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Benzene rings are broken during ozonolysis, and alkenes treated with hot $\ce{KMnO4}$ undergo oxidative ozonolysis.

So does that mean that the double bonds of benzene also are broken by hot $\ce{KMnO_4}$ ?

If this is the case then why doesn't benzene (pictured here) also break?

enter image description here

Can I make the conclusion that benzene rings are broken during ozonolysis but not by hot $\ce{KMnO_4}$ ?

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As you are seeing in the pictured reaction, hot potassium permanganate does not break the benzene ring itself. It just reacts with the alkyl groups, oxidizing them to give the carboxylic acid functions shown.

Note carefully: an ordinary double bond can also be oxidized with potassium permanganate, but that does not work with benzene because you do not really have double bonds. Instead benzene rings have a special, delocalized bonding that confers extra stability (which shows up as resisting the potassium permanganate). You will learn more when you study aromaticity.

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