Question

At 0°C, the density of a certain oxide of a gas at 2 bar is same as that of dinitrogen at 5 bar. What is the molecular mass of the oxide?

Answer 1

Density (d) of the substance at temperature (T) can be given by the expression,

`d = "Mp"/"RT"`

Now, density of oxide (d₁) is given by,

`"d"_1 = ("M"_1"p"_1)/"RT"`

Where, M₁ and p₁ are the mass and pressure of the oxide respectively.

Density of dinitrogen gas (d₂) is given by,

`"d"_2 = ("M"_2"p"_2)/"RT"`

Where, M₂ and p₂ are the mass and pressure of the oxide respectively.

According to the given question,

`"d"_1 = "d"_2`

`therefore "M"_1"p"_1 = "M"_2"p"_2`

Given

`"p"_1 =  "2 bar"`

`"p"_2 = "5 bar"`

Molecular mass of nitrogen, M₂ = 28 g/mol

Now `"M"_1 = ("M"_2"p"_2)/"p"_1`

= (28xx5)/2`

= 70 g/mol

Hence, the molecular mass of the oxide is 70 g/mol.