1)

An ideal gas has pressure 'p'  , volume 'V'  and absolute temperature 'T' .If 'm' is the mass of each molecule  and 'K'  is the Boltzmann constant, then the density of the gas is 


A) $\frac{pm}{MT}$

B) $\frac{KT}{pm}$

C) $\frac{Km}{pT}$

D) $\frac{pK}{Tm}$

Answer:

Option A

Explanation:

For  ideal gas, pV=nRT

 pV= $\frac{m'}{M} RT$ (where, m' is the mass of the gas and M molecular weight)

$p=\frac{m'T}{V}\frac{RT}{M}$

$\therefore$   $p=\frac{\rho RT}{M}$

 where, $\rho$  =$\frac{m'}{V}$ = density of the gas

$\Rightarrow$    $  \rho=\frac{ pM}{RT}=\frac{pM}{NkT}$, where N is Avogadro number

$\Rightarrow$    $  \rho=\frac{ pm}{KT}, $  where    $ m=\frac{M}{N}$= mass of each molecule.