The relation between gram molecular mass and gram molecular volume is established by Avogadro's law. Explain?

Avogadro's law: Equal volumes of all gases under similar conditions of temperature and pressure contain equal number of molecules.

22.4 L of any gas at STP weighs equal to its molecular mass expressed in grams. This mass is called as Gram molecular mass and the volume is called as Gram molecular volume.

$Molecularmass=2\times Vapourdensity$

As $Vapourdensity=\frac{MassofcertainamountofgasatSTP}{Massofsamevolumeof{H}_{2}atSTP}$

Therefore, $Molecularmass=2\times \frac{MassofcertainamountofgasatSTP}{Massofsamevolumeof{H}_{2}atSTP}$

$Molecularmass=2\times \frac{Massof1LofthegasatSTP}{Massof1Lof{H}_{2}atSTP}$

$Molecularmass=2\times \frac{Massof1LofgasatSTP}{0.089g}$

By rearranging,

$$\begin{gathered} Molecularmass=\frac{2}{0.089}\times Massof1LofgasatSTP \\ Molecularmass=22.4\times Massof1LofgasatSTP \\ Molecularmass=Massof22.4LofthegasatSTP \end{gathered}$$

Hence,

STP= Standard temperature and pressure (T=0 °C and P=1 atm. If P=1 bar, then at STP volume is 22.7 L as 1atm= 1.01 bar)