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In this compound, we know that [CoF6] is 3- itself since the K has a +1 charge. This is similar to a compound like AlCl3 where the +3 charge on the aluminum crosses over to become a subscript of the chlorine and the -1 charge of the chlorine crosses and becomes a subscript of the Aluminum. So, the [CoF6] has a total charge of 3-, and we know that fluorine's charge is -1 since the oxidation number of halogens is usually -1. There are 6 fluorines which gives us a 6- charge, but the total charge of the anion ([CoF6]3-) is 3-. So, to bring the charge up to 3-, Co must have a 3+ charge to balance with the 6- charge from the fluorine. Hope that was helpful.
Since K3[CoF6] does not indicate a charge, we know that the metal must cancel out any of the charges that the other elements have in order to give us a total charge of zero. In this example the total charge, excluding the metal Co, is +3 (for K) -6 (for F). These add up to a -3 charge. Since the whole compound has no charge that means that Co must have a +3 charge in order to cancel out the -3 charge from K and F.
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