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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?

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#### Solution

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"_1"p"_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"_2"p"_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`

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

Given

`"p"_1 = "2 bar"`

`"p"_2 = "5 bar"`

Molecular mass of nitrogen, M_{2} = 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.

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