Ncert Exercises & Solutions

5.4 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?

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

$d = \frac{M p}{R T}$

Now, density of oxide ( $d_{1}$ ) is givin by,

$d_{1} = \frac{M_{1} p_{1}}{R T}$

Where,

M_{1} a n d P_{1}

are the mass and pressure of the oxide respectively. Density of dinitrogen gas (

d_{2}

) is givin by,

d_{2} = \frac{M_{2} p_{2}}{R T}

Where,

M_{2} a n d p_{2}

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}

Givine,

p_{1} = 2 b a r

p_{2} = 5

bar

Molecular mass of nitrogen,

M_{2}

= 28/g mol

Now,

M_{1} = \frac{M_{2} p_{2}}{p_{1}}

= \frac{28 \times 5}{2}

= 70 g / m o l