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.

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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 conditions 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
Let’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

This is Ashish Thapa. It's just a name after all. Just had a thought that our names should signify our situation and should be dynamic. What if our name upgraded with respect to experiences acquired.

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