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what is a wurtz reaction? what is its use?

Use -  Higher alkanes are obtained by heating an alkylhalide (R - X) with sodium metal in dry ether solution.

R - X + 2 Na + X - R    ether _>        R - R                    +           2 NaX

                                                 symmetrical alkane

For example,

  CH₃ - Br + 2Na  + Br - CH₃  ether _> CH₃ -  CH₃  + 2NaBr 

Methyl bromide                                        ethane

The reaction between two different alkylhalides and sodium gives a mixture of products that are difficult to separate. For example, methyl chloride and ethyl chloride when treated with sodium give three products : propane from the combination of methylchloride and ethylchloride,ethane from the combination of two molecules of methyl chloride, n - butane from two molecules of ethyl chloride.