Derive the ideal gas equation by combining the empirical gas laws.

Explanation

The ideal gas equation is an equation, which relates all the properties of an ideal gas. An ideal gas obeys Boyle.s law and Charles. law and Avogadro.s law. According to Boyle.s law,
PV = constant `" "...`(1)
According to Charles.s law, V/T = constant `" ".... (2)`
According to Avogadro.s law, Vin=constant `" ".... (3)`

After combining equations (1), (2) and (3), you can get the following equation. PV/nT = constant `" "...(4)`
The above relation is called the combined law of gases. If you consider a gas, which contains `mu` moles of the gas, the number of atoms contained will be equal to `mu` times the Avogadro number `N_(A)`
`i.e, n= muN_(A) " "....(5)`
Using equation (5), equation (4) can be written as
`PV//muN_(A)T=` constant
The value of the constant in the above equation is taken to be ka, which is called as Boltzmann constant `(1.38 xx 10^(-23) JK^(-1))`. Hence, we have the following equation
`PV//mu_(A)T=K_(B)`
`PV=muN_(A)k_(B) T`
Here `muN_(A) k_(B)=R`, which is termed as universal gas constant whose value `8.31 J MOL^(-1) K^(-1)`.
`PV= RT " "...(6)`
Ideal gas equation is also called as equation of state because it gives the relation between the state variables and it is used to describe the state of any gas.