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I know that dilute sulfuric acid and very dilute nitric acid don't have any oxidizing tendency while dilute/conc $\ce{HNO3}$ and conc $\ce{H2SO4}$ do.

Why do these more concentrated acids have this property?

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Thanks for all the feedback ;) Now I have found out the answer on the Internet.

For the diluted ( or very diluted, for nitric acid) form of these acids, the anions are quite stable as there are sufficient water molecules that form bonds with them. Moreover, there's the concentration effect-- hydrogen ions are more abundant as they come fro two sources-- water and acid. As a result, hydrogen ions act as an oxidizing agent instead.

For the conc form of these acids, relatively less water molecules are present to form bonds with anions to stabilize them. Moreover, hydrogen ions are not as abundant as the anions. Also, nitrate ions and sulfate ions are stronger oxidizing agents in comparison to hydrogen ions. Thus the conc form of acids exhibits oxidizng properties.

As for why nitric acid have oxiding properties even at diluted form, it is due to the fact that nitrate ions are more unstable than sulfuric ions. Nitrogen has to maintain a positive (+) charge to retain the structure of nitrate. Nitrogen is a fairly electronegative atom and it prefers to gain electrons than to lose one. This makes NO3- unstable. Therefore NO3- is reactive and readily acts as an oxidizing agent. While sulfate ions, while reaching their maximum oxidation state, have a neutral charge.

It may not be the most accurate and perfect answer tho. Feel free to correct me if I have made a mistake. Many thanks!

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Oxyanions have a central atom surrounded by a number of more electronegative O atoms and the central atom is significantly positively charged. They are subject to reduction. There are three main factors first the electronegativity of the central atom the more electronegative the stronger the oxidant, second the more O's the stronger the oxidant and third the stronger the X-O bond strength the weaker the oxidant. Simple examples nitrate is stronger than carbonate, nitrite, and sulfate for each of the reasons. Sulfate and perchlorate are at least kinetically less reactive because their bonds to O have significant double bond character from charge feedback into 3d orbitals. The second factor in their reactions is that these bonds to O must be broken; this requires that an excess of H3O+ be present to form water. At low acid concentrations the anions are not oxidizers at high acid concentrations they are progressively stronger and the kinetics also improve. The statement has been made that electrode potentials do not apply. That is incorrect! Standard potential at all activities = 1 need to be adjusted by actual activities and concentrations according to the Nernst equation. Ignoring activities and just using concentrations will give some idea of what is going on.

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