A sample of oxygen occupies 10.0 L under a pressure of 105 kPa. At what
pressure will it occupy 13.4 L if the temperature does not change?
P1V1 = P2V2
To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at a constant temperature. According to Boyle's Law, the product of the initial pressure and initial volume is equal to the product of the final pressure and final volume.
The equation for Boyle's Law can be written as:
P1 * V1 = P2 * V2
where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure, and V2 is the final volume.
Given:
Initial volume (V1) = 10.0 L
Initial pressure (P1) = 105 kPa
Final volume (V2) = 13.4 L
We need to find the final pressure (P2).
Using the equation P1 * V1 = P2 * V2, we can rearrange it to solve for P2:
P2 = (P1 * V1) / V2
Substituting the given values:
P2 = (105 kPa * 10.0 L) / 13.4 L
Calculating:
P2 ≈ 78.36 kPa
Therefore, the pressure at which the oxygen will occupy 13.4 L is approximately 78.36 kPa if the temperature remains constant.