Final answer:
The minimum cation to anion ratio for a coordination number of 3 ensures the balance of total positive and negative charges by transposing and simplifying the charges of the ions to the simplest whole-number ratio.
Step-by-step explanation:
The minimum cation to anion ratio for a coordination number of 3 can be determined by ensuring the total charge of cations equals the total charge of anions. When dealing with a coordination compound, for example, if the cation has a charge of 3+ (Al3+) and the anion has a charge of 1- (Cl-), we would transpose the numbers to get AlCl3. However, when a coordination compound has a coordination number of 3, we generally expect the ligands attached to the central metal cation to be neutrally charged or to carry a charge that, when combined in threefold, balances the charge of the cation.
According to the rules of writing formulas for ionic compounds, we write the cation followed by anion with charges, swap the charge as a subscript of the opposite ion, and simplify the subscript to the simplest whole-number ratio. Applying these rules, the ratio must be such that the total charges balance out. For instance, if we had a cation with a charge of 3+ (such as Al3+) and an anion with a charge of 1- (such as Cl-), the resulting formula reflecting the minimum ratio for coordination number 3 would be AlCl3, which also represents the simplest whole-number ratio of the ions.