Final answer:
For the free expansion of 5 moles of an ideal gas into a vacuum resulting in a doubled volume, the work done is zero because there is no external pressure to work against.
Step-by-step explanation:
Expansion of an Ideal Gas into Vacuum
When 5 moles of an ideal gas at 1 bar and 298 Kelvin is expanded into a vacuum to double its volume, the work done by the gas is zero. This is because in a vacuum, there is no external pressure to do work against as the gas expands. This type of expansion is known as a free expansion and is an example of an irreversible process where no external work is performed, despite the change in volume.
In thermodynamic processes like isothermal expansion under conditions where external pressure is present, calculations for work done can be more complex, involving integrals of pressure with respect to volume. However, in the case of free expansion, the absence of external pressure simplifies the situation significantly.