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Methane can be converted into ethane by:
A. chlorination followed by the reaction with alcoholic $KOH$
B. chlorination followed by the reaction with aqueous $KOH$
C. chlorination followed by Wurtz reaction
D. chlorination followed by decarboxylation

Answer
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Hint: It is known to us that haloalkane reactions are carried out by two types of mechanism, one by nucleophilic substitution mechanism and other by \[\beta \] elimination mechanism. One of the efficient methods for the synthesis of higher alkane is by the reaction of alkyl halides with metallic sodium under the action of dry ether.

Complete step by step answer:
We know that the reaction of alkanes with halogen in the presence of light results in the formation of haloalkane which are commonly called alkyl halide. Therefore, for the given reaction, the first step is the reaction of methane with chlorine in the presence of light to form methyl chloride. The reaction is shown below.
\[C{H_4} + C{l_2} \to C{H_3}Cl + HCl\]
Now, the second step of the reaction is the reaction of methyl chloride (alkyl halide) with metallic sodium under the action of dry ether. This reaction is termed as Wurtz reaction. It is a coupling reaction. Wurtz reaction is most commonly used in organic and organometallic chemistry. In this reaction, exchange of halogen and metal occurs to form the carbon-carbon bond. This proceeds through nucleophilic substitution reaction. The complete reaction of methyl chloride with metallic sodium under the action of dry ether to form ethane is shown below.
\[C{H_3}Cl + 2Na + ClC{H_3} \to C{H_3}C{H_3}\]
Hence, we can say that methane can be converted into ethane by chlorination followed by Wurtz reaction.

The correct option is C.

Note:
As we know that, ethane is a symmetrical alkane. Wurtz reaction is basically used for the preparation of symmetrical alkane. It is not used for the production of asymmetrical alkane.