[colarris (OP)]

How fast to the electrons move in a wire when it is connected to a battery and what happns to them when they reach the end?

[RD]

electrons move at a snail's pace ...

.... in this wire [copper 1mm diameter carrying 3amps] the electrons are flowing at the rate of −0.00029 m/s, or very nearly −1.0 m/hour.

http://en.wikipedia.org/wiki/Drift_velocity#Numerical_example

[chris]

1 metre per hour sounds pretty slow; but for something on the scale of an electron, that's pretty impressive isn't it?

[damocles]

and when they reach the end, they initiate an electrode half-reaction which matches up with the electrode half-reaction that produced the electrons in the first place.

For example, with a copper/zinc cell the electrons are produced by a chemical reaction that oxidizes the solid zinc electrode (anode)

Zn -> Zn(2+) + 2 e(-)

whereupon the electrons move along the wire until they reach the other electrode, where the reaction is

Cu(2+) + 2 e(-) -> Cu, and extra copper gets deposited on the copper electrode. (cathode)

[colarris (OP)]

electrons move at a snail's pace ...

.... in this wire [copper 1mm diameter carrying 3amps] the electrons are flowing at the rate of −0.00029 m/s, or very nearly −1.0 m/hour.

http://en.wikipedia.org/wiki/Drift_velocity#Numerical_example

Oh wow!! So there is a chance that all the electrons from the power source may never even make it through the wire or circuit during the life of the power source??

[Bored chemist]

Well, sort of.
The calculated drift velocity is how fast them move due to the current.
But there's also their random movement.
If my maths is right then, to a rough approximation, that's the speed of sound multiplied by the square root of the ratio of the mass of an air molecule to the mass of an electron.
That's about 75 Km/sec

[damocles]

There is also the fact that there is no need for any particular electron to "make it through". The whole situation can be likened to a production line where free electrons are being created at one end and removed at the other. There are plenty of free electrons in the wire so that when the current is started electron production and removal and drift all start at (roughly) the same time, and when the circuit is interrupted all three processes stop at roughly the same time -- if there is an interruption anywhere along the line the whole process jams up.

(Actually I have just spotted a defect in my analogy -- if a production line is interrupted there is the possibility of production continuing downstream of the interruption. I will just say that this is not that sort of production line, and that no analogy is perfect)

[AndroidNeox]

electrons move at a snail's pace ...

.... in this wire [copper 1mm diameter carrying 3amps] the electrons are flowing at the rate of −0.00029 m/s, or very nearly −1.0 m/hour.

http://en.wikipedia.org/wiki/Drift_velocity#Numerical_example

colarris, interesting question! RD, thanks for the info... that's very cool to know.