Final answer:
Changing PK to 0.2 halves the pressure from its original value, resulting in a final pressure of 0.10 atm due to the volume doubling as per the ideal gas law PV = NkT.
Step-by-step explanation:
If PK is changed to 0.2 in a scenario where the density of a gas is half its original value without any loss of molecules, we should consider the ideal gas law described by the equation PV = NkT. According to this law, at a constant temperature (T), the pressure (P) is inversely proportional to the volume (V). Consequently, if the volume doubles due to the decrease in density, the pressure would have to halve. Therefore, changing PK to 0.2 would result in the final pressure Pf being 0.10 atm (half of 0.2 atm), since the problem implies a direct relationship between PK and the pressure.