# The Formula for Boyle's Law

## The volume of a mass of gas is inversely proportional to its pressure

Boyle's law is a special case of the ideal gas law. This law applies only to ideal gases held at a constant temperature, allowing only the volume and pressure to change.

## Boyle's Law Formula

Boyle's law is expressed as:
PiVi = PfVf
where
Pi = initial pressure
Vi = initial volume
Pf = final pressure
Vf = final volume

Because the temperature and the amount of gas don't change, these terms don't appear in the equation.

What Boyle's law means is that the volume of a mass of gas is inversely proportional to its pressure. This linear relationship between pressure and volume means doubling the volume of a given mass of gas decreases its pressure by half.

It is important to remember the units for initial and final conditions are the same. Do not start with pounds and cubic inches for initial pressure and volume units and expect to find pascals and liters without converting the units first.

There are two other common ways to express the formula for Boyle's law.

According to this law, at a constant temperature, the product of pressure and volume is a constant:

PV = c

or

P ∝ 1/V

## Boyle's Law Example Problem

A 1 L volume of a gas is at a pressure of 20 atm. A valve allows the gas to flow into a 12 L container, connecting the two containers. What is the final pressure of this gas?

A good place to start this problem is to write out the formula for Boyle's law and identify which variables you know and which remain to be found.

The formula is:

P1V1 = P2V2

You know:

Initial pressure P1 = 20 atm
Initial volume V1 = 1 L
final volume V2 = 1 L + 12 L = 13 L
final pressure P2 = variable to find

P1V1 = P2V2

Dividing both sides of the equation by V2 gives you:

P1V1 / V2 = P2

Filling in the numbers:

(20 atm)(1 L)/(13 L) = final pressure

final pressure = 1.54 atm (not the correct number of significant figures, just so you know)

If you're still confused, you may wish to review another worked Boyle's Law problem.

## Interesting Boyle's Law Facts

• Boyle's law was the first physical law written as an equation that described the dependence of two variables. Before this, one variable was all you got.
• Boyle's law is also known as the Boyle-Mariotte law or Mariotte's law. Anglo-Irish Boyle published his law in 1662, but French physicist Edme Mariotte came up with the same relation independently in 1679.
• Although Boyle's law describes the behavior of an ideal gas, it can be applied to real gases at a normal temperature and low (ordinary) pressure. As temperature and pressure increase, gases start to deviate from any variation of the ideal gas law.

## Boyle's Law and Other Gas Laws

Boyle's law is not the only special case of the ideal gas law. Two other common laws are Charles' law (constant pressure) and Gay-Lussac's law (constant volume).