Question

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

Options

• `"pm"/"KT"`

• `"KT"/"pm"`

• `"Km"/"pT"`

• `"pK"/"Tm"`

Answer 1

An ideal gas has pressure 'p' volume 'V' and absolute temperature 'T'. If 'm' is the mass of each molecules and 'K' is the Boltzmann constant, then density of the gas is `underlinebb("pm"/"KT")`.

Explanation:

Ideal gas equation, pV = nRT

pV = `"m'"/"M"`RT here, m' is the mass of the gas and M molecular weight p = `"m'"/"V""RT"/"M"`

∴ p = `(rho"RT")/"M"`

∴ ρ = `"m'"/"V"` density of the gas

N is Avogadro, number

ρ = `"pm"/"KT"`, where m = `"M"/"N"` mass of each molecule.