared, we will analyze three different reactions mentioned in the video transcript: coal-based electrolysis, Bode's reaction, and Franklin's reaction.
### Step-by-Step Solution:
1. **Coal-Based Electrolysis**:
- In this reaction, the electrolysis of sodium salt of carboxylic acid (RCOONa) occurs.
- During the electrolysis, carbon dioxide (CO2) is evolved, and the alkyl radical (R·) is formed.
- When R· combines with itself (R· + R·), it forms a symmetrical alkane.
- If we consider the simplest case where R is a one-carbon alkyl group (CH3), the product formed will be ethane (C2H6).
- Therefore, methane (CH4) cannot be formed from this reaction.
2. **Bode's Reaction**:
- This reaction involves the reaction of an alkyl halide (R-X) with sodium in the presence of dry ether.
- Similar to the previous reaction, this process also proceeds through a free radical mechanism.
- The alkyl radical (R·) is formed and combines with another R· to form a symmetrical alkane.
- If we take the simplest alkyl halide (CH3X), the product will again be ethane (C2H6).
- Thus, methane cannot be formed from this reaction either.
3. **Franklin's Reaction**:
- This reaction involves the reaction of an alkyl halide with zinc in the presence of dry ether.
- The process also leads to the formation of alkyl radicals (R·).
- When these radicals combine, they form a symmetrical alkane.
- Using the simplest alkyl halide (CH3X), the product formed will again be ethane (C2H6).
- Therefore, methane cannot be formed from this reaction as well.
### Conclusion:
From all three reactions analyzed (coal-based electrolysis, Bode's reaction, and Franklin's reaction), it is clear that methane gas cannot be prepared. The minimum product formed in each case is ethane (C2H6), not methane (CH4).
Thus, the answer to the question is that methane gas cannot be prepared by any of the mentioned reactions.
### Final Answer:
Methane gas cannot be prepared by coal-based electrolysis, Bode's reaction, or Franklin's reaction.
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