Final answer:
Linkage isomers of Co(NH₃)₃(H₂O)₂(CN)₃ involve the CN ligands binding through either the carbon or nitrogen atoms. With three CN ligands, there are 23 = 8 different isomers, but only the count of each type of linkage is relevant.
Step-by-step explanation:
The student has asked to draw all linkage isomers of the coordination compound Co(NH₃)₃(H₂O)₂(CN)₃. In linkage isomers, ligands can coordinate to the central metal atom in different ways. The cyano ligand (CN) can bind either through the carbon (forming a cyano linkage) or nitrogen atom (forming an isocyano linkage). Since there are three CN ligands in the compound, and each can bind in one of two ways, there are a total of 23 = 8 different linkage isomers for this compound. However, since there is no chemical difference between the cyano ligands, only the number of cyano versus isocyano linkages needs to be considered.