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A ideal gas has pressure 'p', volume 'V...

A ideal gas has pressure 'p', volume 'V' and absolute temperature 'T'. It 'm' is the mass of each molecules and 'K' is the Boltzmann constant , the density of the gas is

A

`(Pm)/(KT)`

B

`(KT)/(Pm)`

C

`(Km)/(PT)`

D

`(PK)/(Tk)`

Text Solution

Verified by Experts

The correct Answer is:
A
For ideal gas PV=nRT
`PV=(m')/(M)RT=(m')/(V).(RT)/(M)` (where m' is the mass of the gas of M molecular weight)
`therefore P=(rhoRT)/(M) ("where " rho " is the density of the gas")`
`therefore rho=(PM)/(RT)=(PM)/(NKT)("where N is Avogadro number")`
`therefore rho=(Pm)/(KT) ("where "m=(M)/(N)="mass of each molecule")`
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