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What is the oxidation state of chlorine in ClO2?

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To complete this you have to keep in mind that, oxygen has an oxidation number of -2 unless in molecules with a polyatomic ions. In addition, when the sum of oxidation compounds is zero is a neutral compound. For ClO2 the oxidation number of oxygen is -2 then the oxydation number of the two atoms is -4. Therefore the oxidation number of Cl is +4. So we add them, 4+(-2)+(-2)=0 therefore it is a neutral compound.