The physical behaviour of a gas is described using four main variables :

- Temperature
- Pressure
- Volume
- Amount (mol number)

## Boyle’s Law

Boyle’s law was formulated by the famous scientist **Robert Boyle** in 1662. It describes the behaviour of gas concerning the relation between pressure and volume at constant temperature and constant mole number.

After his experiment, Boyle discovers that the pressure and the volume of gases are inversely proportional. So when the volume of a gas decreases the pressure increases. This relation is represented in the following graph.

The syringe can prove Boyle’s law : Imagine that you hold the tip of a syringe on the tip of your finger so no gas can escape. Now push down on the plunger of the syringe.

What happens to the volume in the syringe? The volume decreases

What happens to the pressure the gas is exerting in the syringe? The pressure increases

This relation can be also expressed as the product of pressure and volume is equal to some constant:

P x V = Constant

Let’s consider a gas under two different conditions of pressure and volume. Boyle’s Law leads to the mathematical expression

** P _{1}V_{1}=P_{2}V_{2}**

Where P_{1} represents the initial pressure, V_{1} represents the initial volume, P_{2} represents the final pressure, and V_{2} represents the final volume.

## Practice problem – Boyle’s law

A weather balloon with a volume of 2000L at a pressure of 96.3 kPa rises to an altitude of 1000m, where the atmospheric pressure is measured to be 60.8 kPa. Assuming there is no change in the temperature or the amount of gas, calculate the weather balloon’s final volume.

## Solution

Given : P1= 96.3 KPa V1 = 2000 L P2 = 60.8 kPa V2 ?

Boyle’s law : P1 V1 = P2 V2

V2 = (P1×V1)/P2 = (96.3×2000 )/60.8 = 3167.76 L

Evaluate your answer : When the pressure decreases, the volume of the balloon should increases (Boyle’s law). The obtained answer (V2=3167.76 L) makes sense because it is bigger than V1 so it follows Boyle’s law.