The balanced chemical equation for the reactions shown is as follows:

C2H6 + Cl2 -> C2H5Cl + HCl
C2H5Cl + Cl2 -> C2H4 + HCl
C2H4 + Cl2 -> C2H4Cl2

Overall reaction:
C2H6 + 2Cl2 -> C2H4Cl2 + 2HCl