Question

The density of a gaseous element is 5 times that of oxygen under similar conditions. If the molecule of the element is triatomic, what will be its atomic mass?

Answer 1

Hint: The vapour density of a gas is defined as the vapour density of the gas related to the vapour density of hydrogen at the same temperature and pressure.
The formula for calculating molar mass of a gas using vapour density is
\[MolarMass=2\times vapour density\]
\[Atomic Mass=\dfrac{Molecular Mass}{Atomicity}\]

Complete step-by-step answer:
The vapour density of a substance helps us to calculate the molar mass of the substance. So, we will use the vapour density to calculate the mass of the unknown element.
Then, we will use that calculated molar mass to calculate the formula of the unknown element.
It is given that the vapour density of the unknown gaseous element is 5 times the vapour density of oxygen.

That is,
\[{{D}_{unknown element}}=5\times {{D}_{oxygen}}\]…….equation 1
Where, D is vapour density
Now, we will calculate the vapour density of oxygen
Using the relation between vapour density and molar mass:
\[Molar Mass = 2\times vapour density\]
From the above relation we can calculate $V{{p}_{{{O}_{2}}}}$
\[V{{p}_{{{O}_{2}}}}=\dfrac{32}{2}=16\]
Where, molar mass of oxygen gas is 32
Let’s suppose ${{X}_{3}}$be the unknown gaseous molecule
Now, we will calculate the vapour density of ${{X}_{3}}$using the information given in equation 1
Therefore, $V{{p}_{{{X}_{3}}}}=5\times 16=80$
Now, we know that,
\[Molar Mass=2\times vapour density\]

So, we will calculate the molecular mass of ${{X}_{3}}$
\[Molecular Mass{{s}_{{{X}_{3}}}}=80\times 2=160\]
The formula for atomic mass is,
Now, to calculate the atomic mass of the unknown element we will divide the molecular mass by the atomicity of the unknown element.
\[Atomic Mass=\dfrac{Molecular Mass}{Atomicity}\]
Therefore, the atomic mass of ${{X}_{3}}$is
\[Atomic Mass{{s}_{{{X}_{3}}}}=\dfrac{160}{3}=53.33\]
Hence, the atomic mass of the unknown gaseous element is 53.33.

Note: Atomic mass should not be confused with atomic mass number. Both are two different things. Atomic mass is the actual mass of an atom whereas atomic mass number is the mass of I mole of the atoms of a substance.