Step 1: Understand the concept of Effective Atomic Number (E.A.N.).
The effective atomic number is calculated as the atomic number of the central metal ion plus the total number of electrons donated by the ligands. For a complex, the E.A.N. is given by:
\[
\text{E.A.N.} = \text{Atomic number of metal} + \text{Total electrons donated by ligands}.
\]
Step 2: Determine the atomic number and ligands.
- The atomic number of cobalt (Co) is 27.
- The ethylenediamine (en) ligand donates 2 electrons per ligand, and there are 2 en ligands, so they donate 4 electrons.
- The chloride (Cl) ion donates 2 electrons, and there are 2 chloride ions, so they donate 4 electrons.
Thus, the total electrons donated by the ligands is 4 (from en) + 4 (from Cl) = 8 electrons.
Step 3: Calculate the E.A.N.
The E.A.N. of cobalt is:
\[
\text{E.A.N.} = 27 + 8 = 36.
\]
Final Answer:
\[
\boxed{36}
\]