Answer:
I use MLX theory to figure out the formal oxidation state of anything. You are even in the fortunate position of knowing that NO2 is an X type ligand.
Step-by-step explanation:
Just break all the metal ligand bonds, see what you have left and add up all the charges. So:
Pt-H20 becomes Pt and H2O. Clearly H2O is neutral. It is an L type ligand so does not contribute to oxidation state.
Pt-Cl becomes Pt and Cl. Clearly Cl by itself would need to be Cl-. To balance that means that for this bond we have Pt+.
Pt-(en) becomes Pt and H2NCH2CH2NH2. The diamine is clearly neutral so this does not contribute to the oxidation state. Here we essentially have two L type ligands in one.
Finally
Pt-NO2 becomes Pt and NO2. Assuming that you have three bonds to the central nitrogen atom that means you have O=N-O <-> O-N=O. I’m sure you can see that this ligand must have a negative charge. It is NO2 (-) and therefore is an X type ligand, this bond must be Pt+ and so contributes 1 to the oxidation state.
We add them together and and we have Pt(0)+Pt(+)+Pt(0)+Pt(+) which is Pt2+. Finally add up the extra charges, in this case we have a 2+ charge so the Pt oxidation state is Pt(IV).
Now apply that to [NO2]-. Break each N-O bond and you have N + O which means N is +4 (combined totals) and the O’s are -4. Add the negative charge to +4 and we get +4–1 so the oxidation state of N is 3+.
So you need to be careful here. The oxidation state of the N in NO2 is 3+ not 1- in the way that you have written it. This is an important distinction. What your question should say is “Why does the NO2 ligand contribute 1- to the oxidation state of Pt in compound X”. It is because NO2- has a single negative charge. It shares this electron with Pt, who in turn has to give up an electron so the oxidation state is affected. It is exactly the same as the same question, just about the Cl ligand instead.
This is not the case for H2O and (en). These are neutral ligands who bond in a dative fashion so Pt doesn’t have to formally give up any electrons.
I hope this helps! Comment if it isn’t clear!