#### 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?

#### Solution 1

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

`d = "Mp"/"RT"`

Now, density of oxide (*d*_{1}) is given by,

`d_1 = (M_1p_1)/"RT"`

Where, *M*_{1} and *p*_{1} are the mass and pressure of the oxide respectively.

Density of dinitrogen gas (*d*_{2}) is given by,

`d_2 = (M_2p_2)/"RT"`

Where, *M*_{2} and *p*_{2} are the mass and pressure of the oxide respectively.

According to the given question,

`d_1 = d_2`

`:. M_1p_1 = M_2p_2`

Given

`p_1 = "2bar'`

`p_2 = "5 bar"`

Molecular mass of nitrogen, *M*_{2} = 28 g/mol

Now `M_1 = (M_2p_2)/p_1`

= (28xx5)/2`

= 70 g/mol

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

#### Solution 2

Using the expression, d =MP/RT , at the same temperature and for same density,

M_{1}P_{1} = M_{2}P_{2} (as R is constant)

(Gaseous oxide) (N_{2})

or

M_{1} x 2 = 28 x 5(Molecular mass of N_{2} = 28 u)

or M_{1} = 70u