If an ideal gas is allowed to expand into a vacuum, this means that the external pressure is 0. This doesn't affect the internal pressure though, correct?

For example:
I have a problem in which one mole of an ideal gas at 300. K and at a volume of 10.0 L expands isothermally into a vacuum, which doubles its volume. If I plugged these values into an equation, I would have:
0.00 atm x 10.0 L= 1.00 x .08206 x 300. L
Which doesn't work. So the pressure used in this equation is not 0, correct?

well the volume doubles, so it's now 20L. Since the problem provided you with everything but the correct pressure, you would be able to calculate the pressure by using PV=nRT. I calculated 1.24 atm or 936 torr.

you might want to double check me though. It's been a while since I've done ideal gases. :)