Question

How is ideal gas law derived?

Answer 1

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