Boyle's Law
Pressure and volume are inversely related at constant temperature.
Formula
Variables
Example
Compress 4 L of gas at 1 atm to 2 L and the pressure rises to 2 atm.
How it works
Boyle's Law describes how a gas responds when temperature is held constant: if the space available for the gas gets smaller, the gas particles hit the container walls more often, so pressure increases. Because the amount of gas and temperature stay the same, pressure and volume change in opposite directions, giving a constant product of P and V. This relationship is a good model for many gas-compression situations as long as the gas behaves approximately ideally.
When to use it
Use this formula for problems involving a fixed amount of gas that is compressed or expanded without changing temperature, such as syringes, pistons, scuba equipment, or sealed gas containers. It is especially useful when one pressure or volume is unknown and the other conditions are unchanged.
Worked example, step by step
A gas occupies 6.0 L at a pressure of 1.5 atm. It is compressed to 3.0 L at constant temperature. What is the new pressure? Step 1: Write Boyle's Law: P1V1 = P2V2 Step 2: Substitute the known values: (1.5 atm)(6.0 L) = P2(3.0 L) Step 3: Calculate the left side: 9.0 atm·L = 3.0 L × P2 Step 4: Solve for P2: P2 = 9.0 ÷ 3.0 = 3.0 atm Final answer: The new pressure is 3.0 atm.
Common mistakes to avoid
- using temperatures in the calculation when temperature is supposed to stay constant
- forgetting that volume and pressure must be in matching units on both sides of the equation
- rearranging the formula incorrectly and dividing by the wrong volume or pressure
Did You Know?
Boyle's law explains why a diver's lungs must never hold breath while ascending — the gas expands.
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