[evan_au (OP)]

I understand that when you produce a sulphuric acid solution, the H₂SO₄ breaks up into H⁺ ions (lost an electron) and SO₄^2- ions (gained 2 electrons).

How many water molecules does it take to gain or lose an electron?
ie just how concentrated are the ions in concentrated sulphuric acid?

Are there other substances that have more concentrated mobile ions than concentrated sulphuric acid?

[chiralSPO]

"concentrated sulfuric acid" is typically about 96% H₂SO₄ and 4% H₂O (by mass), which works out to just over 18 moles per liter (36 moles of ionizable protons per liter). The first pKa of sulfuric acid is sufficiently low that almost all of that "water" is probably hydronium (H₃O⁺) with HSO₄^– counterions.

As far as your question regarding actual concentration of ions in sulfuric acid, this will depend on how you want to define the ions. No where is solution is there an actual "free" proton--they are all associated to some extent with surrounding water or sulfuric acid or bisulfate species.

We can measure the conductivity (for applied DC voltages) or impedance (for applied AC voltages), but these depend quite strongly on the strength of the applied voltage (and frequency of the AC voltage, in the case of impedance).

We can also calculate or measure the concentration of "available" or "ionizable" protons (essentially a function of the concentration of the acid, and the strength of the acid, and your definition of what counts as "ionizable").

As far as other acids go: phosphoric acid (H₃PO₄ is often sold as 85% with 15% water (again, by mass. you can also get 100% phosphoric acid, but that's a solid at room temp), which ends up having, theoretically, 45.6 moles of available protons per liter. Phosphoric acid is a weaker acid than sulfuric acid though (1st pKa is about 2.1), so I believe the concentration of mobile ions is significantly less.

You can also go the other way--so called "super acids" (http://en.wikipedia.org/wiki/Superacid) like CF₃SO₃H HPF₆ (pka = ), and H₂SbF₇ are much more ionizeable, and can dissociate much more readily, even in anhydrous organic solvents. "Magic acid" (FSO₃H–SbF₅)is so strong it can protonate methane!