The ratio of the initial to the final pressure of a given mass of gas is 1:1.5. Calculate the final volume of the gas if the initial volume was 3000cm3 3 at...

The ratio of the initial to the final pressure of a given mass of gas is 1:1.5. Calculate the final volume of the gas if the initial volume was 3000cm${}^3$ at the same temperature

Answer Details

The problem involves using Boyle's law, which states that the pressure of a gas is inversely proportional to its volume at a constant temperature. Mathematically, P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, respectively, and P2 and V2 are the final pressure and volume, respectively. Given the ratio of the initial to final pressure as 1:1.5, we can assume that the final pressure is 1.5 times the initial pressure. Therefore, P2 = 1.5 * P1. Using the formula P1V1 = P2V2 and substituting the known values, we get: P1 * 3000 = (1.5 * P1) * V2 Simplifying the equation, we get: V2 = (P1 * V1) / (1.5 * P1) = 2000cm3 Therefore, the final volume of the gas is 2000cm3. So the answer is 200cm3.