Question

An ideal gas occupies a volume 'V' at a pressure 'P' and absolute temperature T. The mass of each molecule is 'm'. If 'Ks' is the Boltzmann's constant, then the density of gas is given by expression ______.

पर्याय

• `("P"."m")/(2"K"_"B"."T")`

• `("K"_"B"."T")/("P"."m")`

• `("P"."m")/("K"_"B"."T")`

• `(3"K"_"B"."T")/(2"P"."m")`

Answer 1

An ideal gas occupies a volume 'V' at a pressure 'P' and absolute temperature T. The mass of each molecule is 'm'. If 'K_B' is the Boltzmann's constant, then the density of gas is given by expression `("P"."m")/("K"_"B"."T")`.

Explanation:

For one mole of an ideal gas 

`"PV" = "N"  "K"_"B" "T"`

where N is Avogadro number

If M is the mass of the gas then the density is given by

`"p" = "M"/"V" or "V" = "M"/"P"`

` therefore "P"."M"/"p"= "NK"_"B" "T"`

` therefore "P" = "PM"/("NK"_"B""T")`

But `"M"/"N" = "m"` = mass of each molecule

`therefore "p" = "Pm"/("K"_"B""T")`