Boyle’s law
At constant temperature, the pressure and volume of a fixed amount of gas are inversely proportional. When one goes up, the other goes down by the same factor.
P1 × V1 = P2 × V2
Squeezing a gas into a smaller space makes its particles hit the walls more often, so the pressure rises. Halve the volume and the pressure doubles.
Worked example: compressing a gas
A gas occupies 4.00 L at 1.00 atm. What is its volume at 2.50 atm, at the same temperature?
P1 × V1 = P2 × V2
1.00 atm × 4.00 L = 2.50 atm × V2
V2 = 4.00 L·atm ÷ 2.50 atm = 1.60 L
Check: the pressure went up, so the volume should go down. It did.
Common mistake
Multiplying where you should divide. Use the check above: if pressure rises, volume must fall. If your answer moved the wrong way, the ratio is upside down.