Preparation Methods of Methane Gas Analysis

To determine the correctness of Statement I and Statement II, let us analyze each statement individually:

Analysis of Statement I:

1. Decarboxylation of sodium ethanoate: When sodium ethanoate ($\text{CH}_3\text{COONa}$) is heated with soda lime ($\text{NaOH} + \text{CaO}$), it undergoes decarboxylation to give methane: $\text{CH}_3\text{COONa} + \text{NaOH} \xrightarrow[\Delta]{\text{CaO}} \text{CH}_4 + \text{Na}_2\text{CO}_3$

2. Kolbe's electrolysis of sodium acetate: During the electrolysis of an aqueous solution of sodium acetate ($\text{CH}_3\text{COONa}$), acetate ions undergo oxidation at the anode to form methyl free radicals, which dimerize to form ethane ($\text{C}_2\text{H}_6$): $\text{Anode reaction: } 2\text{CH}_3\text{COO}^- \rightarrow 2\text{CH}_3^\bullet + 2\text{CO}_2 + 2e^-$ $2\text{CH}_3^\bullet \rightarrow \text{C}_2\text{H}_6 \text{ (Ethane)}$ Therefore, methane cannot be prepared by Kolbe's electrolysis.

3. Reaction of $\text{CH}_3\text{MgBr}$ with water: Methylmagnesium bromide ($\text{CH}_3\text{MgBr}$) reacts with water (a proton donor) to yield methane: $\text{CH}_3\text{MgBr} + \text{H}_2\text{O} \rightarrow \text{CH}_4 + \text{Mg(OH)Br}$

Since Kolbe's electrolysis does not yield methane, Statement I is false.

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Analysis of Statement II:

1. Preparation from unsaturated hydrocarbons: Unsaturated hydrocarbons (alkenes and alkynes) contain at least two carbon atoms ($C \ge 2$). Hydrogenation of unsaturated hydrocarbons yields alkanes containing two or more carbon atoms (such as ethane, propane, etc.). Hence, methane ($\text{CH}_4$), having only one carbon atom, cannot be synthesized from unsaturated hydrocarbons.

2. Preparation by Wurtz reaction: The Wurtz reaction involves the coupling of two alkyl halide molecules in the presence of sodium metal in dry ether: $2\text{R-X} + 2\text{Na} \xrightarrow{\text{dry ether}} \text{R-R} + 2\text{NaX}$ The resulting alkane ($\text{R-R}$) must contain at least two carbon atoms (e.g., ethane when $\text{R} = \text{CH}_3$). Consequently, methane cannot be prepared by the Wurtz reaction.

Thus, Statement II is true.

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Conclusion:

• Statement I is false.
• Statement II is true.

This corresponds to Option D.