Step 1: Analyzing the Complexes.
We are given a problem asking for the correct complex. The problem revolves around coordination chemistry and the proper complex formed with the given ligands.
Step 2: Breaking down the Options.
- (A) \([Co(NH_3)_6]^{3+}\) indicates a coordination complex with ammonia as the ligand, which does not match the problem context.
- (B) \([Co(NH_3)_6](H_2O)^{3+}\) includes both ammonia and water ligands, which is not the desired formation here.
- (C) \([Co(CN)_6]^{3-}\) correctly represents a cobalt complex with cyanide as the ligand and a 3- charge, matching the problem’s description.
- (D) \([CoCl(NH_3)_6]^{2+}\) is incorrect as it involves chloride, which is not consistent with the problem's setup.
Step 3: Conclusion.
The correct answer is (C) \([Co(CN)_6]^{3-\)} as it fits the coordination complex formed with cyanide ions.