# How is ideal gas law derived?

##### 1 Answer

Jan 2, 2014

There are several ways to derive the Ideal Gas Law, but the simplest way is to use the three simple gas laws.

AVOGADRO'S LAW states the volume of a gas is directly proportional to the number of moles.

V ∝ n

BOYLE'S LAW states that the volume of a gas is inversely proportional to its pressure.

V ∝ 1/P

CHARLES'S LAW states that the volume of a gas is directly proportional to its Kelvin temperature.

V ∝ T

If we combine these laws, we get

V ∝ nT/P

We covert the proportionality to an equality

V = knT/P

We replace k with the universal gas constant R and get

V = nRT/P

This can be rearranged to give the IDEAL GAS LAW

PV = nRT