What is the relationship between the mass and volume of a gas?

(N/A) In $1811$,the Italian scientist Amedeo Avogadro combined the conclusions of Dalton's atomic theory and Gay-Lussac's law of combining volumes,which is now known as Avogadro's law.
Avogadro's Law: It states that equal volumes of all gases under the same conditions of temperature and pressure contain an equal number of molecules.
Mathematical Formula: According to Avogadro's law,when temperature and pressure remain constant,the volume $(V)$ is directly proportional to the amount of gas ($n$ in moles).
$V \propto n$ (at constant $T$ and $p$) .....(Eq.-$i$)
where,$n$ is the number of moles of the gas.
$V = k_{4} n$ (Eq.-$ii$)
Since the number of moles $n = \frac{m}{M}$,where $m$ is the mass of the gas and $M$ is the molar mass,we can substitute this into the equation:
$V = k_{4} \left( \frac{m}{M} \right)$ .....(Eq.-$iii$)
Rearranging for molar mass $M$:
$M = k_{4} \left( \frac{m}{V} \right)$ .....(Eq.-$iv$)
Since density $d = \frac{m}{V}$,we get:
$M = k_{4} d$ .....(Eq.-$v$)
Conclusion: The density of a gas is directly proportional to its molecular mass at constant temperature and pressure.