Answer:The metal complex formed would have the following formula [Cr(NO₂)₆]³⁻. The complex has a net negative charge and hence it can only be isolated as a salt with a positive cation so the formed complex could be isolated as potassium salt. The formula for salt would be K₃[Cr(NO₂)₆].
Step-by-step explanation:
The metal ion given to us is Cr³⁺ (Chromium) in +3 oxidation state.
The electronic configuration for the metal ion is [Ar]3d³ so there are vacant 3d metal orbitals which are available and hence 6 NO₂⁻ ligands can easily attack the metal center and form a metal complex.
The charge on the overall complex can be calculated using the oxidation states of metal and ligand which is provided.
The (chromium ) Cr³⁺ metal has +3 charge and 6 NO₂⁻ (nitro) ligands have -6 charge and since the ligands will be providing a total of 6 - (negative) charge and hence only 3- (negative ) charge can be neutralized so a net 3- negative charge would be present on the overall complex which is basically present at the metal center :
charge on the complex=+3-6=-3
Let X be the Oxidation state of Cr in complex =[Cr(NO₂)₆]³⁻
X-6=-3
X=-3+6
X=+3
so our calculated oxidation state of Cr is +3 which matches with the provided in question.
As we can see that the overall metal complex has a net negative charge and hence and only positively charged cations can form a salt with this metal complex and hence only potassium K⁺ ions can form salt with the metal complex.
since overall charge present on the metal complex is -3 so 3 K⁺ ion would be needed to neutralize it and hence the formula of the metal salt would be K₃[Cr(NO₂)₆].