Chlorination of methane proceeds via a free radical chain mechanism. The whole reaction takes place in the given three steps.

Step 1: Initiation:

The reaction begins with the homolytic cleavage of Cl – Cl bond as:

Step 2: Propagation:

In the second step, chlorine free radicals attack methane molecules and break down the C–H bond to generate methyl radicals as:

                                  $C{H}_4+CI\stackrel{h\nu }{\to }C{H}_3+H-CI$ 

                                  Methane

These methyl radicals react with other chlorine-free radicals to form methyl chloride along with the liberation of a chlorine-free radical.

              $C{H}_3+CI-CI\to C{H}_3-CI + Cl·$

                                                     Methyl chloride                   

Hence, methyl free radicals and chlorine-free radicals set up a chain reaction. While HCl and CH3Cl are the major products formed, other higher halogenated compounds are also formed as:

                                          $C{H}_{3}Cl+CI\to ·C{H}_{2}CI+HCI$
$C{H}_{2}CI+CI-CI\to C{H}_{2}C{I}_2+CI·$

Step 3: Termination:
Formation of ethane is a result of the termination of chain reactions taking place as a result of the consumption of reactants as:

    $CI·+CI·\to CI-CI$
$H_{3}C·+·C{H}_3\to H_{3}C-C{H}_3$

                                   (Ethane)

Hence, by this process, ethane is obtained as a by-product of chlorination of methane