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Is nitration of benzene possible without using the mixture of concentrated nitric and sulfuric acids $(\ce{HNO3}$ and $\ce{H2SO4})$?

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It's getting on for 3 decades since since I've done organic, so a proper organic chemist can probably give a more complete answer, but yes, there are other ways to do this. In the $\ce{HNO3}$/$\ce{H2SO4}$ system the "real" nitrating agent is nitronium, $\ce{NO2+}$, so anything that can form that will nitrate benzene. One example is simply to use a nitronium salt such as nitronium tetrafluoroborate, $\ce{NO2+ BF4-}$. As for others I would be surprised to find that something like $\ce{NO2F}$/$\ce{BF3}$ doesn't work, but I don't know for certain - it's been a looooong time!

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    $\begingroup$ Acetyl nitrate, AcONO2, is also used - the reagent is pre-formed by reaction of nitric acid and acetic anhydride $\endgroup$ Apr 9, 2016 at 15:16
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For some substrates, nitric acid plus nitrous acid works. In this system the generated electrophil is not $\ce{NO2^+}$, but $\ce{NO^+}$ formed from the nitrous acid accepting protons from the stronger nitric acid. If the substrate is sufficiently reactive, as with the parent benzenoid compound benzene, then it can be attacked by the $\ce{NO^+}$. Then the nitroso group is oxidized by the nitric acid (regenerating the nitrous acid, which is thus acting as a catalyst).

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