Determining Pressure Using Boyle's Law
Understanding Boyle's Law
P1V1 = P2V2
where P1 and V1 are the initial pressure and volume of the gas, while P2 and V2 are the final pressure and volume of the gas, respectively.
Problem Statement
A gas is placed in a 5.0-mL syringe. It exerts 141 mm Hg of pressure on the inside walls of the syringe. The syringe's plunger is pressed, reducing the volume of the syringe to 2.9 mL. The cap was not removed from the syringe, so none of the gas escapes. Assuming the temperature of the gas does not change, use Boyle's Law to determine the pressure of the compressed gas.Solution
Given:The initial volume of gas V1 = 5 mL
Initial pressure is P1 = 141 mm of Hg
Final volume is V2 = 2.9 mL
As it is given P1V1 = P2V2
Insert the values:
141 x 5 = P2 x 2.9
P2 = 243.10 mm of Hg
Therefore, the pressure of the compressed gas is 243.10 mm of Hg.
What is the relationship described by Boyle's Law?
Boyle's Law describes the inverse relationship between the pressure and volume of a gas at constant temperature.