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

Options

A. `(Pm)/(KT)`
B. `(KT)/(Pm)`
C. `(Km)/(PT)`
D. `(PK)/(Tm)`

Answer

A

Explanation

For an ideal gas, PV = nRT
`thereforePV=(m')/MRT`
where m' = Mass of the gas, M = Molecular weight
`thereforeP=(m')/V(RT)/M`
`thereforeP=(rhoRT)/M[rho=(m')/v="Density of the gas"]`
`thereforerho=(PM)/(RT)=(PM)/(NKT)` as R = NK
where N = Avogadro's number and K = Boltzman constant
`thereforerho=(Pm)/(KT)`
where `M/N` = m = Mass of each molecule `" "`...Option(a)