Is it possible for a conductor to run out of free electrons? For example, imagine I apply a high voltage to a piece of conductor (copper) and make the electrons jump out of it like a automotive spark plug. Can the copper after a prolonged period of time run out of free electrons and stop generating sparks?
 A: Once an electron is removed from a body, the remainder is positively charged and attracts all the electrons around it. It only takes a tiny fraction of all free electrons in copper to be removed for the electric field generated by the now-charged conductor to overcome any electric field created by the "high voltage" you describe, thus preventing further removal of the electrons.
A: Copper contains $6\cdot 10^{23}$ free electrons per mole, that is $10^5$ Coulomb. One mole of Cu is about 8 $cm^3$ so a copper sphere of radius about 1.2 cm. The potential of such a sphere with a $10^5$ C charge would be +$10^{17}$ V, a number that does not make sense experimentally. The sphere would disintegrate long before you reach that value. So no, it is impossible to run out of conduction electrons.
A: I am not sure, but it seems that free electrons can be smallest possible anions in solutions (solvated electrons), so I guess one can eventually run out of such free electrons as a result of electrolysis (for example, as the quantity of an alkali metal dissolved in ammonia reduces to zero after current in the electrolyte has been sustained for a long time). 
