Answer
The perfect gas law can be derived by using Boyle's, Charles's law and
Avagadro's Principle.
Boyle's Law states that at a constant temp, for a perfect gas, the pressure
of a fixed mass of gas varies inversely with the volume of the gas i.e.
$$
p \cdot V=\text { constant } \quad\quad\quad(1)
$$
Charles's Law states that at a constant pressure, for a perfect gas, the
volume of a fixed mass of gas varies directly with the absolute temperature of the gas i.e.
$$
V=\text { constant } \cdot T \quad\quad\quad(2)
$$
Also, Charles's law (Gay-Lussac's Law to be precise) states that at a constant
volume, for a fixed mass of gas the pressure of the gas is directly proportional
to the absolute Temperature of the gas i.e.
$$
p=\text { constant } \cdot T\quad\quad\quad(3)
$$
Avogadro's principle states that equal volumes of gas contain the same
number of molecules at a constant temperature and pressure. i.e.
$$
V=\text { constant } \cdot n \quad\quad\quad(4)
$$
where $\mathrm{n}=$ number of molecules
Hence multiplying equations $(3)$ and $(4)$ we get Perfect Gas Law i.e.
$$
p \cdot V=\text { constant } \cdot n \cdot T \quad\quad\quad(5)
$$
where the constant $\mathrm{n}$ takes the form of "R" which is Universal Gas Constant
Work Step by Step
\begin{equation}
\mathrm{p} \cdot \mathrm{V}=\mathrm{R} \cdot \mathrm{n} \cdot \mathrm{T}
\end{equation}
