The reaction pathway for the conversion of ethane (C2H6) to butane (C4H10) can be achieved through the following steps:

Dehydrogenation of ethane (C2H6) to ethylene (C2H4) - This step involves the removal of hydrogen atoms from ethane to form ethylene, which is a key intermediate in the process.

C2H6 -> C2H4 + H2

Chlorination of ethylene (C2H4) to ethyl chloride (C2H5Cl) - Ethylene can react with chlorine to form ethyl chloride, an alkyl chloride compound.

C2H4 + Cl2 -> C2H5Cl

Hydrogenation of ethyl chloride (C2H5Cl) to butane (C4H10) - Ethyl chloride can be hydrogenated to form butane.

C2H5Cl + H2 -> C4H10

Through these steps, ethane can be converted to butane via ethylene and ethyl chloride intermediates.