Derive Ideal gas equation.

The ideal gas equation is obtained by combining Boyle’s law. Charles’ law and Avogadro’s law.
If V is the volume, P is the pressure, T is the absolute temperature and ‘n’ the number of moles of the ideal gas,
$\mathrm{V}\mathrm{\infty }\frac{1}{\mathrm{P}}$(T, n are constant) Boyle’s law
$\mathrm{V}\infty \mathrm{T}$(P, n are constant) Gay-Lussac’s law (or Charles’ law)
$\mathrm{V}\mathrm{\infty }\mathrm{n}$ (P,T are constant) Avogadro’s law
From the above equations,
$\mathrm{V}\mathrm{\infty }\frac{\mathrm{nT}}{\mathrm{P}}\Rightarrow \mathrm{V}=\mathrm{R}\frac{\mathrm{nT}}{\mathrm{P}}\text{ or }\mathrm{PV}=\mathrm{nRT}\text{ or }\frac{\mathrm{PV}}{\mathrm{nT}}=\mathrm{R}$
                                                                  (univeral gas const)
This is called ideal gas equation or equation of state.
Where ‘R’ is called gas constant and independent of the amount and nature of gas.
So, it is called as Universal gas constant or Molar gas constant.
R = 0.0821 lit. atm mol^-1K^–1
= 8.314 J/mol-1K^–1