Final answer:
The subject of the question is Chemistry at the High School grade level. The problem can be solved using Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume when temperature is kept constant. The new volume is found to be 6.40 liters after the pressure change.
Step-by-step explanation:
The question concerns a gas sample at room temperature that initially occupies a volume of 32.0 L at a pressure of 782 torr and is compressed to a pressure of 3910 torr. To solve for the new volume when the pressure changes, we can use Boyle's Law, which states that for a fixed amount of gas at constant temperature, the pressure and volume of the gas are inversely proportional (P1V1 = P2V2).
Using the formula:
V2 = (P1 * V1) / P2
Plugging in the values:
V2 = (782 torr * 32.0 L) / 3910 torr
V2 = 25,024 torr*L / 3910 torr
V2 = 6.40 L
The new volume of the gas when the pressure increases to 3910 torr will be 6.40 L assuming temperature remains constant.