the gas contained in a piston is compressed from an original volume of 1.15 L to a new volume of 0.45 L. Assuming that the temperature of the gas remains constant what is the new pressure exerted on the gas if the original pressure was 2.15 atm?
P1V1 = P2V2
5.49atm
To determine the new pressure exerted on the gas, we can use Boyle's Law, which states that the pressure and volume of a given amount of gas are inversely proportional at constant temperature. Boyle's Law is mathematically expressed as:
P1 * V1 = P2 * V2
Where:
P1 = original pressure
V1 = original volume
P2 = new pressure
V2 = new volume
Given:
P1 = 2.15 atm
V1 = 1.15 L
V2 = 0.45 L
Now we can substitute the values into the equation and solve for P2:
P1 * V1 = P2 * V2
2.15 atm * 1.15 L = P2 * 0.45 L
2.4725 atm⋅L = P2 * 0.45 L
Now, divide both sides of the equation by 0.45 L:
2.4725 atm⋅L / 0.45 L = P2
P2 ≈ 5.49 atm
Therefore, the new pressure exerted on the gas is approximately 5.49 atm.