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The order of increasing oxidation number of nitrogen is: -3 < -2 < -1 < 0 < +1 < +2 < +3 < +4 < +5.
In N2O3, the oxidation state of nitrogen is +3 because oxygen is usually assigned an oxidation state of -2, and there are three oxygen atoms in N2O3. The sum of the oxidation states in a neutral compound should be zero, so the oxidation state of nitrogen must be +3 in order to balance the -6 from the three oxygen atoms.
The number of protons, which determines the element's identity, must remain constant for an atom to remain that element. In the case of a nitrogen atom, it must always have 7 protons to be considered nitrogen.
The oxidation number of phosphorus in PL3 is -3. Each hydrogen has an oxidation number of +1, so in order for the overall charge of the compound to be neutral, phosphorus must have an oxidation number of -3.
The oxidation number of aluminum (Al) in Al2S3 is +3, while the oxidation number of sulfur (S) is -2. Each aluminum atom has an oxidation number of +3, and each sulfur atom has an oxidation number of -2 in order to balance the charge in the compound.
The oxidation number of B in H3BO3 is +3. Each hydrogen atom has an oxidation number of +1, and the overall molecule has a neutral charge. Since oxygen has an oxidation number of -2, the oxidation number of B must be +3 in order to balance the charges.