Boyle's Law in a Syringe
A sealed syringe holds 50.0 mL of air at 1.00 atm. The plunger is pushed in (at constant temperature) until the pressure reaches 2.50 atm. What is the new volume of the gas?
Given
Initial pressure: P1 = 1.00 atm
Initial volume: V1 = 50.0 mL
Final pressure: P2 = 2.50 atm
Assumption: temperature and amount of gas are constant
Find
The final volume V2 in mL.
Principle
At constant temperature, the volume of a fixed amount of gas is inversely proportional to its pressure: the product P x V stays constant. Doubling the pressure halves the volume. This is the physical origin of Boyle's law — particles strike the walls more often when confined to a smaller space.
Formula
Solution
Write Boyle's law: P1 x V1 = P2 x V2.
Solve for V2: V2 = (P1 x V1) / P2.
Substitute: V2 = (1.00 atm x 50.0 mL) / 2.50 atm = 50.0 / 2.50 mL = 20.0 mL.
Sanity check: pressure went up, so volume must go down. 20.0 mL < 50.0 mL, consistent with the inverse relationship.
Unit check
Atmospheres cancel (atm/atm) and only mL remains, so V2 carries the correct volume unit. The result is also in the same unit as V1, which a proportion problem requires.
What this means physically
Squeezing the gas to 2.5 times the pressure compresses it to exactly 2/5 of its volume — the inverse relationship Boyle found in the 1660s, still visible every time a syringe plunger is pushed.
Students solve for V2 as P2/P1 x V1 (multiplying instead of dividing) or forget that pressure and volume move in opposite directions. A pressure increase must shrink the volume — if the answer is bigger than V1, something is backwards.