[mathjax]

An oxide of nitrogen contains one-half of its own volume of nitrogen. If the vapor density of nitrogen oxide is 23. Find the molecular formula of nitrogen oxide.

From question

n volume of nitrogen oxide contains $\frac{n}{2}$ volume of nitrogen.

1 volume of nitrogen oxide contains $\frac{1}{2}$ volume of nitrogen.

From Avogadro hypothesis we know that equal volume of gases at similar conditionsÂ contain same number of molecules

So we can write,

N molecule of nitrogen oxide contains $\frac{n}{2}$ molecule of nitrogen

Since nitrogen is diatomic molecule $\frac{1}{2}$ molecule is equivalentto 1 atom

1 molecule of nitrogen oxide contains 1 atom of nitrogen.

We know,

Molecular weight of nitrogen = 14

Molecular weight of oxygen = 16

As we have 1 atom of nitrogen in one molecule of nitrogen

oxide.

Vapor density of nitrogen oxide = 23

We know,

Molecular weight = vapor density *2

so Molecular weight = 46

Letâ€™s suppose that number of oxygen atoms be x.then,

$14+x*16 = Molecular weight$

$14+16*x= 46$

$16*x = 32$

$X=2$

Therefore the molecular formula of nitrogen oxide is NO2