Question

What is the vapour density of carbon dioxide?
\[[C=12,O=16]\]
A.$32$
B.$16$
C.$44$
D.$22$

Answer 1

Hint: The density of the particular gas as well as the vapour relative to hydrogen at same pressure and temperature is known as vapour density of gas. Vapor density can be calculated as \[\text{Vapour Density(X)=}\dfrac{Molecular\text{ }weight\text{ }of\text{ X}}{2}\]. Molecular weight is the average mass of a molecule of a compound compared to one-twelfth the mass of carbon $12$ and calculated as the sum of the atomic weights of the constituent atoms.

Complete step-by-step answer:Atomic weight of carbon \[\left( C \right)\] and oxygen \[\left( O \right)\] and the compound \[C{{O}_{2}}\]
The vapour density of a compound $X$ is given by the formula
\[\text{Vapour Density(X)=}\dfrac{Molecular\text{ }weight\text{ }of\text{ X}}{2}\]
So, our first task is to calculate the molecular weight of the given compound, in this case \[C{{O}_{2}}\].
To calculate the molecular weight, we add the molecular weight of each element multiplied by the number of atoms of that element present in the compound. The molecular weight of Carbon is $12$ and molecular weight of oxygen is given to be $16.$
\[\text{Molecular weight (C}{{\text{O}}_{2}})=12+2\times 16=12+34=44g\]
Now, we will use this molecular weight in the formula to calculate vapour density.
Vapour density of carbon dioxide can be calculated as; \[V.D.(C{{O}_{2}})=\dfrac{Molecular\text{ }weight\text{ }of\text{ }C{{O}_{2}}}{2}\]
\[\Rightarrow V.D.(C{{O}_{2}})=\dfrac{44}{2}\]
\[\Rightarrow V.D.(C{{O}_{2}})=22\]
The vapour density of \[C{{O}_{2}}\]is $22$ which means that the mass of $X$ litres of hydrogen gas or the molecular mass of \[C{{O}_{2}}\] is \[44\text{ }gm\] and vapour density of carbon dioxide \[C{{O}_{2}}\] is \[22.\]

Therefore, the correct answer is D i.e. $22$ is the vapour density of carbon dioxide.

Note: Vapour density is density of a vapour in relation to that of hydrogen. It may be defined as mass of a certain volume of a substance divided by mass of same volume of hydrogen and also Molecular weight is the average mass of a molecule of compound compared to $\dfrac{1}{{{12}^{th}}}$ mass of carbon $12$ and calculated as sum of atomic weights of constituent atoms.