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First off, I am currently confused about why neon can even be ionized at all. But since it can be ionized, this is the energy required to give a mole of neon a charge of +8: 207,390,000 joules!! Or ~0.5 GJ! Giving one-fifth of a kilogram of neon the maximum charge would be like the energy from 50 armor-piercing rounds of the ISU-150 assault tank, or approximately one Tour-de-France! Charging up one kilo of neon would be basically either throwing a lightning bolt or melting a tonne of steel.

My question is, what insidious chemical or procedure could rip away all of neon's electrons like that? Or is it just simply impossible to do?

I suspect that it is possible to do (otherwise how would they be able to calculate the energy expenditure), but how is the question.

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Of course you can take all the electrons off an atom - it is then called "fully stripped" in atomic physics. You don't need to do it to an entire mole, mind you. In accelerators one would send energetic neon ions through a background gas or a thin foil, and the interactions will result in various charge states coming out, up to and including fully stripped.

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    $\begingroup$ As an example, the Relativistic Heavy Ion Collider (RHIC) smashes bare gold nuclei ($\ce{Au^{79+}}$) and uranium nuclei (presumably also devoid of electrons, $\ce{U^{92+}}$) into each other during experiments. At least part of the ionizations are performed by electron bombardment. Of course, these species will never be found inside a flask in the lab, as they would immediately tear dozens of electrons out of whatever came into contact with them. $\endgroup$ – Nicolau Saker Neto Jul 18 '15 at 1:22
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First - in chemistry there's technically no such thing as bare multivalent cation, second - as you think, there's no such energetic chemical reaction, third - ionisation energy is physical property (although important for chemistry) and

..."is usually measured in an electric discharge tube in which a fast-moving electron generated by an electric current collides with a gaseous atom of the element, causing it to eject one of its electrons. - Source "Encyclopedia Britannica"

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