Boyle's Law

Relates the pressure and volume of a fixed amount of gas at constant temperature: compressing raises pressure.

P_1 V_1 = P_2 V_2

P1V1 = P2V2

What it means

Boyle's law says that for a fixed amount of gas at fixed temperature, pressure and volume move in opposite directions: squeeze the gas into half the volume and its pressure doubles. Physically, a smaller container means molecules collide with the walls more often, and more collisions per second is exactly what higher pressure is. The product PV stays constant, so knowing any three of the four values pins down the fourth. When to use it: for a single gas sample whose pressure or volume changes while temperature and the amount of gas stay fixed — syringes, piston problems, divers' air tanks.

Variables

Symbol	Name	Unit	Meaning
$P1$	Initial pressure	atm (or Pa, kPa)	Pressure of the gas before the change.
$V1$	Initial volume	L (or m^3)	Volume of the gas before the change.
$P2$	Final pressure	atm (or Pa, kPa)	Pressure of the gas after the change.
$V2$	Final volume	L (or m^3)	Volume of the gas after the change.

Assumptions

The amount of gas (n) does not change during the compression or expansion.
The temperature stays constant, so kinetic energy per molecule is unchanged.
The gas behaves ideally: negligible molecular volume and no intermolecular forces.

Worked example

Problem

A 2.00 L sample of gas at 1.00 atm expands to 5.00 L at constant temperature. What is the new pressure?

Given:

P1 = 1.00 atm, V1 = 2.00 L
V2 = 5.00 L (gas expands), n and T constant

Write Boyle's law: P1V1 = P2V2.
Solve for P2: P2 = P1V1 / V2.
Substitute: P2 = (1.00 atm)(2.00 L) / 5.00 L.
Calculate: 1.00 × 2.00 = 2.00; 2.00 / 5.00 = 0.400 atm.

P2 = 0.400 atm

Expanding the gas to a volume 2.5 times larger cuts the pressure to 1/2.5 of its original value — the classic inverse relationship.