Derive the relation between density $(d)$ and molar mass $(M)$ for an ideal gas.

(N/A) According to the ideal gas equation,$pV = nRT$.
$\therefore \frac{p}{RT} = \frac{n}{V}$ (Eq.-$i$).
We know that the number of moles $(n) = \frac{\text{mass }(m)}{\text{molar mass }(M)}$ (Eq.-$ii$).
Substituting the value of $n$ from (Eq.-$ii$) into (Eq.-$i$):
$\frac{p}{RT} = \left(\frac{m}{V}\right) \frac{1}{M}$.
Since density $(d) = \frac{\text{mass }(m)}{\text{volume }(V)}$,we can substitute $d$ into the equation:
$\frac{p}{RT} = \frac{d}{M}$.
Rearranging the equation to solve for $d$ or $M$:
$d = \frac{pM}{RT}$ or $M = \frac{dRT}{p}$.
This shows that the molar mass $(M)$ is directly proportional to the density $(d)$ of the gas at constant pressure and temperature.