Write the formula for the complex ion formed by the metal ion cr3+ and six no2- ions as ligands. decide whether the complex could be isolated as a chloride salt or a potassium salt, and write the formula for the appropriate salt

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].

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].