Final answer:
Using Boyle's Law, which states that pressure and volume of a gas are inversely proportional at constant temperature and amount of gas, the new volume can be determined based on the change in pressure.
Step-by-step explanation:
The question deals with the behavior of a gas when its pressure changes while the temperature and the amount of gas remain constant. To solve this, we use Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume when the temperature and the amount of gas are constant. In mathematical terms, Boyle's Law is given by P1V1 = P2V2, where P1 is the initial pressure, V1 is the initial volume, P2 is the new pressure, and V2 is the new volume.
In the given problem, the gas has an initial volume of 26.7 L at an initial pressure of 762 torr. If the pressure is changed and the temperature and amount of gas remain constant, we need to find the new volume.
Using Boyle's Law, we rearrange the equation to solve for the new volume (V2): V2 = (P1V1) / P2. Without a specific new pressure value (P2) provided, we cannot calculate the exact new volume. However, we can deduce that if the pressure increases, the volume will decrease (since they are inversely proportional), and if the pressure decreases, the volume will increase.
Based on the possible answers given:
- If the pressure were to double (which would be 1524 torr), the volume would halve, resulting in a new volume of 13.35 L (Option a).
- If the pressure stayed the same, the volume would not change, thus remaining at 26.7 L (Option b).
- If the pressure were halved (which would be 381 torr), the volume would double, resulting in a new volume of 53.4 L (Option c).
- If the pressure were quartered (which would be 190.5 torr), the volume would quadruple, resulting in a new volume of 106.8 L (Option d).
Without additional information, we cannot select a single correct option. However, we can conclude that changes in pressure, when all else is constant, will result in an inversely proportional change in volume.