Final answer:
Using Boyle's law, which states that pressure is inversely proportional to volume for a given amount of gas at constant temperature, the original volume of the gas that had its pressure decreased from 1.5 atm to 0.50 atm and produced a new volume of 750 mL would be 250 mL.
Step-by-step explanation:
The question involves the relationship between the pressure and volume of a gas, which is described by Boyle's law. Boyle's law states that at constant temperature, the pressure of a gas is inversely proportional to its volume. This means that if pressure increases, volume decreases proportionally and vice versa, as long as the number of moles and temperature are kept constant. This can be expressed algebraically as P1 × V1 = P2 × V2, where P1 and V1 are the initial pressure and volume of the gas, and P2 and V2 are the final pressure and volume of the gas.
To solve the problem presented:
Initial pressure (P1) = 1.5 atm
Final pressure (P2) = 0.50 atm
Final volume (V2) = 750 mL
Assuming that the amount of gas and the temperature are constant, we can use Boyle's law to find the original volume (V1).
Substituting the known values into the equation:
P1 × V1 = P2 × V2
(1.5 atm) × V1 = (0.50 atm) × (750 mL)
To find V1, we divide both sides by 1.5 atm:
V1 = (0.50 atm × 750 mL) / 1.5 atm
This calculation gives us:
V1 = 250 mL
So, the original volume was 250 mL.