Using Boyle's Law, we understand that pressure and volume are inversely proportional for a given mass of gas at a constant temperature. However, in this question with 8 strokes of a vacuum pump removing more gas than the container's volume, the pressure would theoretically fall to near zero, indicating nearly a vacuum.
The problem involves applying the Boyle's Law, which states that for a given mass of an ideal gas at constant temperature, the product of pressure and volume is constant. In this scenario, if a vacuum pump with a capacity of 500cm³ is used to exhaust a container of 1000cm³, which originally has a pressure of 108kNm², we assume that each stroke of the pump removes the gas effectively and reduces the volume of gas in the container by 500cm³. After 8 strokes, the volume of gas removed will be 4000cm³, which exceeds the original volume.
Realistically, the container would be empty before 8 strokes, but theoretically, and for the sake of calculation, if the full amount could be removed, the final pressure would approach zero (neglecting the volume of remaining gas molecules).
For an actual calculation, the volume of the container remains constant, and with each stroke, some of the gas is removed, decreasing the pressure proportionally. However, since the full capacity of the pump has exhausted more volume than that of the container within 8 strokes, the final result would ultimately tend toward a vacuum, meaning that the pressure would be as low as the pump can achieve, assuming perfect efficiency and no leaks.