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?
To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature. Mathematically, this can be represented as:
P1 * V1 = P2 * V2
where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Given:
Initial volume (V1) = 10.0 L
Initial pressure (P1) = 105 kPa
Final volume (V2) = 13.4 L
Let's plug in the values into the equation and solve for P2:
P1 * V1 = P2 * V2
105 kPa * 10.0 L = P2 * 13.4 L
Now we can solve for P2:
P2 = (105 kPa * 10.0 L) / 13.4 L
P2 = 787.31 kPa
Therefore, the final pressure (P2) will be approximately 787.31 kPa if the temperature does not change.
To find the pressure at which the sample of oxygen will occupy 13.4 L, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature.
Boyle's Law equation: P1 * V1 = P2 * V2
Where:
P1 = initial pressure (105 kPa)
V1 = initial volume (10.0 L)
P2 = final pressure (unknown)
V2 = final volume (13.4 L)
To solve for P2, we can rearrange the equation:
P2 = (P1 * V1) / V2
Substituting the given values into the equation:
P2 = (105 kPa * 10.0 L) / (13.4 L)
P2 = 78.36 kPa
Therefore, the pressure at which the sample of oxygen will occupy 13.4 L is approximately 78.36 kPa.