Final answer:
Using Boyle's Law, the final volume of the gas when the pressure is increased from 300 mm Hg to 500 mm Hg is calculated to be 180 mL, as the pressure and volume of a gas are inversely proportional under constant temperature and amount of gas.
Step-by-step explanation:
A gas has a volume of 300 mL at 300 mm Hg. To find the volume of the gas when the pressure is changed to 500 mm Hg, we can use Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume when the temperature and amount of gas remain constant. The relationship is defined by the equation P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume, respectively.
First, identify the initial and final pressures and the initial volume: P1 = 300 mm Hg, V1 = 300 mL, and P2 = 500 mm Hg. Then, solve for the final volume (V2) by rearranging the equation to V2 = P1V1/P2.
Inserting the known values: V2 = (300 mm Hg × 300 mL) / 500 mm Hg. Performing the calculation gives V2 = 90,000 mmHg·mL / 500 mm Hg = 180 mL.
Hence, the final volume of the gas when the pressure is increased to 500 mm Hg is 180 mL.